Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

Abstract

In this paper, an adaptive dynamic surface control approach is developed for a class of multi-input multioutput nonlinear systems with unknown nonlinearities, bounded time-varying state delays, and in the presence of time-varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some time-varying values where the values, times, and patterns of the failures are unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. With the help of neural networks to approximate the unknown nonlinear functions and combining the dynamic surface control approach with the backstepping design method, a novel control approach is constructed. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed-loop signals is guaranteed, and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark as well as a chemical reactor system. The simulation results show the effectiveness of the proposed method. of the traditional backstepping design method [32,33]. The problem of 'explosion of complexity' is the complexity of the controller that grows drastically as the order of the system increases. The 'explosion of complexity' is caused by repeated differentiation of certain nonlinear functions.One of the other serious problems that are frequently encountered in many practical control systems and brings uncertainties to the systems is time delays. Because of the effect of time delays, these systems may own instability and poor performance [34]. So far, considerable attention has been devoted to the stability analysis and control design for time delay systems [35][36][37][38][39][40][41][42][43][44]. The existence of time delays renders the actuator failure compensation problem much more complex and difficult. Many valuable research and practical results have been achieved in actuator failure compensation for linear time delay systems [45][46][47][48][49][50][51][52]. To the best of the author's knowledge, relatively, a few papers were published regarding actuator failure compensation for nonlinear time delay systems [53][54][55][56][57][58]. In [53], an adaptive actuator failure compensation scheme was developed for a class of multi-input nonlinear time delay systems with known parameters, nonlinearity, constant delay, constant control gains, and unknown actuator failure parameters. In [54], a robust state feedback controller was presented for time delay multi-input systems with known parameters, known constant control gains, unknown nonlinearity, and unknown constant delays. The proposed robust actuator failure compensator in [54] promised the boundedness of all the signals in the closed-loop system; however, the tracking problem was not considered. In [55][56][57], the adaptive actuator failure compensation schemes were presented for paramet...

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