Fully cooperative games with state and input constraints using reinforcement learning based on control barrier functions

This paper provides a novel safe reinforcement learning (RL) control algorithm to solve safe optimal problems for fully cooperative (FC) games of discrete-time multiplayer nonlinear systems with state and input constraints. The FC game is a special case of nonzero-sum (NZS) games, where all players cooperate to accomplish a common task. The algorithm is proposed based on the policy iteration (PI) framework utilizing only the measured data along the system trajectories in the environment. Different from most works about PI, an effective method of obtaining initial safe and stable control policies is given here. In addition, control barrier functions (CBFs) and an input constraint function are introduced to augment reward functions. And the monotonically nonincreasing property of the iterative value function in the PI algorithm maintains the safe set forward invariant. Then, the neural networks are employed to approximate the system dynamics, the iterative control policies, and the iterative value function, respectively. Furthermore, the proposed algorithm is supported by theoretical proofs that guarantee both safety and convergence. Finally, the effectiveness and safety of the algorithm are illustrated by the results of the simulation.