Novel iterative neural dynamic programming for data-based approximate optimal control design

As a powerful method of solving the nonlinear optimal control problem, the iterative adaptive dynamic programming (IADP) is usually established on the known controlled system model and is particular for affine nonlinear systems. Since most nonlinear systems are complicated to establish accurate mathematical models, this paper provides a novel data-based approximate optimal control algorithm, named iterative neural dynamic programming (INDP) for affine and non-affine nonlinear systems by using system data rather than accurate system models. The INDP strategy is built within the framework of IADP, where the convergence guarantee of the iteration is provided. The INDP algorithm is implemented based on the model-based heuristic dynamic programming (HDP) structure, where model, action and critic neural networks are employed to approximate the system dynamics, the control law and the iterative cost function, respectively. During the back-propagation of action and critic networks, the approach of directly minimizing the iterative cost function is developed to eliminate the requirement of establishing system models. The neural network implementation of the INDP algorithm is presented in detail and the associated stability is also analyzed. Simulation studies are conducted on affine and non-affine nonlinear systems, and further on the manipulator system, where all results have demonstrated the effectiveness of the proposed data-based approximate optimal control method.