Event-triggered adaptive neural network-based optimal control of strictly feedback switched nonlinear systems with state constraints

In this article, we present an innovative approach for controlling nonlinear switched systems (NSSs) with strict feedback utilizing adaptive neural networks (ANNs). Our methodology encompasses several facets, addressing key challenges inherent to these systems. To commence, we tackle the constrained nature of NSSs with strict feedback by designing a barrier Lyapunov function. This function ensures that all states within the switched systems remain within prescribed constraints. Additionally, we harness neural networks (NNs) to approximate the unknown nonlinear functions inherent to the system. Furthermore, we deploy an ANN state observer to estimate unmeasurable states. Our approach then proceeds to develop a cost function for the subsystem. Building upon this, we apply the Hamiltonian-Jacobi-Bellman (HJB) solution in conjunction with observer and behavior critic architectures, all rooted in backstepping control (BC) principles. This integration yields both a virtual optimal controller and a real optimal controller. Furthermore, we introduce a novel ANN event-triggered control (ETC) strategy tailored explicitly for strictly feedback systems. This strategy proves highly effective in reducing the utilization of communication resources and eliminating the occurrence of Zeno behavior. Our analysis provides formal proof that all states within the closed-loop system exhibit half-leaf consistency and are ultimately bounded, regardless of arbitrary switching conditions. Finally, we substantiate the efficacy and viability of our control scheme through comprehensive numerical simulations.