Minimax Linear Quadratic Gaussian Control of Nonlinear MIMO System with Time Varying Uncertainties

In this paper, a robust nonlinear control scheme is proposed for a nonlinear multi-input multi-output (MIMO) system subject to bounded time varying uncertainty which satisfies a certain integral quadratic constraint condition. The scheme develops a robust feedback linarization approach which uses standard feedback linearization approach to linearize the nominal nonlinear dynamics of the uncertain nonlinear system and linearizes the nonlinear time varying uncertainties at an arbitrary point using the mean value theorem. This approach transforms uncertain nonlinear MIMO systems into an equivalent MIMO linear uncertain system model with unstructured uncertainty. Finally, a robust minimax linear quadratic Gaussian (LQG) control design is proposed for the linearized model. The scheme guarantees the internal stability of the closed loop system and provides robust performance. In order to illustrate the effectiveness of this approach, the proposed method is applied to a tracking control problem for an air-breathing hypersonic flight vehicle (AHFV).