Neural Network-based Model-free Learning Approach for Approximate Optimal Control of Nonlinear Systems

2020 ◽  
Author(s):  
Zhenhui XU ◽  
Tielong SHEN ◽  
Daizhan CHENG
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Nonlinear Systems ◽  
Learning Approach ◽  
Model Free

scholarly journals Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration

2021 ◽  
Vol 11 (5) ◽  
pp. 2312
Author(s):  
Dengguo Xu ◽  
Qinglin Wang ◽  
Yuan Li
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Policy Iteration ◽  
Control Law ◽  
Globally Asymptotically Stable ◽  
Control Approach ◽  
Input Uncertainties ◽  
Theoretical Results

In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.

Diagonal recurrent neural network observer-based adaptive control for unknown nonlinear systems

2020 ◽  
Vol 42 (15) ◽  
pp. 2833-2856
Author(s):  
Ahmed Elkenawy ◽  
Ahmad M El-Nagar ◽  
Mohammad El-Bardini ◽  
Nabila M El-Rabaie
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Adaptive Control ◽  
Nonlinear Systems ◽  
Recurrent Neural Network ◽  
Learning Algorithm ◽  
Lyapunov Stability Theory ◽  
Adaptive Dynamic Programming ◽  
External Disturbances ◽  
System States

This paper proposes an observer-based adaptive control for unknown nonlinear systems using an adaptive dynamic programming (ADP) algorithm. First, a diagonal recurrent neural network (DRNN) observer is proposed to estimate the unknown dynamics of the nonlinear system states. The proposed neural network offers a simpler structure with deeper memory and guarantees the faster convergence. Second, a neural controller is constructed via ADP method using the observed states to get the optimal control. The optimal control law is determined based on the new structure of the critic network, which is performed using the DRNN. The learning algorithm for the proposed DRNN observer-based adaptive control is developed based on the Lyapunov stability theory. Simulation results and hardware-in-the-loop results indicate the robustness of the proposed ADP to respond the system uncertainties and external disturbances compared with other existing schemes.

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