State Dependent Riccati Equation Based Sliding Mode Control For Nonlinear Systems With Mismatched Uncertainities

The paper introduces an approach to controller design for nonlinear systems having matched or mismatched uncertainties via State Dependent Riccati Equation (SDRE) based Sliding Mode Control (SMC). The controller is first designed for the nominal part of the nonlinear system using SDRE based SMC. Then, effects of disturbances and/or unmodelled dynamics which satisfy the so-called "matching conditions" are included to the system dynamics and the SDRE based SMC controller is modified in order to suppress the effect of disturbances. Finally, SDRE based SMC is combined with the "unity vector approach" which is suggested for SMC of Linear Time Invariant (LTI) systems with mismatched disturbance. Therefore the unity vector approach for the LTI systems is extended to nonlinear systems by means of SDRE and SMC which simplifies the robust controller design for nonlinear systems. The proposed control design is illustrated with a rigid satellite system to show the effectiveness of method. To compare the effect of disturbances in the controller performance, the satellite system is controlled with and without "unity vector approach". It is then shown that robustness is ensured with the inclusion of unity vector approach and the proposed method enables quick system response and less energy consumption.