HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 06 Aug 2024 20:58:42 GMT2024-08-06T20:58:42Z502641- LMI conditions for time-varying uncertain systems can be non-conservativehttp://hdl.handle.net/10722/135117Title: LMI conditions for time-varying uncertain systems can be non-conservative
Authors: Chesi, G
Abstract: Establishing robust asymptotic stability of uncertain systems affected by time-varying uncertainty is a key problem. LMI sufficient conditions have been proposed in the literature for addressing this problem based on homogeneous polynomial Lyapunov functions. Unfortunately, till now it has been unclear whether these conditions are also necessary. This paper proposes a proof in order to show that one of these conditions is not only sufficient but also necessary for a sufficiently large degree of the Lyapunov function. © 2011 Elsevier Ltd. All rights reserved.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1351172011-01-01T00:00:00Z
- On the L2 gain of 2D mixed continuous-discrete-time systems via complex LFR and Lyapunov functionshttp://hdl.handle.net/10722/285040Title: On the L2 gain of 2D mixed continuous-discrete-time systems via complex LFR and Lyapunov functions
Authors: Chesi, G
Abstract: This paper addresses the problem of establishing upper bounds of the L2 gain of 2D mixed continuous-discrete-time systems. A novel linear matrix inequality condition is proposed based on the introduction of a complex linear fractional representation of the systems and on the use of complex Lyapunov functions depending rationally on a parameter. As shown by an illustrative example, the computational burden of the proposed condition may be rather smaller than existing conditions.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10722/2850402019-01-01T00:00:00Z
- Input-feedforward-passivity-based distributed optimization over directed and switching topologieshttp://hdl.handle.net/10722/284692Title: Input-feedforward-passivity-based distributed optimization over directed and switching topologies
Authors: Li, M; Chesi, G; Hong, Y
Abstract: In this paper, a distributed optimization problem is investigated via input feedforward passivity. First, an input-feedforward-passivity-based continuous-time distributed algorithm is proposed. It is shown that the error system of the proposed algorithm can be interpreted as output feedback interconnections of a group of Input Feedforward Passive (IFP) systems. Second, based on this IFP framework, the distributed algorithm is studied over weight-balanced directed and uniformly jointly strongly connected switching topologies. Specifically, the continuous-time distributed algorithm for uniformly jointly strongly connected digraphs has never been considered before. Sufficient convergence conditions are derived for the design of a suitable coupling gain.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10722/2846922019-01-01T00:00:00Z
- Designing parametric linear quadratic regulators for parametric LTI systems via LMIshttp://hdl.handle.net/10722/284557Title: Designing parametric linear quadratic regulators for parametric LTI systems via LMIs
Authors: Chesi, G; Shen, T
Abstract: This paper addresses the problem of determining parametric linear quadratic regulators (LQRs) for continuous-time linear-time invariant systems affected by parameters through rational functions. Three situations are considered, where the sought controller has to minimise the best cost, average cost, and worst cost, respectively, over the set of admissible parameters. It is shown that candidates for such controllers can be obtained by solving convex optimisation problems with linear matrix inequality (LMI) constraints. These candidates are guaranteed to approximate arbitrarily well the sought controllers by sufficiently increasing the size of the LMIs. In particular, the candidate that minimises the average cost approximates arbitrarily well the true LQR over the set of admissible parameters. Moreover, conditions for establishing the optimality of the found candidates are provided. Some numerical examples illustrate the proposed methodology.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10722/2845572019-01-01T00:00:00Z
- Checking structural stability of BDC-decomposable systems via convex optimisationhttp://hdl.handle.net/10722/284558Title: Checking structural stability of BDC-decomposable systems via convex optimisation
Authors: Blanchini, F; Chesi, G; Colaneri, P; Giordano, G
Abstract: In this letter we show how the problem of assessing structural local stability of BDC-decomposable systems, left open in recent literature, can be solved via convex optimisation. First we give a simple test, based on a sufficient condition, that requires checking the strict co-positivity of a multivariate polynomial. Then we provide a stronger test, based on a necessary and sufficient condition, which can be numerically implemented via LMI-based convex optimisation. The proposed approach certifies the structural stability of non-trivial systems, including a biological network discussed in the literature.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10722/2845582020-01-01T00:00:00Z
- Smooth dynamics for distributed constrained optimization with heterogeneous delayshttp://hdl.handle.net/10722/284559Title: Smooth dynamics for distributed constrained optimization with heterogeneous delays
Authors: Li, M; Yamashita, S; Hatanaka, T; Chesi, G
Abstract: This letter investigates the distributed constrained optimization problem under inter-agent communication delays from the perspective of passivity. First, we propose a continuous-time algorithm for distributed constrained optimization with general convex objective functions. The asymptotic stability under general convexity is guaranteed by the phase lead compensation. The inequality constraints are handled by adopting a projection-free generalized Lagrangian, whose primal-dual gradient dynamics preserves passivity and smoothness, enabling the application of the LaSalle's invariance principle in the presence of delays. Then, we incorporate the scattering transformation into the proposed algorithm to enhance the robustness against unknown and heterogeneous communication delays. Finally, a numerical example of a matching problem is provided to illustrate the results.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10722/2845592020-01-01T00:00:00Z
- Solving polynomial systems: An LMI-based approachhttp://hdl.handle.net/10722/99089Title: Solving polynomial systems: An LMI-based approach
Authors: Chesi, G; Hung, YS
