Event-Based Adaptive Neural Tracking Control for Discrete-Time Stochastic Nonlinear Systems: A Triggering Threshold Compensation Strategy

This paper investigates the event-triggered (ET) tracking control problem for a class of discrete-time strict-feedback nonlinear systems subject to both stochastic noises and limited controller-to-actuator communication capacities. The ET mechanism with fixed triggering threshold is designed to decide whether the current control signal should be transmitted to the actuator. A systematic framework is developed to construct a novel adaptive neural controller by directly applying the backstepping procedure to the underlying system. The proposed framework overcomes the noncausality problem, avoids the possible controller-related singularity problem, and gets rid of the neural approximation of the virtual control laws. Under the ET mechanism, the corresponding ET-based actuator is put forward by introducing an ET threshold compensation operator. Such a compensation operator (with an adjustable design parameter) is subtly designed based on a hyperbolic tangent function and a sign function. The threshold compensation error is analytically characterized in terms of a time-varying parameter, and the error bound is shown to be relatively small that is dependent on the adjustable design parameter. Compared with the traditional ET-based actuator without the compensation operator, the proposed ET-based actuator exhibits several distinguished features including: 1) improvement of the tracking accuracy (especially at the triggering instants); 2) further mitigation of the communication load; and 3) enlargement of the allowable range of the ET threshold. These features are illustrated by numerical and practical examples.