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

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.