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.

本文关注由多个耦合子系统组成的系统的控制。在这样的架构中，需要不同本地控制器之间的通信以实现更好的整体控制性能。然而，控制性能的任何最终改进都需要足够显着，以保证与在控制器之间引入通信通道相关的额外设计复杂性和更高的能耗和成本。因此，实用的分布式控制设计旨在在最大限度地减少控制器之间的通信使用和最大限度地提高系统范围的性能之间实现可接受的平衡。在本文中，提出了一种为平衡性能和通信的离散时间线性系统合成稳定分布式控制律的新方法。该方法采用了一个监督代理，虽然不一定在每个采样时刻，但它周期性地解决优化问题，以便为系统合成一个稳定的状态反馈控制律。最大化控制律的稀疏性同时最小化无限范围性能成本的在线优化问题被表述为双线性矩阵不等式（BMI）问题；随后，它被放松为线性矩阵不等式（LMI）问题，并且（i）收敛到解决方案以及（ii）提前终止保证了可行（但次优）的控制律得到证明。在切换控制法则下闭环系统的稳定性是通过在 LMI 问题中包含驻留时间约束来保证的。最后，通过数值模拟实例证明了该方法的有效性。