Abstract: This paper considers the problem of computing the real solutions of systems of polynomial equalities and inequalities, and proposes a new approach based on convex linear matrix inequality (LMI) optimizations. In particular, the original polynomial systems is converted into an equivalent one whose number of solutions of the equality part that do not satisfy the inequalities (infeasible equality solutions) is reduced by introducing suitable auxiliary polynomials. Moreover, the solutions of this system can be computed by finding vectors with given polynomial structure in suitable linear spaces, operation that can be easily performed if the dimension of these linear spaces is not large. Examples show that the number of infeasible equality solutions can be drastically reduced, hence allowing for an easier and more accurate computation of the results. ©2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/990892006-01-01T00:00:00Z
- Robust commutation time for switching polynomial systemshttp://hdl.handle.net/10722/99085Title: Robust commutation time for switching polynomial systems
Authors: Chesi, G; Hung, YS
Abstract: This paper considers the stability analysis of switching polynomial systems. In particular, the problem of computing upper bounds of the minimum commutation time ensuring stability with respect to finite and infinite input sequences is dealt with. It is shown that such upper bounds can be established by solving LMI feasibility tests for given polynomial Lyapunov functions in the former case and homogeneous polynomial Lyapunov functions in the latter case. Lastly, the structure of the obtained tests is exploited to derive a search for less conservative upper bounds in a reduced number of variables through the solution of convex LMI optimizations at each iteration. © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/990852007-01-01T00:00:00Z
- On the convexity of sublevel sets of polynomial and homogeneous polynomial Lyapunov functionshttp://hdl.handle.net/10722/99245Title: On the convexity of sublevel sets of polynomial and homogeneous polynomial Lyapunov functions
Authors: Chesi, G; Hung, YS
Abstract: Polynomial and homogeneous polynomial Lyapunov functions have recently received a lot of attention from the control community. However, no condition is still available to establish if their sublevel sets are convex, property that can be useful in several applications. This paper proposes some conditions to investigate this convexity property based on polynomial relaxations that can be handled through convex linear matrix inequalities optimizations. © 2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/992452006-01-01T00:00:00Z
- Trajectories bounds for nonlinear systems: A BMI approachhttp://hdl.handle.net/10722/98944Title: Trajectories bounds for nonlinear systems: A BMI approach
Authors: Chesi, G; Hung, YS
Abstract: This paper deals with the analysis and synthesis of nonlinear systems, and considers the problems of computing extremal values of the trajectories over a given set of initial conditions as well as finding output controllers minimizing these extremal values under time-domain constraints. It is shown that upper bounds of the sought extremal values as well as candidates of the sought controllers can be computed by solving a one-parameter sequence of BMI optimizations. Moreover, a necessary and sufficient condition is proposed to establish the tightness of the found upper bound in spite of the conservatism introduced by the non-convexity of BMI optimizations and the chosen degree of the Lyapunov function and relaxing polynomials. © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/989442007-01-01T00:00:00Z
- Visual servoing: A global path-planning approachhttp://hdl.handle.net/10722/98978Title: Visual servoing: A global path-planning approach
Authors: Chesi, G; Hung, YS
Abstract: This paper considers the problem of realizing visual servoing taking into account constraints such as visibility and workspace constraints while minimizing a cost function such as spanned image area and trajectory length. A new path-planning scheme is proposed by, first, introducing a robust object reconstruction which allows one to obtain feasible image trajectories. Second, the rotation path is parameterized through a particular extension of the Euler parameters in order to obtain an equivalent expression of the rotation matrix as a quadratic function of unconstrained variables, hence largely simplified with respect to standard parameterizations which involve transcendental functions. Then, polynomials of arbitrary degree are used to complete the parametrization and formulate a general optimization where a number of constraints and costs can be considered. The optimal trajectory is followed by tracking the image trajectories with standard IBVS controllers. © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/989782007-01-01T00:00:00Z
- On the gap between positive polynomials and SOS of polynomialshttp://hdl.handle.net/10722/57458Title: On the gap between positive polynomials and SOS of polynomials
Authors: Chesi, G
Abstract: This note investigates the gap existing between positive polynomials and sum of squares (SOS) of polynomials, which affects several analysis and synthesis tools in control systems based on polynomial SOS relaxations, and about which almost nothing is known. In particular, a matrix characterization of the PNS, that is the positive homogeneous forms that are not SOS, is proposed, which allows to show that any PNS is the vertex of an unbounded cone of PNS. Moreover, a complete parametrization of the set of PNS is introduced. © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/574582007-01-01T00:00:00Z
- Image noise induced errors in camera positioninghttp://hdl.handle.net/10722/57440Title: Image noise induced errors in camera positioning
Authors: Chesi, G; Hung, YS
Abstract: The problem of evaluating worst-case camera positioning error induced by unknown-but-bounded (UBB) image noise for a given object-camera configuration is considered. Specifically, it is shown that upper bounds to the rotation and translation worst-case error for a certain image noise intensity can be obtained through convex optimizations. These upper bounds, contrary to lower bounds provided by standard optimization tools, allow one to design robust visual servo systems. © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/574402007-01-01T00:00:00Z
- Global path-planning for constrained and optimal visual servoinghttp://hdl.handle.net/10722/57470Title: Global path-planning for constrained and optimal visual servoing
Authors: Chesi, G; Hung, YS
