Polyhedral Control Design: Theory and Methods

TL;DR

This survey reviews polyhedral computing methods for constrained linear control systems, emphasizing convex optimization techniques for designing robust, optimal, and invariant controllers, and discusses their complexity and potential.

Contribution

It provides a comprehensive overview of recent advances in polyhedral control design, highlighting new methods for invariant sets, Lyapunov functions, and model predictive control.

Findings

Polyhedral methods enable robust control invariant set computation.

Convex optimization is central to designing set-based controllers.

Polyhedral techniques face complexity challenges but offer significant potential.

Abstract

In this article, we survey the primary research on polyhedral computing methods for constrained linear control systems. Our focus is on the modeling power of convex optimization, featured to design set-based robust and optimal controllers. In detail, we review the state-of-the-art techniques for computing geometric structures such as robust control invariant polytopes. Moreover, we survey recent methods for constructing control Lyapunov functions with polyhedral epigraphs as well as the extensive literature on robust model predictive control. The article concludes with a discussion of both the complexity and potential of polyhedral computing methods that rely on large-scale convex optimization.