Robust State Feedback Control Design with Probabilistic System Parameters

TL;DR

This paper introduces a polynomial chaos framework for analyzing and designing controllers for linear systems with probabilistic parameters, offering stability guarantees and computational advantages over Monte-Carlo methods.

Contribution

It presents a novel polynomial chaos-based method for stability analysis and controller synthesis, with convex optimization formulations and exponential mean square stability guarantees.

Findings

Polynomial chaos approach is computationally more efficient than Monte-Carlo methods.

The method successfully designs an optimal EMS-stabilizing controller for an F-16 aircraft model.

The approach provides stability guarantees for systems with probabilistic parameters.

Abstract

In this paper, a new polynomial chaos based framework for analyzing linear systems with probabilistic parameters is presented. Stability analysis and synthesis of optimal quadratically stabilizing controllers for such systems are presented as convex optimization problems, with exponential mean square stability guarantees. A Monte-Carlo approach for analysis and synthesis is also presented, which is used to benchmark the polynomial chaos based approach. The computational advantage of the polynomial chaos approach is shown with an example based on the design of an optimal EMS-stabilizing controller, for an F-16 aircraft model.