Abstract: Visual servoing consists of steering a robot from an initial to a desired location by exploiting the information provided by visual sensors. This paper deals with the problem of realizing visual servoing for robot manipulators taking into account constraints such as visibility, workspace (that is obstacle avoidance), and joint constraints, while minimizing a cost function such as spanned image area, trajectory length, and curvature. To solve this problem, a new path-planning scheme is proposed. First, a robust object reconstruction is computed from visual measurements which allows one to obtain feasible image trajectories. Second, the rotation path is parameterized through an extension of the Euler parameters that yields an equivalent expression of the rotation matrix as a quadratic function of unconstrained variables, hence, largely simplifying standard parameterizations which involve transcendental functions. Then, polynomials of arbitrary degree are used to complete the parametrization and formulate the desired constraints and costs as a general optimization problem. The optimal trajectory is followed by tracking the image trajectory with an IBVS controller combined with repulsive potential fields in order to fulfill the constraints in real conditions. © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/574702007-01-01T00:00:00Z
- Analysis and synthesis of nonlinear systems with uncertain initial conditionshttp://hdl.handle.net/10722/57490Title: Analysis and synthesis of nonlinear systems with uncertain initial conditions
Authors: Chesi, G; Hung, YS
Abstract: This technical note considers the problem of computing extremal values of the trajectories over a given set of initial conditions as well as finding output controllers minimizing these extremal values under time-domain constraints for nonlinear systems. It is shown that upper bounds of the sought extremal values as well as candidates of the sought controllers can be computed by solving a one-parameter sequence of bilinear matrix inequality (BMI) optimizations obtained through the square matricial representation (SMR) of polynomials. Moreover, a necessary and sufficient condition is proposed to establish the tightness of the found upper bound in spite of the conservatism introduced by the nonconvexity of BMI optimizations and the chosen degree of the Lyapunov function and relaxing polynomials. © 2008 IEEE.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/574902008-01-01T00:00:00Z
- Estimation of the camera pose from image point correspondences through the essential matrix and convex optimizationhttp://hdl.handle.net/10722/62039Title: Estimation of the camera pose from image point correspondences through the essential matrix and convex optimization
Authors: Chesi, G
Abstract: Estimating the camera pose in stereo vision systems is an important issue in computer vision and robotics. One popular way to handle this problem consists of determining the essential matrix which minimizes the algebraic error obtained from image point correspondences. Unfortunately, this search amounts to solving a nonconvex optimization, and the existing methods either rely on some approximations in order to get rid of the non-convexity or provide a solution that may be affected by the presence of local minima. This paper proposes a new approach to address this search without presenting such problems. In particular, we show that the sought essential matrix can be obtained by solving a convex optimization built through a suitable reformulation of the considered minimization via appropriate techniques for representing polynomials. Numerical results show the proposed approach compares favorably with some standard methods in both cases of synthetic data and real data. © 2009 IEEE.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/620392009-01-01T00:00:00Z
- Passivity analysis of discrete-time hybrid systems using piecewise polynomial storage functionshttp://hdl.handle.net/10722/54076Title: Passivity analysis of discrete-time hybrid systems using piecewise polynomial storage functions
Authors: Bemporad, A; Bianchini, G; Brogi, F; Chesi, G
Abstract: This paper proposes some sufficient criteria based on the computation of polynomial and piecewise polynomial storage functions for checking passivity of discrete-time hybrid systems in piecewise affine or piecewise polynomial form. The computation of such storage functions is performed by means of convex optimization techniques via the sum of squares decomposition of multivariate polynomials. © 2005 IEEE.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/540762005-01-01T00:00:00Z
- An LMI approach for robust stability of genetic networkshttp://hdl.handle.net/10722/61974Title: An LMI approach for robust stability of genetic networks
Authors: Chesi, G; Hung, YS
Abstract: This paper addresses the problem of establishing robust stability of uncertain genetic networks with SUM regulatory functions. For these networks we derive a sufficient condition for robust stability by introducing a bounding set of the uncertain nonlinearity, and we show that this condition can be formulated as a linear matrix inequality (LMI) optimization obtained via the square matricial representation (SMR) of polynomials by adopting polynomial Lyapunov functions and polynomial descriptions of the bounding set. Then, we propose a method for computing a family of bounding sets by means of convex optimizations. It is worthwhile to remark that these results are derived in spite of the fact that the variable equilibrium point cannot be computed being the solution of a system of parameter-dependent nonlinear equations, and is hence unknown.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/619742008-01-01T00:00:00Z
- Robust detection and tracking of multiple moving objects with 3d features by an uncalibrated monocular camerahttp://hdl.handle.net/10722/62097Title: Robust detection and tracking of multiple moving objects with 3d features by an uncalibrated monocular camera
Authors: Poon, HS; Mai, F; Hung, YS; Chesi, G
Abstract: This paper presents an algorithm for detecting multiple moving objects in an uncalibrated image sequence by integrating their 2D and 3D information. The result describes the moving objects in terms of their number, relative position and motion. First, the objects are represented by image feature points, and the major group of point correspondences over two consecutive images is established by Random Sample Consensus (RANSAC). Then, their corresponding 3D points are reconstructed and clustering is performed on them to validate those belonging to the same object. This process is repeated until all objects are detected. This method is reliable on tracking multiple moving objects, even with partial occlusions and similar motions. Experiments on real image sequences are presented to validate the proposed algorithm. Applications of interest are video surveillance, augmented reality, robot navigation and scene recognition. © Springer-Verlag Berlin Heidelberg 2009.
