Event-Triggered Adaptive Dynamic Programming for Hierarchical Sliding-Mode Surface-Based Optimal Control of Switched Nonlinear Systems

In this paper, a novel hierarchical sliding-mode surface (HSMS)-based adaptive event-triggered optimal control (ETOC) method is proposed for switched nonlinear systems using single-critic adaptive dynamic programming (ADP). Initially, an ameliorative HSMS containing all system states is constructed to improve the system response rate. With positive quadratic functions being assigned for the developed HSMS-based cost function, the original stabilization problem is further transformed into an array of ETOC problems. Subsequently, by implementing a single-critic neural network (NN) whose weights are tuned based on an aperiodic manner and the historical data, a series of event-triggered Hamilton-Jacobi-Bellman (HJB) equations are approximately solved. Meanwhile, the condition for the persistence of excitation existing in the traditional actor-critic dual NNs framework is relaxed. Furthermore, the uniformly ultimate boundedness (UUB) of all signals in the closed-loop system is guaranteed by the Lyapunov extension theorem. Finally, a practical continuous stirred tank reactor plant is provided to substantiate the efficacy of the proposed HSMS-based adaptive single-critic ETOC method. Note to Practitioners —Switched nonlinear systems have attracted much attention due to their flexibility in characterizing multi-mode features in practice. The control synthesis and stability analysis of switched nonlinear systems have been the research focus in the control field. However, with the development of adaptive dynamic programming (ADP), it is no longer limited to the study of control synthesis and stability of switched systems. How to improve the response rate and achieve optimal control of switched nonlinear systems with less control cost becomes critical. On the other hand, the persistent information transmission of control signals not only occupies more bandwidth, but also causes severe transmission delays, thus it is important to conduct the signal transmission only when necessary. This paper discusses the optimal control problem for switched nonlinear systems. Meanwhile, an event-triggered adaptive dynamic programming optimal control policy based on a hierarchical sliding-mode surface is proposed, which consumes less control cost while improving the system response rate and saving communication resources.