Event-triggered H∞ control for unknown constrained nonlinear systems with application to robot arm

In this paper, an event-triggered safe $H_{\infty }$ control approach is investigated for nonlinear continuous-time systems with asymmetric constrained-input and state constraints. The proposed method is based on adaptive dynamic programming and addresses systems with completely unknown dynamics. Firstly, the unknown dynamics is identified using three neural networks. Secondly, a novel nonquadratic type function is introduced to address the asymmetric constrained-input. Next, the intention behind integrating the value function with the control barrier function is to guide the system state to evolve within the safe area. This also leads to a novel safe Hamilton-Jacobi-Isaacs equation. Next, the event-triggered condition is established with a designated threshold, ensuring the system stability. Unlike the classical actor-critic neural network approach, we only require a critic neural network to estimate the safe Hamilton-Jacobi-Isaacs equation, thereby achieving online solution under state constraints. Utilizing the Lyapunov stability approach and considering the joint impact of asymmetric constrained-input and state constraints, the system state and critic neural network weights exhibit uniformly ultimately bounded, effectively eliminating Zeno behavior. In conclusion, the efficacy of the proposed scheme is demonstrated through a simulation example involving a robot arm system.