Description: MIRAGE
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/620972009-01-01T00:00:00Z
- Designing image trajectories in the presence of uncertain data for robust visual servoing path-planninghttp://hdl.handle.net/10722/62098Title: Designing image trajectories in the presence of uncertain data for robust visual servoing path-planning
Authors: Chesi, G
Abstract: Path-planning allows one to steer a camera to a desired location while taking into account the presence of constraints such as visibility, workspace, and joint limits. Unfortunately, the planned path can be significantly different from the real path due to the presence of uncertainty on the available data, with the consequence that some constraints may be not fulfilled by the real path even if they are satisfied by the planned path. In this paper we address the problem of performing robust path-planning, i.e. computing a path that satisfies the required constraints not only for the nominal model as in traditional path-planning but rather for a family of admissible models. Specifically, we consider an uncertain model where the point correspondences between the initial and desired views and the camera intrinsic parameters are affected by unknown random uncertainties with known bounds. The difficulty we have to face is that traditional path-planning schemes applied to different models lead to different paths rather than to a common and robust path. To solve this problem we propose a technique based on polynomial optimization where the required constraints are imposed on a number of trajectories corresponding to admissible camera poses and parameterized by a common design variable. The planned image trajectory is then followed by using an IBVS controller. Simulations carried out with all typical uncertainties that characterize a real experiment illustrate the proposed strategy and provide promising results. © 2009 IEEE.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/620982009-01-01T00:00:00Z
- Investigating the load flow equations in power systems via LMI-based techniqueshttp://hdl.handle.net/10722/126029Title: Investigating the load flow equations in power systems via LMI-based techniques
Authors: Chesi, G; Hung, YS
Abstract: Solving the load flow equations is an important problem in power systems. This paper proposes an approach for addressing this problem via a convex optimization with LMI constraints. This approach ensures to find all solutions provided that the dimension of a linear space provided by the optimization is smaller than a known threshold. Then, this paper considers the characterization of the set of admissible power, in particular the computation of the largest admissible power, which amounts to solving a nonconvex optimization problem. It is shown that an upper bound of the sought power can be obtained via convex LMI optimization. Moreover, a necessary and sufficient condition for establishing whether the upper bound is tight or not is provided. Some numerical examples illustrate the proposed approach. ©2009 ACA.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1260292009-01-01T00:00:00Z
- Position and motion estimation for visual robot control with planar targetshttp://hdl.handle.net/10722/126140Title: Position and motion estimation for visual robot control with planar targets
Authors: Yung, HL; Chesi, G; Hung, YS
Abstract: This paper addresses two problems in visually-controlled robots. The first consists of positioning the end-effector of a robot manipulator on a plane of interest by using a monocular vision system. The problem amounts to estimating the transformation between the coordinates of an image point and its three-dimensional location supposing that only the camera intrinsic parameters are known. The second problem consists of positioning the robot end-effector with respect to an object of interest free to move on a plane, and amounts to estimating the camera displacement in a stereo vision system in the presence of motion constraints. For these problems, some solutions are proposed through dedicated optimizations based on decoupling the effects of rotation and translation and based on an a-priori imposition of the degrees of freedom of the system. These solutions are illustrated via simulations and experiments. ©2009 ACA.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1261402009-01-01T00:00:00Z
- Projective reconstruction of ellipses from multiple imageshttp://hdl.handle.net/10722/124711Title: Projective reconstruction of ellipses from multiple images
Authors: Mai, F; Hung, YS; Chesi, G
Abstract: This paper presents a new approach for reconstructing 3D ellipses (including circles) from a sequence of 2D images taken by uncalibrated cameras. Our strategy is to estimate an ellipse in 3D space by reconstructing N (≥ 5) 3D points (called representative points) on it, where the representative points are reconstructed by minimizing the distances from their projections to the measured 2D ellipses on different images (i.e., 2D reprojection error). This minimization problem is transformed into a sequence of minimization sub-problems that can be readily solved by an algorithm which is guaranteed to converge to a (local) minimum of the 2D reprojection error. Our method can reconstruct multiple 3D ellipses simultaneously from multiple images and it readily handles images with missing and/or partially occluded ellipses. The proposed method is evaluated using both synthetic and real data. © 2009 Elsevier Ltd. All rights reserved.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1247112010-01-01T00:00:00Z
- On the multiple-view triangulation problem with perspective and non-perspective cameras: a virtual reprojection-based approachhttp://hdl.handle.net/10722/184981Title: On the multiple-view triangulation problem with perspective and non-perspective cameras: a virtual reprojection-based approach
Authors: Chesi, G
Abstract: This paper considers the multiple-view triangulation problem in a vision system with perspective and nonperspective cameras. In particular, cameras that can be modeled through a spherical projection followed by a perspective one, such as perspective cameras and fisheye cameras, are considered. For this problem, an approach based on reprojecting the available image points onto virtual image planes is proposed, which has the advantage of transforming the original problem into a new one for which the existing methods for multipleview triangulation with perspective cameras can be used. In particular, algebraic and geometric errors of such methods are now evaluated on the virtual image planes, and the solution of the new problem exactly approaches the sought scene point as image noise and calibration errors tend to zero. The proposed approach is illustrated by several numerical investigations with synthetic and real data.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1849812012-01-01T00:00:00Z
