Control of Uncertain PWA Systems using Difference-of-Convex Decompositions
Siddharth H. Nair, Yvonne R. St\"urz
TL;DR
This paper develops a method for controlling uncertain discrete-time PWA systems by leveraging Difference-of-Convex decompositions to derive stability certificates and stabilizing policies.
Contribution
It introduces a novel approach using DC decomposition to design Lyapunov functions and feedback policies for uncertain PWA systems.
Findings
Successfully derives quadratic Lyapunov functions for stability analysis.
Designs stabilizing affine policies in a higher-dimensional space.
Produces time-varying PWQ Lyapunov functions and PWA feedback policies.
Abstract
In this report, we analyze and design feedback policies for discrete-time Piecewise-Affine (PWA) systems with uncertainty in both the affine dynamics and the polytopic partition. The main idea is to utilise the Difference-of-Convex (DC) decomposition of continuous PWA systems to derive quadratic Lyapunov functions as stability certificates and stabilizing affine policies in a higher dimensional space. When projected back to the state space, we obtain time-varying PWQ Lyapunov functions and time-varying PWA feedback policies.
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Taxonomy
TopicsStability and Control of Uncertain Systems · Distributed Control Multi-Agent Systems · Advanced Control Systems Optimization