Global boundedness of discrete-time adaptive control just using estimator projection

Abstract

In this paper, we study a discrete-time indirect adaptive control algorithm which contains a constrained gradient parameter estimator and a pole assignment control law synthesis module. This adaptive control algorithm does not involve modifications like data normalization, use of deadzones, or injection of persistently excited signals. Also it requires no a priori knowledge of system modelling errors. It is shown that global robustness properties still hold when this simple algorithm is applied to systems with bounded disturbances and arbitrarily small fast parasitic dynamics. The problem of indirect decentralized adaptive control of interconnected systems is also considered. We use the above adaptive algorithm to design completely decentralized local adaptive controllers for each isolated subsystem by ignoring interactions between subsystems. We show that the local controllers designed in this way are robust in the sense that all signals in the closed loop adaptive system are bounded for bounded initial conditions, reference inputs, disturbances and an arbitrarily small amount of interaction between subsystems and unmodelled dynamics of each subsystem.