Constrained Multi-Agent Consensus Control Based on Optimistic Policy Iteration

This paper introduces a safe Reinforcement Learning (RL)-based optimal consensus control method for constrained discrete-time (DT) multi-agent systems (MASs). To address the tracking performance and control input constraints, a novel barrier function (BF) is incorporated into the performance index function, effectively transforming the constrained optimization problem into an unconstrained one. Based on this approach, a constrained optimistic policy iteration (OPI) algorithm is developed to achieve optimal consensus control. This algorithm generalizes classical value iteration (VI) and policy iteration (PI) algorithms and is implemented using two neural networks (NNs). Through rigorous theoretical analysis, the convergence and optimality of the proposed control method are proven. Finally, simulations of a nonlinear DT MAS validate the effectiveness of the method.