Networked control of multi-agent systems based on distributed observers

Abstract

This thesis investigates the observer design and control synthesis for multi-agent systems (MASs) on directed graphs subject to actuator faults or malicious attacks. The methodology of distributed observers is employed to improve the transient, fault-tolerant, and attack-resilient performance of MASs.

First, this thesis employs a series of distributed prescribed-time observers (DPTOs) to reconstruct the compensation signals for the followers in the framework of formation-containment (FC) control. The decoupling between formation control of leaders and containment control of followers is achieved thanks to the compensation signal of followers. A necessary and sufficient condition for the FC problem is obtained for the first time. Based on this condition, a heuristic iterative algorithm is proposed to synthesize the general FC problem of high-order linear time-invariant MASs.

Second, another kind of DPTO is developed to estimate the states of the non-autonomous leaders in the MASs, whose input signals are potentially fault-corrupted. The proposed observers can achieve distributed zero-error estimation in a predefined-time manner. Based on the DPTO and a decentralized fault-tolerant tracking scheme, the prescribed-time fault-tolerant FC problem on directed graphs can be solved step by step. The proposed protocol guarantees that the control errors converge into an explicit residual set in a prescribed time interval and then shrink to zero asymptotically.

Third, a hierarchical resilient control scheme is designed to achieve the resilient time-varying formation-tracking (TVFT) tasks of MASs against composite attacks, which owns a distributed topology-assignable observer, or called twin layer (TL), apart from the cyber-physical layer (CPL). The resilient TVFT task is decoupled into the defense against Denial-of-Services (DoS) attacks on the TL and the defense against actuation attacks (AAs) on the CPL. First, a Zeno-free event-triggered protocol is introduced to alleviate the communication burden on the TL. A topology repairing strategy for the TL is further proposed to improve network connectivity against DoS attacks. Second, a decentralized adaptive controller against unbounded AAs is proposed, which possesses the chattering-free merit and uniformly ultimately bounded (UUB) convergence.

Fourth, the problem of resilient output TVFT of heterogeneous MASs against Byzantine attacks is solved via the TL approach. The TL decouples the defense scheme into the defense against Byzantine edge attacks (BEAs) on the TL and the defense against Byzantine node attacks (BNAs) on the CPL. A trusted-node strategy for the TL is proposed, which improves the network robustness against BEAs via protecting a small fraction of key nodes. It is proven that strongly trustworthy $(2f+1)$-robustness is effective for the resilience of the TL. Furthermore, a decentralized adaptive controller on the CPL against BNAs is proposed, which ensures the control error converges into an explicit bound with an assignable exponential convergence rate.

The above distributed observers decouple the conventional distributed control scheme into a hierarchical framework, including distributed observation and subsequent observer-based decentralized control. This hierarchical framework could effectively suppress the propagation process of actuation faults and node attacks. Moreover, given that the topology-assignable ability of the distributed observation process, some edge attacks can also be tackled tactfully via the proposed TL approach.