Machine learning based-distributed optimal control algorithm for multiple nonlinear agents with input constraints

This paper utilizes the machine learning theory to propose an algorithm for solving the distributed optimal control of multiple nonlinear agents with saturating actuators. Unlike the existing algorithm based on an critic/actor/disturber framework with three neural networks (NNs) to approximate Hamilton-Jacobi-Isaac solution for each nonlinear agent, the algorithm in the paper is proposed with only one NN. It is shown that when the algorithm is executed online, the NN weight approximation errors and states are uniformly ultimately bounded (UUB) as well as the NN weights and optimal control policies are guaranteed to be converged to the approximately optimal values concurrently, and nonquadratic cost functions with constrained-inputs are minimized. To show the effectiveness of the proposed algorithm, simulations for multiple controlled Van der Pol oscillators are carried out and compared.