Event-based online learning control design with eligibility trace for discrete-time unknown nonlinear systems

Abstract

As a heuristic algorithm to solve the nonlinear optimal control problem, adaptive dynamic programming is commonly constructed from one-step temporal difference learning. Eligibility trace can effectively speed up controller learning by considering the multi-step information in reinforcement learning. However, eligibility trace will bring in additional computational consumption and increase the learning burden. This paper attempts to take advantage of eligibility trace and avoids the high learning consumption at the same time. Therefore, an event-based neural dynamic programming (λ) [ENDP(λ)] algorithm via the actor–critic framework is constructed to solve the near-optimal control problem of unknown discrete-time systems. First, the modified forward view with eligibility trace is derived, which is suitable for engineering practice. Second, based on the event-triggered mechanism, ENDP(λ) is designed to relieve the pressure of communication consumption. Then, the event-based system is proven to ensure the input-to-state stability under a suitable triggering condition. Moreover, three neural networks are given to approximate the one-step cost function, the n-step cost function, and the control law, respectively. Finally, two typical experimental simulation examples are presented to verify the effectiveness of the ENDP(λ) algorithm.