Adaptive‐dynamic‐programming‐based fuzzy control for triangular structure nonlinear uncertain systems with unknown time delay

Abstract

Summary This paper develops a novel fuzzy adaptive backstepping dynamic surface control scheme for a class of strict‐feedback nonlinear systems with unknown time delay based on adaptive dynamic programming. The whole control scheme is composed of 2 parts, ie, feedforward control and feedback optimal control. Fuzzy logic systems are used to identify nonlinear systems. The control design method, which combined the backstepping design technique and the dynamic surface control approach, is applied to convert triangular structure systems to affine nonlinear systems; it not only can solve the problem of “explosion of complexity” but also can avoid the appearance of unknown terms. The closed‐loop system is guaranteed to be uniformly ultimately bounded based on the Lyapunov and optimal control theory, and the system output can track the desired reference signal in an optimal manner. The simulation results of numerical examples are presented to show the effectiveness of the proposed approach.

Adaptive optimal dynamic surface control of strict‐feedback nonlinear systems with output constraints

“…Based on ADP idea, output feedback fuzzy optimal scheme was designed in the work of Sun et al, where fuzzy universal approximator was introduced to replace NNs. Under the framework of ADP, Sui et al adopted DSC approach to design controllers for systems with unknown time delay to achieve optimum and it is generalized to switched systems with hysteresis in the work of Sui et al Adaptive neural tracking control scheme was presented for switched nonlinear pure‐feedback nonlower triangular systems in the work of Niu et al In addition, adaptive neural tracking control was developed for stochastic switched nonlower triangular nonlinear systems with input saturation in the work of Cui et al Finite time control problems of nonstrict feedback nonlinear systems were discussed in other works …”

“…Although output constraints were considered in adaptive control in related works, the optimization problems were neglected in the literature. In other works, the original systems were transformed into the nonlinear affine systems related to errors. Motivated by the previous works, adaptive optimal control scheme is developed by combining NM with ADP.…”

“…In other works, the original systems were transformed into the nonlinear affine systems related to errors. Motivated by the previous works, adaptive optimal control scheme is developed by combining NM with ADP. The main contributions of the paper are summarized as follows: In this paper, a novel control strategy is proposed for output constrained systems by combining DSC with optimal control.…”

“…The main contributions of the paper are summarized as follows: In this paper, a novel control strategy is proposed for output constrained systems by combining DSC with optimal control. Our control target is the output constrained systems, which are different from the investigated systems with delay and hysteresis using DSC in related works . To satisfy output constraints in optimal control, the online PI is developed compared with the control strategy based on offline PI in the work .…”

A unified framework of rapid exponential stability and optimal feedback control for nonlinear systems

“…Recently, Sui et al [22][23][24][25] developed, investigated, and analyzed the non-triangular stochastic nonlinear systems via adaptive fuzzy control theory. However, the nonlinear system is considered and investigated in this article and the uncertain stochastic nonlinear systems with non-triangular form is investigated and analyzed in Sui et al [22][23][24] Furthermore, it is a keynote step which is the criterion of stochastically semiglobal finite-time stable for the uncertain stochastic nonlinear systems with non-triangular form. In addition, the sufficient conditions of rapidly exponentially stabilizing are developed and analyzed using a variant of continuous Lyapunov functions and HJBE for nonlinear systems in this article.…”