Neural network-based adaptive decentralized safe control for interconnected nonlinear systems with time delays

This paper addresses the safety control issue for interconnected nonlinear systems with time delays and asymmetric input constraints by proposing a decentralized dynamic event-triggered (DET) controller based on the adaptive dynamic programming (ADP) method. Unlike other studies on large-scale interconnected systems, the equilibrium point of the system under our study is not zero. Firstly, by incorporating a discount factor and introducing a barrier function and a Lyapunov-Krasovskii (L-K) function, we construct a cost function for the interconnected system with a non-zero equilibrium point, time delay, and constraints, thereby transforming the constrained decentralized control problem into an unconstrained optimal control problem (OCP). Subsequently, an event-based Hamilton-Jacobi-Bellman (HJB) equation is established. To enhance computational efficiency, a DET mechanism is proposed. Then, the event-triggered HJB equation is solved utilizing the learning method based on ADP. Simultaneously, the weights of the neural network (NN) are optimized using a gradient descent algorithm and experience replay (ER) techniques. By employing ER technology, we have eliminated the system's requirement for continuous excitation. Furthermore, through theoretical analysis, we have demonstrated the uniform ultimate boundedness (UUB) of the system states and neural network weights, and excluded Zeno behavior. Finally, the effectiveness of the proposed method is validated by using a spring-pendulum example.