Optimal Structured Static State-Feedback Control Design with Limited Model Information for Fully-Actuated Systems

TL;DR

This paper explores how limited model information affects the design of structured static state-feedback controllers for fully-actuated systems, identifying optimal strategies and trade-offs in performance.

Contribution

It introduces a framework for control design with constrained model access, computes optimal strategies, and analyzes the trade-offs between information availability and control performance.

Findings

Optimal control design strategies are derived for local model information access.

The study quantifies the trade-off between model information and closed-loop performance.

Performance bounds are established based on the amount of model information used.

Abstract

We introduce the family of limited model information control design methods, which construct controllers by accessing the plant's model in a constrained way, according to a given design graph. We investigate the closed-loop performance achievable by such control design methods for fully-actuated discrete-time linear time-invariant systems, under a separable quadratic cost. We restrict our study to control design methods which produce structured static state feedback controllers, where each subcontroller can at least access the state measurements of those subsystems that affect its corresponding subsystem. We compute the optimal control design strategy (in terms of the competitive ratio and domination metrics) when the control designer has access to the local model information and the global interconnection structure of the plant-to-be-controlled. Lastly, we study the trade-off between the amount of model information exploited by a control design method and the best closed-loop performance (in terms of the competitive ratio) of controllers it can produce.