Dynamic surface control for nonlinear fractional-order chaotic systems with time delays

Abstract

Due to the uncertainty and randomness, the chaotic behavior of nonlinear system has become an important factor affecting the stability of the system. Therefore, it is very necessary to ensure that the nonlinear system has strong robustness against the external stochastic interference. This paper presents a new dynamic surface controller for nonlinear systems with time delays. In order to be closer to the actual engineering complex operation environment, the fractional calculus operator is added in the system. The dynamic surface control and time-delay effect is first applied to the second-order nonlinear fractional-order system. To deal with the problem of number explosion and time-delay in traditional inversion methods, a fractional-order filter and an alpha-order Pade approximation method are designed. After fully considering the tracking error, virtual control error and filtering error, the dynamic surface controller is established and its stability is verified. It can be seen from the simulation results that the system tracks the set function trajectory in finite time, and the controller has a good effect.