Data-driven approximate optimal tracking control schemes for unknown non-affine non-linear multi-player systems via adaptive dynamic programming

Game theory, optimal control theory and adaptive dynamic programming (ADP) to deal with the optimal tracking control issue for unknown non-affine multi-player systems are integrated. It is known that non-zero-sum games of non-linear multi-player systems rely on solving a set of Hamilton-Jacobi equations, which are generally difficult to be computed analytically due to the non-linear nature. Traditional ADP methods require the knowledge of accurate system models, and only consider the simple affine system version. A novel data-driven Q-learning approach, which only needs the measurable data generated by running systems, is proposed. To implement this method, neural networks (NNs) are utilised, and NN weights are updated through the least-square form.