Decentralized adaptive output feedback dynamic surface control for stochastic nonstrict‐feedback interconnected nonlinear systems with actuator failures and input quantization via command filter

Abstract

In this article, a new decentralized adaptive neural output feedback control scheme based on first‐order command filter is proposed for stochastic nonstrict‐feedback interconnected systems with prescribed performance, input quantization, actuator failures and unmodeled dynamics. The unknown smooth functions are eliminated by using the radial basis function neural networks. The immeasurable states in the system are estimated using the decentralized K‐filters, unmodeled dynamics is processed using dynamic signal, and the hyperbolic tangent function is applied to the construction of the prescribed performance function. The hysteretic quantizer and actuator failure are denoted in the form of linearization, and a smoothing function is introduced to compensate for the effects of quantization and bounded stuck faults. Based on the dynamic surface control (DSC) method and using the properties of Gaussian function to deal with stochastic nonstrict‐feedback interconnected systems, the first‐order command filter is used to replace the first‐order filter in the traditional DSC to eliminate the influence of filtering error on the systems, and an error compensation signal is introduced at the recursive each step of the design to construct a new error dynamic surface, which simplifies the derivation process and the design of the controller. Finally, the Lyapunov method is used to prove that all the signals in the whole controlled system are semiglobally uniformly ultimately bounded in probability and the tracking error is within the time‐varying constraint. The effectiveness of the proposed decentralized adaptive control method is verified by a numerical simulation and an example simulation.

Adaptive actor‐critic neural optimal control for constrained nonstrict feedback nonlinear systems via command filter

“…Remark In order to avoid the algebraic loop problem in the nonlinear nonstrict systems, a simple scheme can be found in Reference 52. This simple scheme depends entirely on the monotone decreasing property of the Gaussian function.…”

“…In this paper, reconstructing the approximation error of the RBFNNs can be applicable to other types of radial basis functions such as sigmoid function and multi‐quadric function. Besides, the lemma 3 in Reference 52 can be removed.…”

“…Subsequently, many results were obtained in the field of unmodeled dynamics. In Reference 52, the issue of the unmodeled dynamics was studied for the stochastic systems in the nonstrict feedback form. In Reference 53, reinforcement learning was adopted to study the optimization of system performance in the sense of the unmodeled dynamics.…”

“…Compared with the existing optimal DSC, 37,38 a set of compensating signals are introduced to countervail the filtering error, and the black‐box functions, such as the Equations (52) and (78) in Reference 37 and the Equations (54) and (80) in Reference 38, can be removed. Different from the existing CFB, 23,24 by defining the compact set and adding the compensation signals into the overall Lyapunov function in the stability analysis, the filtering error can be strictly proved bounded while the basis for the boundedness of the filtering error is ambiguous in the lemma 2 in Reference 23 and the Equation (57) in Reference 24. Unlike the scheme dealing with nonstrict feedback systems in Reference 52, by reconstructing the approximation error of the RBFNNs, the algebraic loop problem can be eliminated without relying on the nature of the Gaussian function. Besides, a hyperbolic‐tangent‐type mapping rule is designed and the restricted states can be mapped to the constraint‐free states.…”

Adaptive neural optimal control via command filter for nonlinear multi‐agent systems including time‐varying output constraints

“…In Reference 42, a transformation technique was utilized to turn a constrained system into a completely unconstrained one by adding new universal‐constrained functions. Based on command filter and decentralized K‐filters, decentralized adaptive output feedback DSC was developed for stochastic large‐scale nonstrict‐feedback nonlinear systems with prescribed performance, actuator failures, input quantization and unmodeled dynamics in Reference 43.…”