- Visual servoing path-planning with sphereshttp://hdl.handle.net/10722/184982Title: Visual servoing path-planning with spheres
Authors: Shen, T; Chesi, G
Abstract: This paper proposes a path-planning approach for visual servoing in the case where the observed object features are points and spheres. Two main situations are considered. In the first situation, it is supposed that at least two points and at least a sphere are observed. In the second situation, it is supposed that at least three spheres are observed. The problem consists of planning a trajectory in order to ensure the convergence of the robot end-point to the desired location while satisfying visibility and workspace constraints, in particular including occlusion and collision avoidance. A solution based on polynomial parametrizations is proposed in order to determine a feasible path in the 3D space, and such a path is then followed by tracking its image projection through image-based visual servoing. Some simulation results illustrate the proposed approach. Copyright © 2012 SciTePress.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1849822012-01-01T00:00:00Z
- Robust domain of attraction: computing and controlling estimates with non-polynomial Lyapunov functionshttp://hdl.handle.net/10722/184983Title: Robust domain of attraction: computing and controlling estimates with non-polynomial Lyapunov functions
Authors: Chesi, G
Abstract: This paper addresses the estimation and control of the robust domain of attraction (RDA) of equilibrium points through rational Lyapunov functions (LFs). Specifically, continuous-time uncertain polynomial systems are considered. The uncertainty is represented by a vector that affects poly-nomially the system and is constrained in a semialgebraic set. The estimation problem consists of computing the largest estimate of the RDA (LERDA) provided by a given rational LF. The control problem consists of computing a polynomial static output controller of given degree for maximizing such a LERDA. It is shown that lower bounds of the LERDA in the estimation problem, or the maximum achievable LERDA in the control problem, can be obtained by solving either an eigenvalue problem or a generalized eigenvalue problem with smaller dimension. The conservatism of these lower bounds can be reduced by increasing the degree of some multipliers introduced in the construction of the optimization problems. Some numerical examples illustrate the use of the proposed results. © 2012 IEEE.
Description: 2012 IEEE International Conference on Control Applications (CCA) is part of 2012 IEEE Multi-Conference on Systems and Control October 3-5, 2012. Dubrovnik, Croatia
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1849832012-01-01T00:00:00Z
- Robust discrete-time consensus of multi-agent systems with uncertain interactionhttp://hdl.handle.net/10722/184984Title: Robust discrete-time consensus of multi-agent systems with uncertain interaction
Authors: Han, D; Chesi, G
Abstract: This paper addresses robust discrete-time consensus problem of multiple agents with uncertain structure, where the network coupling weights are supposed polynomial functions of an uncertain vector constrained in a semialgebraic set. Based on the Lyapunov stability theory, a necessary and sufficient condition for robust discrete-time consensus is proposed. Then, we investigate the robust discrete-time consensus with positive weighted network, and a necessary and sufficient condition is also provided based on the property of an uncertain matrix. Corresponding sufficient conditions for robust discrete-time consensus are derived by solving a linear matrix inequality (LMI) problem built by exploiting sum-of-squares (SOS) polynomials. Some examples illustrate the proposed results. © 2012 IEEE.
Description: 2012 IEEE International Conference on Control Applications (CCA) is part of 2012 IEEE Multi-Conference on Systems and Control October 3-5, 2012. Dubrovnik, Croatia
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1849842012-01-01T00:00:00Z
- A geometric approach to multiple-view triangulation for fisheye camerashttp://hdl.handle.net/10722/184985Title: A geometric approach to multiple-view triangulation for fisheye cameras
Authors: Chesi, G
Description: Topics: Machine Vision and its Applications; Session 9 - Poster Session 2: no. 9-5
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1849852013-01-01T00:00:00Z
- A gram-SOS approach for robust stability analysis of discrete-time systems with time-varying uncertaintyhttp://hdl.handle.net/10722/184986Title: A gram-SOS approach for robust stability analysis of discrete-time systems with time-varying uncertainty
Authors: Chesi, G
Abstract: This paper addresses the problem of establishing robust asymptotical stability of discrete-time systems affected by time-varying parametric uncertainty. Specifically, it is supposed that the coefficients of the system depend linearly on the uncertainty, and that the uncertainty is confined into a polytope. In the continuous-time case, the problem can be addressed by imposing that the system admits a common homogeneous polynomial Lyapunov function (HPLF) at the vertices of the polytope. Unfortunately, such a strategy cannot be used in the discrete-time case since the derivative of the HPLF is nonlinear in the uncertainty. The problem is addressed in this paper through linear matrix inequalities (LMIs) by proposing a novel method for establishing decrease of the HPLF. This method consists, firstly, of introducing a Gram matrix built with respect to the state and parametrized by an arbitrary vector function of the uncertainty, and secondly, of requiring that a transformation of the introduced Gram matrix is a sum of squares (SOS) of matrix polynomials. The proposed method provides a condition for robust asymptotical stability that is sufficient for any degree of the HPLF candidate and that includes quadratic robust stability as special case. © 2013 AACC American Automatic Control Council.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1849862013-01-01T00:00:00Z
- On the Mahler measure of matrix pencilshttp://hdl.handle.net/10722/184987Title: On the Mahler measure of matrix pencils
Authors: Chesi, G
