Polynomial Chaos-Based Adaptive Control for Nonlinear Systems

TL;DR

This paper introduces a polynomial chaos-based adaptive control method for uncertain nonlinear systems, enabling robust control design and stability verification using spectral decomposition and stochastic modeling.

Contribution

It presents a novel control strategy combining polynomial chaos expansion with adaptive control for nonlinear systems with uncertainties.

Findings

Successfully applied to aircraft autopilot with uncertain aerodynamics

Achieved asymptotic weak stability in probability

Provided a deterministic approach to stochastic stability verification

Abstract

In this work we present a nonlinear adaptive suboptimal control strategy for uncertain nonlinear systems. Stochastic parametric uncertainty is dealt with by employing spectral decomposition of the random variables by means of the generalized polynomial chaos expansion. The projection of uncertainty onto the orthogonal polynomial basis, prescribed by the Wiener-Askey scheme, provides a deterministic model from which the control laws are designed. We apply the nonlinear feedback control law to an automatic pilot system for recovering an aircraft with uncertain aerodynamic data from stall while providing acceptable dynamic response. The control law is obtained by approximating the Hamilton-Jacobi-Bellman equation by a pertubational procedure and asymptotic weak stability in probability of the controlled nonlinear system is verified in a deterministic way.