Robust minimax optimal control of nonlinear uncertain systems using feedback linearization with application to hypersonic flight vehicles

Abstract

For a class of multi input and multi output nonlinear uncertain systems, a feedback linearization method combined with minimax linear quadratic regulator (LQR) control is proposed. The nominal nonlinear model is assumed to be feedback linearizable with full relative degree. The uncertainties are assumed to be parametric or parameterized and satisfy a certain integral quadratic constraint condition. The proposed method systematically incorporates the parametric uncertainty bound in the design procedure and gives a locally stabilized closed loop system. This procedure consists of feedback linearization of the nominal model and linearization of the remaining nonlinear uncertain terms with respect to each individual uncertainty at a local operating points. This two-stage linearization process, followed by a robust minimax LQR control design, provides a robustly stable closed loop system. To demonstrate the effectiveness of the proposed approach, an application study is provided on longitudinal stabilization of an air-breathing hypersonic flight vehicle in the presence of uncertainties.