Abstract: It is well-known that determining the Mahler measure is important in networked control systems. Indeed, this measure allows one to derive stabilizability conditions in such systems. This paper investigates the Mahler measure in networked control systems linearly affected by a single uncertain parameter constrained into an interval, i.e. systems described by a matrix pencil. It is shown that conditions for establishing an upper bound of the largest Mahler measure over the matrix pencil can be formulated through linear matrix inequalities (LMIs). In particular, two LMI conditions are proposed, one based on the construction of a parameter-dependent Lyapunov function, and another based on eigenvalue analysis through the determinants of augmented matrices. The proposed LMI conditions have the advantage to be exact, i.e. they are sufficient for any size of the LMIs and they are also necessary for a certain size of the LMIs which is known a priori. © 2013 AACC American Automatic Control Council.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1849872013-01-01T00:00:00Z
- Exploiting Elasticity in Tensor Ranks for Compressing Neural Networkshttp://hdl.handle.net/10722/301976Title: Exploiting Elasticity in Tensor Ranks for Compressing Neural Networks
Authors: RAN, J; LIN, R; So, HKH; Chesi, G; Wong, N
Description: Track 1: Neural Networks for Pattern Recognition - Poster Session PS T1.13 - paper no. 2730
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10722/3019762021-01-01T00:00:00Z
- Convergent upper bounds of peak response of LTI and polytopic LTV systems through LMIshttp://hdl.handle.net/10722/301515Title: Convergent upper bounds of peak response of LTI and polytopic LTV systems through LMIs
Authors: Chesi, G; Shen, T
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10722/3015152020-01-01T00:00:00Z
- Resource allocation over time-varying balanced digraphs with discrete-time communicationhttp://hdl.handle.net/10722/301698Title: Resource allocation over time-varying balanced digraphs with discrete-time communication
Authors: Su, L; LI, M; Gupta, V; Chesi, G
Description: Orginal conference dates: 24-28 August 2020
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10722/3016982020-01-01T00:00:00Z
- On complexity reduction for multiple-view L2 triangulation via LMIshttp://hdl.handle.net/10722/301696Title: On complexity reduction for multiple-view L2 triangulation via LMIs
Authors: Chesi, G
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10722/3016962021-01-01T00:00:00Z
- Optimized vision-based robot motion planning from multiple demonstrationshttp://hdl.handle.net/10722/272177Title: Optimized vision-based robot motion planning from multiple demonstrations
Authors: Shen, T; Radmard, S; Chan, A; Croft, EA; Chesi, G
Abstract: This paper combines workspace models with optimization techniques to simultaneously address whole-arm collision avoidance, joint limits and camera field of view (FOV) limits for vision-based motion planning of a robot manipulator. A small number of user demonstrations are used to generate a feasible domain over which the whole robot arm can servo without violating joint limits or colliding with obstacles. Our algorithm utilizes these demonstrations to generate new feasible trajectories that keep the target in the camera’s FOV and achieve the desired view of the target (e.g., a pre-grasping location) in new, undemonstrated locations. To fulfill these requirements, a set of control points are selected within the feasible domain. Camera trajectories that traverse these control points are modeled and optimized using either quintic splines (for fast computation) or general polynomials (for better constraint satisfaction). Experiments with a seven degree of freedom articulated arm validate the proposed scheme.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/2721772018-01-01T00:00:00Z
- On the complexity of SOS programming and applications in control systemshttp://hdl.handle.net/10722/272178Title: On the complexity of SOS programming and applications in control systems
Authors: Chesi, G
Abstract: The minimization of a linear cost function subject to the condition that some matrix polynomials depending linearly on the decision variables are sums of squares of matrix polynomials (SOS) is known as SOS programming. This paper proposes an analysis of the complexity of SOS programming, in particular of the number of linear matrix inequality (LMI) scalar variables required for establishing whether a matrix polynomial is SOS. This number is analyzed for real and complex matrix polynomials, in the general case and in the case of some exact reductions achievable for some classes of matrix polynomials. An analytical formula is proposed in each case in order to provide this number as a function of the number of variables, degree and size of the matrix polynomials. Some tables reporting this number are also provided as reference for the reader. Two applications in control systems are presented in order to show the usefulness of the proposed results.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/2721782018-01-01T00:00:00Z
- Consensus of heterogeneous multi-agent systems with diffusive couplings via passivity indiceshttp://hdl.handle.net/10722/272179Title: Consensus of heterogeneous multi-agent systems with diffusive couplings via passivity indices
Authors: Li, M; Su, L; Chesi, G
Abstract: This letter is concerned with the problem of output consensus for two classes of heterogeneous nonlinear multi-agent systems which are interconnected via diffusive couplings over directed graphs. Specifically, for agents that are input feedforward passive (IFP), a condition in terms of passivity indices is proposed for asymptotic output consensus. Moreover, it is shown that the proposed condition can be exploited to design the coupling gain that ensures asymptotic consensus via a semidefinite program, and the existence of such a coupling gain can be guaranteed provided all the agents are IFP. For agents that are input feedforward output feedback passive, a condition in terms of passivity indices for practical output consensus is provided, in which the relationship between the coupling gain and the consensus error bound is revealed.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10722/2721792019-01-01T00:00:00Z
- Stability test for complex matrices over the complex unit circumference via LMIs and applications in 2D systemshttp://hdl.handle.net/10722/272180Title: Stability test for complex matrices over the complex unit circumference via LMIs and applications in 2D systems
