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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 minimising the use of communication between controllers and maximising the system-wide performance. In this article, a new approach to the problem of synthesising stabilising 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 optimisation problem in order to synthesise a stabilising state feedback control law for the system. The online optimisation problem, which maximises sparsity of the control law while minimising 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.

Supervised-distributed control with joint performance and communication optimisation