OPTIMIZATION AND CONTROL ISSUES WITH NETWORK CONNECTED DYNAMIC SYSTEMS

Abstract

"Multi-agent systems (MASs)" is usually used to describe a group of agents or subsystems which communicate over a network and work cooperatively to achieve specified control tasks. In many application, the subsystems are required to reach an agreement upon certain quantities of interest, which is referred to as "consensus control"; if the quantities are the optimal solution of a global function, it is referred to as "distributed optimization". Taking the advantage of the communication network, MASs can achieve complicate control tasks in a distributed manner. However, due to information exchange over the communication network, even one adversary or faulty agent can degrade the performance of the whole system. This thesis focus on these two important and correlated issues in MASs: distributed optimization and robust cooperative control. The distributed optimization problem (DOP) is first investigated over both fixed and time-varying directed communication structures within a continuous-time framework. An augmented Lagrangian function is designed to analyse the properties of optimal solutions over an asymmetric Laplacian matrix. Based on this analysis, a consensus-based algorithm is proposed to solve the distributed optimization problem on unbalanced directed graphs such that the algorithm asymptotically converges to optimal solutions. To remove the requirement of the convexity of local objective functions, adaptive control techniques are introduced. By the virtue of the carefully designed adaptive law, the proposed adaptive optimization algorithm achieves global convergence with nonconvex local objective functions, unknown network connectivity and locally Lipschitz gradients. Furthermore, the adaptive optimization algorithm is combined with an event-triggered mechanism, which reduces the communication costs. Since the triggering function only depends on the information in the connected neighbourhood, the scalability of the adaptive optimization algorithm is preserved. Then the distributed coordination (DOC) problem, regarded as an extension of DOPs, is addressed with discrete-time communication. An event-triggered optimization algorithm is designed to achieve asymptotic convergence when the dynamics of the subsystem are linear. Different from the previous event-triggered optimization scheme, the triggering function of each subsystem only depends on its own states. Then the robust cooperative control problem is addressed within the scenario of cooperative guidance. A new robust cooperative guidance problem in the presence of misbehaving subsystems is first formulated. A robust cooperative guidance law integrated with a local filtering algorithm is designed. Without the knowledge of faulty interceptors (no fault diagnosis procedure is needed), the proposed guidance law achieves a simultaneous arrival between normal subsystems if the misbehaviour of faulty subsystems can be characterized by a threat model. The convergence of algorithm is guaranteed by analysing the contracting behaviour of time-to-go estimates of normal subsystems.

Date of Award	1 Aug 2019
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Zhongdong Wang (Supervisor) & Zhengtao Ding (Supervisor)