A Mean Value Theorem Approach to Robust Control Design for Uncertain Nonlinear Systems

TL;DR

This paper introduces a robust control design method for uncertain nonlinear systems using a mean value theorem-based linearization and minimax LQR, demonstrated on hypersonic vehicle tracking.

Contribution

It develops a novel two-step scheme combining feedback linearization and mean value theorem for structured uncertainty modeling in nonlinear control.

Findings

Effective velocity and altitude tracking for hypersonic flight vehicle.

Structured uncertainty model improves robustness.

Method outperforms traditional control approaches.

Abstract

This paper presents a scheme to design a tracking controller for a class of uncertain nonlinear systems using a robust feedback linearization approach. The scheme is composed of two steps. In the first step, a linearized uncertainty model for the corresponding uncertain nonlinear system is developed using a robust feedback linearization approach. In this step, the standard feedback linearization approach is used to linearize the nominal nonlinear dynamics of the uncertain nonlinear system. The remaining nonlinear uncertainties are then linearized at an arbitrary point using the mean value theorem. This approach gives a multi-input multi-output (MIMO) linear uncertain system model with a structured uncertainty representation. In the second step, a minimax linear quadratic regulation (LQR) controller is designed for MIMO linearized uncertain system model. In order to demonstrate the effectiveness of the proposed method, it is applied to a velocity and altitude tracking control problem for an air-breathing hypersonic flight vehicle.