Backstepping-Based Tracking Control of Nonlinear Systems With Concurrent State-Triggering Mechanism

This paper investigates tracking control of nonlinear systems in state-triggering setting. Since the trigger mechanism may result in system states being discontinuous throughout the whole control operation, the controller design process and stability analysis algorithms based on conventional backstepping design are not applicable for such discontinuous systems due to the non-differentiability of the virtual control. To tackle this dilemma, the first-order filter is introduced to smooth the discontinuous virtual control. Nonlinear impulse dynamics technique is adopted to verify the boundedness of the error variables generated by the filter in stability analysis. Furthermore, the adaptive parameters are solely updated at triggering points to alleviate the communication burden. Particularly, all states are required to be updated synchronously with the established concurrent state-triggering mechanism. It is indicated that with the developed backstepping-based state-triggering control scheme, the entire closed-loop signals are bounded, the system output tracks a prescribed reference trajectory and Zeno behaviour is absent. Finally, the simulation study illustrates the applicability of the proposed control scheme. Note to Practitioners —The study of tracking control for nonlinear systems is prevalent in various practical engineering applications, such as the gripping operation of a single-link manipulator, the orbiting of a spacecraft, and the cruising process of an unmanned aerial vehicle. Moreover, with the rapid development of networking, communication resources are often limited. Continuous information transmission in the sensor-to-controller channel can generate communication blockage and degrade transmission efficiency. Therefore, it is crucial to utilize the limited bandwidth resources to solve the tracking control problem of nonlinear systems. In this paper, we propose a backstepping-based state-triggering control scheme, where the triggered states and triggered adaptive parameters are used for the whole control design. The proposed scheme accomplishes the tracking control task well, especially in applications with limited bandwidth and energy. It is more consistent with requirements of the actual engineering.