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In Chap. 5, we demonstrate that NLTV controllers have an advantage over LTI controllers in stabilizing an LTI decentralized system. In Chap. 6, we explore the design of optimal LTI controllers. In this chapter, we turn our attention to the goal of obtaining optimal LQR performance, with a focus on those systems for which the optimal controller is not LTI. We first provide an example for which the gap between the optimal centralized performance and the optimal decentralized performance can be arbitrarily large. We then consider a large class of systems for which they are equal, namely those systems which are centrally controllable and observable and for which the associated directed graph is strongly connected, and provide a controller synthesis procedure which yields a linear, periodic, near-optimal controller. |
