Premium
Single‐network ADP for solving optimal event‐triggered tracking control problem of completely unknown nonlinear systems
Author(s) -
Xu Ning,
Niu Ben,
Wang Huanqing,
Huo Xin,
Zhao Xudong
Publication year - 2021
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22491
Subject(s) - hamilton–jacobi–bellman equation , dynamic programming , control theory (sociology) , state vector , optimal control , computer science , lyapunov function , nonlinear system , tracking error , artificial neural network , bounded function , mathematical optimization , bellman equation , recurrent neural network , controller (irrigation) , mathematics , artificial intelligence , control (management) , mathematical analysis , physics , classical mechanics , quantum mechanics , agronomy , biology
In this paper, we propose an optimal event‐triggered tracking control scheme for completely unknown nonlinear systems under the adaptive dynamic programming (ADP) framework. A data‐driven model based on recurrent neural networks (RNNs) is first constructed to model the system uncertainties including the drift dynamics and the input gain matrix, and the modeling error caused by NN approximation is well eliminated through adding a compensation term in the data‐driven model such that the model state can asymptotically track the system state. Apart from the traditional construction of optimal tracking controllers, in this paper, an augmented system is developed and a discounted performance function is considered to achieve the optimality. By employing the Bellman optimal principle, an event‐triggered tracking Hamilton–Jacobi–Bellman (HJB) equation is then formulated. The approximate solution of the HJB equation can be obtained by virtue of a critic NN, which significantly simplifies the implementation architecture of ADP. Both the historical state data and the current state data are incorporated into the updating of the weight vector in the critic NN, in this circumstance, the persistence of excitation assumption is not needed anymore. It is strictly proven via Lyapunov stability theory that the tracking error state and the critic NN weight are uniformly ultimately bounded. Simulation results examine the validity of the design scheme.