Optimal Robust Nonlinear Controller Design for a Class of Nonlinear Fractional-Order Systems

In this paper, an optimal robust nonlinear control approach based on the state-dependent Riccati equation (SDRE) is presented for a class of fractional-order nonlinear systems. The SDRE control is a method for the solution of nonlinear systems optimal problems, which has some disadvantages, such as it is not robust against disturbances and uncertainties and has not finite time convergence ability. Sliding mode control (SMC) is also a common method for nonlinear systems control, although it is not an optimal control method, it has great advantages such as robustness which has made it very popular. In the proposed method, a combination of SMC and SDRE methods is used for optimal and robust nonlinear control, which is suitable for a class of fractional-order nonlinear systems. The proposed control method has a robust structure against mismatched disturbances. The closed loop system stability is guaranteed by the Lyapunov theory and simulation examples show the performance improvement of the proposed method.