Synthesis for Constrained Nonlinear Systems using Hybridization and Robust Controllers on Simplices

TL;DR

This paper introduces a hybridization-based controller synthesis method for constrained nonlinear systems, utilizing triangulation and robust affine controllers on simplices, demonstrated on a pendulum-cart system.

Contribution

It extends hybrid control techniques to handle disturbances in nonlinear systems via triangulation-based hybridization and robust local controllers, enabling automated and tractable synthesis.

Findings

Successfully controls a pendulum on a cart.

Method is fully automated and computationally feasible.

Provides conservative but effective control solutions.

Abstract

In this paper, we propose an approach to controller synthesis for a class of constrained nonlinear systems. It is based on the use of a hybridization, that is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined on a triangulation of the state-space where on each simplex of the triangulation, the nonlinear dynamics is conservatively approximated by an affine system subject to disturbances. Except for the disturbances, this hybridization can be seen as a piecewise affine hybrid system on simplices for which appealing control synthesis techniques have been developed in the past decade. We extend these techniques to handle systems subject to disturbances by synthesizing and coordinating local robust affine controllers defined on the simplices of the triangulation. We show that the resulting hybrid controller can be used to control successfully the original constrained nonlinear system. Our approach, though conservative, can be fully automated and is computationally tractable. To show its effectiveness in practical applications, we apply our method to control a pendulum mounted on a cart.