Supervised-distributed control with joint performance and communication optimisation

Abstract

This paper is concerned with the control of systems composed of multiple coupled subsystems. In such architectures, communication between different local controllers is desired in order to achieve a better overall control performance. Any resultant improvement in control performance needs, however, to be significant enough to warrant the additional design complexity and higher energy consumption and costs associated with introducing communication channels between controllers. A practical distributed control design aims, therefore, to achieve an acceptable balance between minimizing the use of communication between controllers and maximizing the system-wide performance. In this article, a new approach to the problem of synthesizing stabilizing distributed control laws for discrete-time linear systems that balances performance and communication is presented. The approach employs a supervisory agent that, periodically albeit not necessarily at every sampling instant, solves an optimization problem in order to synthesize a stabilizing state feedback control law for the system. The online optimization problem, which maximizes sparsity of the control law while minimizing an infinite-horizon performance cost, is formulated as a bilinear matrix inequality (BMI) problem; subsequently, it is then relaxed to a linear matrix inequality (LMI) problem, and (i) convergence to a solution as well as (ii) that early termination guarantees a feasible (but suboptimal) control law are proved. Stability of the closed-loop system under what is a switched control law is guaranteed by the inclusion of dwell-time constraints in the LMI problem. Finally, the efficacy of the approach is demonstrated through numerical simulation examples.

Simultaneous and Sequential Control Design for Discrete-Time Switched Linear Systems Using Semi-Definite Programming

“…It is well known that dwell time constraints can be used in order to design control modes able to switch in a stable fashion [3]. In particular, ensuring stability between two control modes with the minimum possible dwell time of 1, ensures a stable switch for any greater dwell time, for the same two control modes [23]. Enforcing direct stable switches between any two admissible control modes can be conservative, and even lead to infeasible problems.…”

“…It can be highlighted that the feasibility of problem (13) depends on the control modes indexed by the set I j s , and thus it is not trivial to evaluate it a priori; this is a topic of future research. Problem ( 13) is inspired by the LMI problem used for fixed dwell time and system dynamics, when the control modes are design sequentially online [23], [24].…”

Clustering Switching Regions for Feedback Controllers: A Convex Approach

“…Then, the boundaries between any parent and children topologies become ellipsoidal surfaces, and thus, sets Υ Λj Λi become ellipsoidal regions [26]. Since (22) can be rewritten as…”

“…In this regard, a blockstructured global feedback is precomputed offline for each possible cooperation scenario by solving an optimization problem subject to linear matrix inequalities (LMIs). Also, [22]- [25] propose LMI-based controllers with structural constraints that foster a decentralization of the network and hence minimize the amount of data that needs to be transmitted. Our approach here consists of a decision procedure that preselects a subset of possible future topologies considering the current configuration of the network.…”

“…Remark 4. Condition (22) can be satisfied by adjusting the bound on the performance costs provided by matrices P Λi for all Λ i ∈ T . For this reason, this constraint does not endanger the feasibility of the proposed set of LMIs.…”