Authors: Chesi, G
Abstract: This paper addresses the problem of establishing whether a matrix with rational dependence on a complex parameter and its conjugate is Hurwitz (i.e., has all eigenvalues with negative real part) over the complex unit circumference. A necessary and sufficient condition is proposed, which requires testing stability of a constant matrix and feasibility of a linear matrix inequality (LMI). Moreover, the numerical complexity of the proposed approach is investigated in terms of size and number of free scalar variables of the LMI by deriving their formulas as functions of the problem data. Also, it is shown that the numerical complexity may be significantly reduced without introducing approximations or conservatism whenever some symmetry properties are satisfied. Lastly, the extension of the proposed approach to the case of Schur stability (i.e., eigenvalues with magnitude smaller than one) and D-stability (i.e., eigenvalues on special regions of the complex plane) are presented. The proposed approach is illustrated by some numerical examples that also show its application to stability analysis of 2D systems with mixed signals.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10722/2721802019-01-01T00:00:00Z
- Structured Feedback Synthesis for Stability and Performance of Switched Systemshttp://hdl.handle.net/10722/296424Title: Structured Feedback Synthesis for Stability and Performance of Switched Systems
Authors: Chesi, G
Description: Keynote Speech
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10722/2964242020-01-01T00:00:00Z
- On the peak of the impulse response of polytopic LTV systemshttp://hdl.handle.net/10722/284957Title: On the peak of the impulse response of polytopic LTV systems
Authors: Chesi, G; Shen, T
Abstract: This paper addresses the problem of determining the peak of the impulse response of polytopic linear time-varying (LTV) systems. In particular, linear systems affected linearly by time-varying structured uncertainty constrained into a polytope are considered. A novel condition for establishing upper bounds of the sought peak is proposed in terms of feasibility of a system of linear matrix inequalities (LMIs). The proposed condition is sufficient for any degree of a polynomial introduced to describe the impulse response, moreover, its conservatism can be decreased by increasing this degree. Some examples illustrate the use of the proposed condition and show the application to a DC motor with time-varying uncertain parameters.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10722/2849572019-01-01T00:00:00Z
- LMI-based determination of the peak of the response of structured polytopic linear systemshttp://hdl.handle.net/10722/329109Title: LMI-based determination of the peak of the response of structured polytopic linear systems
Authors: Chesi, Graziano; Shen, Tiantian
Abstract: <p>This paper addresses the problem of determining the peak of the response to a linear time-invariant (LTI) signal of a linear system whose system matrices are rational functions of an uncertainty vector constrained into a convex bounded polytope. The uncertainty can be time-invariant, bounded-rate time-varying or arbitrarily time-varying. A novel approach based on linear matrix inequalities (LMIs) is proposed for obtaining upper bounds of the sought peak based on the construction of a structured polynomial Lyapunov function in the state and in the uncertainty. A priori and a posteriori conditions for establishing optimality of the obtained upper bounds are also provided. As shown by some numerical examples, which includes the model of an electric circuit, the proposed approach may have significant advantages with respect to the existing methods in terms of conservatism or computational burden.<br></p>
Sun, 01 Jan 2023 00:00:00 GMThttp://hdl.handle.net/10722/3291092023-01-01T00:00:00Z
- Robust structural stability, stability margins, and maximum uncertainty amplification for 2D uncertain systems via structured Lyapunov functions and matrix annihilatorshttp://hdl.handle.net/10722/329170Title: Robust structural stability, stability margins, and maximum uncertainty amplification for 2D uncertain systems via structured Lyapunov functions and matrix annihilators
Authors: Chesi, Graziano
Abstract: <p>This article considers two-dimensional (2-D) uncertain systems with homogeneous or mixed dynamics, and addresses the following three problems: establishing robust structural stability, computing robust structural stability margins, and determining the maximum uncertainty amplification that preserves robust structural stability. Two sufficient linear matrix inequality (LMI) conditions are proposed for establishing robust structural stability obtained by introducing an equivalent closed-loop complex system and by searching for real or complex structured Lyapunov functions and matrix annihilators parameterized by the uncertainties and auxiliary quantities. Moreover, it is shown that lower bounds of the introduced robust structural stability margins and maximum uncertainty amplification can be obtained by solving quasi-convex optimization problems under some restrictions on the sought Lyapunov functions or on the set of uncertainties. Lastly, the nonconservatism of the proposed results is analyzed, showing that the proposed LMI condition based on the use of complex Lyapunov functions is not only sufficient but also necessary under some assumptions.<br></p>
Sat, 01 Jul 2023 00:00:00 GMThttp://hdl.handle.net/10722/3291702023-07-01T00:00:00Z
- LMI-based estimation of scene points in vision systems with generalized camerashttp://hdl.handle.net/10722/211751Title: LMI-based estimation of scene points in vision systems with generalized cameras
Authors: Chesi, G
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2117512014-01-01T00:00:00Z
- Minimizing trigonometric matrix polynomials over semi-algebraic setshttp://hdl.handle.net/10722/211753Title: Minimizing trigonometric matrix polynomials over semi-algebraic sets
Authors: Chesi, G
Abstract: This paper addresses the problem of minimizing the minimum eigenvalue of a trigonometric matrix polynomial. The contribution is to show that, by exploiting Putinar's Positivstellensatz and introducing suitable transformations, it is possible to derive a nonconservative approach based on semidefinite programming (SDP) whose computational burden can be significantly smaller than that of an existing method recently published. Other advantages of the proposed approach include the possibility of taking into account the presence of constraints in the form of semi-algebraic sets and establishing tightness of a found lower bound. © 2014 Elsevier. Ltd All rights reserved.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2117532015-01-01T00:00:00Z
