A data-driven online ADP control method for nonlinear system based on policy iteration and nonlinear MIMO decoupling ADRC

The action-critic approximate dynamic programming (ADP) depends on its network structure and training algorithm. Since there are some inherent shortcomings of the neural network, this paper proposes a data-driven nonlinear online ADP control method without the neural network. Firstly, a multi-input multi-output (MIMO) policy iteration method is utilized for the proposed ADP. For its policy evaluation, the cost function is approximated with a quadratic function and least square method; for its policy improvement, the optimal control is approximated by solving the quadratic function linearly. In this way, an optimal control equation in form of variable coefficients and system states is deduced. Secondly, a nonlinear MIMO decoupling Active Disturbance Rejection Control method is used to obtain the variable coefficients in real time, which endows the ADP method with a nonlinear performance during its policy improvement. Once the variable coefficients are determined, the data-driven nonlinear ADP control method is deduced. Finally, the examples of an under-actuated nonlinear system and a real application are taken to demonstrate the optimal control effect. Compared with some published methods and their simulation, this method and its simulation excel in the method of policy improvement, nonlinear ability and control performance etc. Thus, the proposed method explores a new way to the ADP, and overcomes the shortcomings of the neural-network-based ADP. Since it enables to work like a PID controller and does not require data collecting, training or extra learning, this proposed ADP is a real data-driven nonlinear online optimal control method.