Event-triggered control for input-constrained nonzero-sum games through particle swarm optimized neural networks

To accommodate the increasing system scale, improve the system operation success rate and save the computational and communication resources, it is urgent to obtain the Nash equilibrium solution for systems with increasing controllers in an effective way. In this paper, nonzero-sum game problem of partially unknown nonlinear systems with input constraints is solved via the particle swarm optimized neural network-based integral reinforcement learning. By introducing the integral reinforcement learning technique, the drift dynamics is not required any more. To further improve the success rate of system operation, extended adaptive particle swarm optimization algorithm which shares the individual historical optimal position with the whole population is adopted in tuning neural network weights, rather than sharing only the current particle in the traditional particle swarm optimization algorithm. The control policy for each player is obtained by solving the coupled Hamilton–Jacobi equation with a single critic neural network, which simplifies the control structure and reduces the computational burden. Moreover, by introducing the event-triggering mechanism, the control policies are updated at event-triggering instants only. Thus, the computational and communication burdens are further reduced. The stability of the closed-loop system is guaranteed by implementing the integral reinforcement learning-based event-triggered control policies via the Lyapunov’s direct method. From the comparative simulation results, the developed integral reinforcement learning-based event-triggered control scheme via the extended adaptive particle swarm optimization performs better than those using gradient descent algorithm, nonlinear programming, particle swarm optimization and other popular training algorithms.