- On the H-infinity norm of 2D mixed continuous-discrete-time systems via rationally-dependent complex Lyapunov functionshttp://hdl.handle.net/10722/211396Title: On the H-infinity norm of 2D mixed continuous-discrete-time systems via rationally-dependent complex Lyapunov functions
Authors: Chesi, G; Middleton, RH
Abstract: This paper addresses the problem of determining the H-infinity norm of 2D mixed continuous-discrete-time systems. A novel approach is proposed based on the use of a class of complex Lyapunov functions with rational dependence on a parameter, which provides upper bounds on the sought norm via linear matrix inequalities (LMIs). It is also shown that the provided upper bounds are nonconservative by using rational functions in the chosen class with degree sufficiently large. Some numerical examples illustrate the proposed approach.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2113962014-01-01T00:00:00Z
- On the unstable of continuous-time linearized nonlinear systemshttp://hdl.handle.net/10722/211402Title: On the unstable of continuous-time linearized nonlinear systems
Authors: Chesi, G
Abstract: It has been shown that quantifying the unstable in linear systems is important for establishing the existence of stabilizing feedback controllers. This paper addresses the problem of quantifying the unstable in continuous-time linearized systems obtained from nonlinear systems for a family of constant inputs, i.e., the largest instability measure for all admissible equilibrium points for all admissible constant inputs. It is supposed that the dynamics of the nonlinear system is polynomial in both state and input, and that the set of constant inputs is a semialgebraic set. Two cases are considered: first, when the equilibrium points are known polynomial functions of the input, and, second, when the equilibrium points are unknown (polynomial or non-polynomial) functions of the input. It is shown that upper bounds of the sought instability measure can be established through linear matrix inequalities (LMIs), whose conservatism can be decreased by increasing the size of such LMIs. Some numerical examples illustrate the proposed results. © 2014 IEEE.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2114022014-01-01T00:00:00Z
- On the robust H-infinity norm of 2D mixed continuous-discrete-time systems with uncertaintyhttp://hdl.handle.net/10722/211403Title: On the robust H-infinity norm of 2D mixed continuous-discrete-time systems with uncertainty
Authors: Chesi, G
Abstract: This paper addresses the problem of determining the robust H∞ norm of 2D mixed continuous-discrete-time systems affected by uncertainty. Specifically, it is supposed that the matrices of the model are polynomial functions of an unknown vector constrained into a semialgebraic set. It is shown that an upper bound of the robust H∞ norm can be obtained via a semidefinite program (SDP) by introducing complex Lyapunov functions candidates with rational dependence on a frequency and polynomial dependence on the uncertainty. A necessary and sufficient condition is also provided to establish whether the found upper bound is tight. Some numerical examples illustrate the proposed approach.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2114032014-01-01T00:00:00Z
- On the topological entropy of continuous-time polytopic systemshttp://hdl.handle.net/10722/211439Title: On the topological entropy of continuous-time polytopic systems
Authors: Chesi, G
Abstract: This paper investigates the topological entropy of continuous-time polytopic systems. The topological entropy is a measure that quantifies the instability in dynamical linear systems and has important applications in autonomous systems. Polytopic systems are dynamical linear systems whose coefficients are functions of an uncertain vector constrained into a polytope. A novel approach is proposed for establishing upper bounds of the largest topological entropy of continuous-time polytopic systems based on the Routh-Hurwitz stability criterion. The upper bounds are established through Linear Matrix Inequality (LMI) feasibility tests, which amount to solving convex optimization problems. A numerical example illustrates the proposed approach. Copyright (c) IARIA.
Description: Free access online proceedings
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2114392015-01-01T00:00:00Z
- On the synthesis of output feedback controllers for increasing the domain of attraction of piecewise polynomial systemshttp://hdl.handle.net/10722/211438Title: On the synthesis of output feedback controllers for increasing the domain of attraction of piecewise polynomial systems
Authors: Luk, CK; Chesi, G
Abstract: This paper addresses the computation of static nonlinear output feedback controllers for increasing the domain of attraction of an equilibrium point of piecewise nonlinear polynomial systems. Specifically, we consider continuous-time dynamical systems where the state space is partitioned into possibly overlapping regions, and where the vector field is defined independently among the regions by polynomial functions. We address the computation of static nonlinear output feedback controllers that increase the estimate of the domain of attraction provided by a polynomial Lyapunov function. The controller can be common or vary among the regions that partition the state space. A strategy based on sum-of-squares (SOS) programming is proposed, which provides guaranteed estimates of the increased domain of attraction and the controllers required to achieve them. Moreover, this strategy can be readily exploited with variable Lyapunov functions through the use of iterative algorithms. Two examples are given to illustrate the proposed strategy. © IEEE.
Description: Best Student Paper Award 2015
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2114382015-01-01T00:00:00Z
- Robustness Analysis of Uncertain Systems with Time-Varying Uncertaintyhttp://hdl.handle.net/10722/237805Title: Robustness Analysis of Uncertain Systems with Time-Varying Uncertainty
Authors: Chesi, G
Description: Invited Speech - T-2: Systems with Uncertainty [The 2010 IEEE International Symposium on Computer-Aided Control System Design (CACSD) Symposium hosted a special track on Systems with Uncertainty]
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/2378052010-01-01T00:00:00Z