Computing controlled invariant sets for hybrid systems with applications to model-predictive control

TL;DR

This paper presents a semidefinite programming approach to compute controlled invariant sets for hybrid systems, enabling safer controller design and application to safety-critical model predictive control.

Contribution

It introduces a novel method using SDP for invariant set computation in hybrid systems, specifically for switching affine systems with polytopic safe sets.

Findings

Effective computation of invariant sets via SDP

Application to safety-critical model predictive control

Enhanced controller design for hybrid systems

Abstract

In this paper, we develop a method for computing controlled invariant sets using Semidefinite Programming. We apply our method to the controller design problem for switching affine systems with polytopic safe sets. The task is reduced to a semidefinite programming problem by enforcing an invariance relation in the dual space of the geometric problem. The paper ends with an application to safety critical model predictive control.