Adaptive Critic Learning for Constrained Optimal Event-Triggered Control With Discounted Cost

• Published in: IEEE transaction on neural networks and learning systems Vol. 32; no. 1; pp. 91 - 104
• Main Authors: Yang, Xiong, Wei, Qinglai
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Adaptive critic designs (ACDs); adaptive critic learning (ACL); adaptive dynamic programming (ADP); Adaptive learning; Adaptive systems; constrained optimal control; Constraints; Continuous time systems; Coordinate transformations; Cost function; Event triggered control; event-triggered control (ETC); Feedback control; Learning; Lower bounds; Nonlinear control; Nonlinear systems; Optimal control; Pendulums; reinforcement learning (RL); Robustness
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2020.2976787

This article studies an optimal event-triggered control (ETC) problem of nonlinear continuous-time systems subject to asymmetric control constraints. The present nonlinear plant differs from many studied systems in that its equilibrium point is nonzero. First, we introduce a discounted cost for such a system in order to obtain the optimal ETC without making coordinate transformations. Then, we present an event-triggered Hamilton-Jacobi-Bellman equation (ET-HJBE) arising in the discounted-cost constrained optimal ETC problem. After that, we propose an event-triggering condition guaranteeing a positive lower bound for the minimal intersample time. To solve the ET-HJBE, we construct a critic network under the framework of adaptive critic learning. The critic network weight vector is tuned through a modified gradient descent method, which simultaneously uses historical and instantaneous state data. By employing the Lyapunov method, we prove that the uniform ultimate boundedness of all signals in the closed-loop system is guaranteed. Finally, we provide simulations of a pendulum system and an oscillator system to validate the obtained optimal ETC strategy.