Design of Linear Parameter Varying Quadratic Regulator in Polynomial Chaos Framework

TL;DR

This paper introduces a novel theoretical framework for designing linear parameter varying controllers using polynomial chaos, accounting for stochastic scheduling variables, and demonstrates improved performance over classical methods.

Contribution

It develops two algorithms based on Galerkin projection and stochastic collocation for LPV controller synthesis within the polynomial chaos framework.

Findings

LPV controllers outperform classical designs in missile system regulation.

Both algorithms effectively minimize stochastic system performance objectives.

The framework handles random scheduling variables in LPV control design.

Abstract

We present a new theoretical framework for designing linear parameter varying controllers in the polynomial chaos framework. We assume the scheduling variable to be random and apply polynomial chaos approach to synthesize the controller for the resulting linear stochastic dynamical system. Two algorithms are presented that minimize the performance objective with respect to the stochastic system. The first algorithm is based on Galerkin projection and the second algorithm is based on stochastic collocation. LPV controllers from both the algorithms are shown to outperform classical LPV designs with respect to regulator design for nonlinear missile system.