Event-Triggered <i>H∞</i> Tracking Control for Dynamic Artificial Neural Network Models With Time-Varying Delays

Dynamic artificial neural network models refer to the dynamic model structures that include artificial neural networks such as multi-layer perceptrons, which are used to model nonlinear system dynamics. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> tracking control for dynamic artificial neural network models with communication delays and external disturbance is investigated in this article. First, we formulate the dynamic artificial neural network model as a sampled-state error dependent model for networked control systems with the event-triggered mechanism, which is designed to reduce the consumption of network resources. The network-induced delay considered in this paper is time varying with a known upper bound. Furthermore, by Lyapunov-based techniques, we present sufficient conditions such that the closed-loop system satisfies the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> tracking performance. In addition, we propose a method to co-design the tracking controller and event-triggering parameters in the form of linear matrix inequalities. The effectiveness of our proposed methods is validated through a simulation example and a turbofan engine hardware-in-the-loop experiment. Note to Practitioners—When mathematical models of the plant dynamics are not available, neural network modeling can serve as a useful method for controller design, provided we have numerical information about the system behavior. The novel stability conditions and the established controller design method can be adapted for different classes of dynamic artificial neural network models, including neural state space models, global input-output models and dynamic recurrent neural networks. This characteristic reduces the constraints on model selection, thus expanding the application scenarios. Instead of the stabilization problem, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> tracking control problem is considered in this paper, which has a wider range of applications. In view of the growing need to reduce unnecessary consumption of communication resources in some digital control systems such as smart power grid, aircraft, industrial automatic production and so on, different from existing results, a discrete-time version of periodic event-triggered mechanism is adopted in analysis and control of dynamic artificial neural networks. In addition, disturbances and time delays which widely exist in engineering are also considered. Therefore, the proposed method is more suitable for practical applications. Finally, the established method is applied to the turbofan engine multivariable trajectory tracking control problem, and the effectiveness is illustrated by experiments. In future research, we will address the design problem of dynamic artificial neural network observer for the situation where the system states are unmeasurable.