Robust nonlinear control of a nonlinear uncertain system with input coupling and its application to hypersonic flight vehicles

For a class of multi input and multi output nonlinear uncertain systems with input coupling term, a robust feedback linearization method combined with a minimax linear quadratic regulator (LQR) control is proposed. The uncertainties in the system and the presence of input terms in the low order derivatives of the outputs due to the input coupling makes the feedback linearization a challenging task. In this paper, we approach this problem in a robust way such that all the uncertainties are lumped together and the coupling term vanishes. The procedure consists of the simplification of the nonlinear model to achieve full vector relative degree and then use the robust feedback linearization method to linearize the nonlinear dynamics. This 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 the longitudinal stabilization of an air-breathing hypersonic flight vehicle in the presence of input coupling and uncertainties.