Controller Synthesis for Discrete-time Hybrid Polynomial Systems via Occupation Measures

TL;DR

This paper introduces a novel convex optimization-based method using occupation measures for synthesizing controllers that stabilize discrete-time hybrid polynomial systems, demonstrated on robotics examples.

Contribution

It presents a new controller synthesis approach for hybrid polynomial systems using occupation measures and semidefinite programming, with polynomial complexity.

Findings

The method successfully stabilizes hybrid polynomial systems in robotics scenarios.

The approach reduces to finite-dimensional semidefinite programs approximating an infinite-dimensional LP.

Computational complexity is polynomial in state and control dimensions for fixed approximation degree.

Abstract

We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We model such a system as a discrete-time hybrid polynomial system, where the state-input space is partitioned into several polytopic regions with each region associated with a different polynomial dynamics equation. Based on the notion of occupation measures, we present a novel controller synthesis approach that solves finite-dimensional semidefinite programs as approximations to an infinite-dimensional linear program to stabilize the system. The optimization formulation is simple and convex, and for any fixed degree of approximations the computational complexity is polynomial in the state and control input dimensions. We illustrate our approach on some robotics examples.