Intelligent tracking control of multi-player linear stochastic systems based on reinforcement learning methods

Current research on intelligent tracking control for infinite-horizon linear stochastic systems with multi-agent interactions and multi-target objectives remains limited. This study utilizes a reinforcement learning (RL)-based strategy iteration framework to address the Pareto optimal tracking control problem in such systems. Through integration of the original control system and reference trajectory into an augmented system, the stochastic linear quadratic tracking (SLQT) cost function is transformed into an augmented state-dependent quadratic formulation. By using the weighted-sum method, multiple different objectives are balanced to minimize the joint cost function, and the Pareto optimal solution is also obtained. The online RL algorithm can solve the related algebraic Riccati equation in the case of unknown partial system information. The implementation of the online algorithm using the "$\mathcal{H}{\text{ - representation}}$" method effectively eradicates redundant elements in calculations, thereby enhancing the computational efficiency of the algorithm. To conclude, the principal results are proved. We derive the Pareto optimal tracking control strategy, and the convergence properties of the proposed algorithm are also demonstrated.