A Polynomial Chaos Framework for Designing Linear Parameter Varying Control Systems

TL;DR

This paper introduces a polynomial chaos-based method for designing controllers for linear parameter varying systems, treating the scheduling variable as random, and guarantees stability through novel algorithms, outperforming classical methods.

Contribution

It develops a polynomial chaos framework for LPV control design, providing algorithms that ensure exponential mean-square stability with improved performance.

Findings

Algorithms guarantee EMS stability of stochastic LPV systems.

Polynomial chaos controllers outperform classical LPV controllers in examples.

Framework handles randomness in scheduling variables effectively.

Abstract

Here we use polynomial chaos framework to design controllers for linear parameter varying (LPV) dynamical systems. We assume the scheduling variable to be random and use polynomial chaos approach to synthesize the controller for the resulting linear stochastic dynamical system. The stability of the LPV system is formulated as an exponential mean-square (EMS) stability problem. Two algorithms are presented that guarantee EMS stability of the stochastic system and correspond to parameter dependent and independent Lyapunov functions, respectively. LPV controllers from the polynomial chaos based framework is shown to outperform LPV controller from classical design for an example nonlinear system.