A System Level Approach to Controller Synthesis

TL;DR

This paper introduces a novel system level approach for controller synthesis that leverages parameterizations and constraints to enable convex optimization for complex, structured control systems with communication and computational limitations.

Contribution

It develops a comprehensive system level framework with parameterizations and constraints, generalizing existing methods and enabling convex synthesis for structured, constrained control systems.

Findings

Defines System Level Parameterizations (SLPs) for stabilizing controllers.

Introduces System Level Constraints (SLCs) for structured control design.

Demonstrates convex solvability of broad class of control problems.

Abstract

Biological and advanced cyberphysical control systems often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation. Fortunately, the corresponding plants and performance requirements are also sparse and structured, and this must be exploited to make constrained controller design feasible and tractable. We introduce a new "system level" (SL) approach involving three complementary SL elements. System Level Parameterizations (SLPs) generalize state space and Youla parameterizations of all stabilizing controllers and the responses they achieve, and combine with System Level Constraints (SLCs) to parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization, generalizing quadratic invariance (QI). SLPs also lead to a generalization of detectability and stabilizability, suggesting the existence of a rich separation structure, that when combined with SLCs, is naturally applicable to structurally constrained controllers and systems. We further provide a catalog of useful SLCs, most importantly including sparsity, delay, and locality constraints on both communication and computing internal to the controller, and external system performance. The resulting System Level Synthesis (SLS) problems that arise define the broadest known class of constrained optimal control problems that can be solved using convex programming. An example illustrates how this system level approach can systematically explore tradeoffs in controller performance, robustness, and synthesis/implementation complexity.