Mixed H2/H∞ Control With Dynamic Event-Triggered Mechanism for Partially Unknown Nonlinear Stochastic Systems

• Published in: IEEE transactions on automation science and engineering 2023-07, Vol.20 (3), p.1934-1944
• Main Authors: Ming, Zhongyang, Zhang, Huaguang, Tong, Xin, Yan, Yuqing
• Format: Article
• Language: English
• Subjects: adaptive dynamic programming (ADP); Behavioral sciences; Games; Interference; Nash equilibrium; neural networks; Optimal control; Power system dynamics; stability analysis; Stochastic systems
• ISSN: 1545-5955
• DOI: 10.1109/TASE.2022.3189392

This technical note discusses the design process of dynamic event-triggered control (DETC) with the mixed H_{2}/H_\infty for partially unknown nonlinear stochastic systems. The purpose of this problem is to design a controller to make the closed-loop system achieve the expected H_{2} performance under the condition that the H_\infty continuous attenuation level is protected. Firstly, a two-player non-zero-sum game for stochastic system is given. Then we prove the optimal control strategy and the worst interference, which constitute the Nash equilibrium solution and can be derived from the corresponding Hamiltonian functions. Furthermore, two neural networks (NNs) are used to realize Nash equilibrium. Under the condition of dynamic event-triggered mechanism (DETM), the control strategy only is updated at the trigger moment. In addition, the stability and weights convergence of the system are proved mathematically. Finally, two numerical example are given to prove it.Note to Practitioners-In the practice of control engineering, mixed H_{2}/H_\infty control can not only evaluate the H_{2} performance index of the transient behavior of the system, but also measure the H_\infty performance index of the system's robustness to external disturbances and parameter uncertainty. And many useful signals and interference vary randomly. Therefore, the optimal control of stochastic systems and dynamics play an important role in the modern industry. Saving control resources is very important for actual production. Therefore DETC is considered in this paper. On the other hand, in practice, accurate system models are difficult to obtain. In order to tackle this difficulty, by designing a novel scheme via integral reinforcement learning technique, the system relaxes the requirement of drift dynamic and Zeno behavior is avoided.