Comparative Analysis of Linear and Exact Control Laws in Zonotope-Based MPC

Zonotopes are a special type of symmetric polytopes that have been an emerging control design tool, being used for such tasks as state estimation and explicit model predictive control. Zonotopes are used to represent sets of control actions and states, encountered by trajectories of the system, originating from a set of initial conditions. However, an inherent limitation of zonotope geometry (their symmetries, for example) limits the range of control design scenarios where zonotopes can be used as an adequate set representation, while the use of linear control laws can prevent change in the desired behavior of the closed-loop system. The first issue can be remedied by the use of constrained zonotopes, which can represent arbitrary polytopes. In this paper we present an analysis of the second problem, demonstrating the effects of linear control law and exact, convex programmingbased control law. We demonstrate the efficacy of the use of the lifting-up method for constrained zonotopes as pertains to control design.