In this article, a novel self-triggered approximate optimal neuro-control scheme is presented for nonlinear systems by utilizing adaptive dynamic programming (ADP). According to the Bellman principle of optimality, the cost function of the general nonlinear system is approximated by building a critic neural network with a nested updating weight vector. Thus, the Hamilton–Jacobi–Bellman equation is solved to indirectly obtain the approximate optimal neuro-control input. In order to reduce the computation, the communication bandwidth, and the energy consumption, an appropriate self-triggering condition is designed as an alternative way to predict the updating time instants of the approximate optimal neuro-control policy. On the basis of Lyapunov’s direct method, the stability of the closed-loop nonlinear system is analyzed and guaranteed to be uniformly ultimately bounded. Simulation results of two practical systems illustrate the present ADP-based self-triggered approximate optimal neuro-control scheme to be reasonable and effective.

In order to address zero-sum game problems for discrete-time (DT) nonlinear systems, this article develops a novel event-triggered control (ETC) approach based on the deterministic policy gradient (PG) adaptive dynamic programming (ADP) algorithm. By adopting the input and output data, the proposed ETC method updates the control law and the disturbance law with a gradient descent algorithm. Compared with the conventional PG ADP-based control scheme, the present controller is updated aperiodically to reduce the computational and communication burden. Then, the actor-critic-disturbance framework is adopted to obtain the optimal control law and the worst disturbance law, which guarantee the input-to-state stability of the closed-loop system. Moreover, a novel neural network weight updating law which guarantees the uniform ultimate boundedness of weight estimation errors is provided based on the experience replay technique. Finally, the validity of the present method is verified by simulation of two DT nonlinear systems.

In this article, the event-triggered robust control of unknown multiplayer nonlinear systems with constrained inputs and uncertainties is investigated by using adaptive dynamic programming. To relax the requirement of system dynamics, a neural network-based identifier is constructed by using the system input-output data. Subsequently, by designing a nonquadratic value function, which contains the bounded functions, the system states, and the control inputs of all players, the event-triggered robust stabilization problem is converted into an event-triggered constrained optimal control problem. To obtain the approximate solution of the event-triggered Hamilton–Jacobi (HJ) equation, a critic network for each player is established with a novel weight updating law to relax the persistence of excitation condition based on the experience replay technique. Furthermore, according to the Lyapunov stability theorem, the present event-triggered robust optimal control ensures the multiplayer system to be uniformly ultimately bounded. Finally, two simulation examples are employed to show the effectiveness of the present method.

This article develops a distributed fault-tolerant consensus control (DFTCC) approach for multiagent systems by using adaptive dynamic programming. By establishing a local fault observer, the potential actuator faults of each agent are estimated. Subsequently, the DFTCC problem is transformed into an optimal consensus control problem by designing a novel local value function for each agent which contains the estimated fault, the consensus errors, and the control laws of the local agent and its neighbors. In order to solve the coupled Hamilton–Jacobi–Bellman equation of each agent, a critic-only structure is established to obtain the approximate local optimal consensus control law of each agent. Moreover, by using Lyapunov’s direct method, it is proven that the approximate local optimal consensus control law guarantees the uniform ultimate boundedness of the consensus error of all agents, which means that all following agents with potential actuator faults synchronize to the leader. Finally, two simulation examples are provided to validate the effectiveness of the present DFTCC scheme.

In this article, an event-triggered decentralized integral sliding mode control (ETDISMC) method is investigated for a class of input-constrained nonlinear large-scale systems with actuator failures based on adaptive dynamic programming (ADP). An integral sliding mode control method is developed to maintain the subsystem trajectories on the sliding mode surface, eliminate the effect of actuator failures, and obtain the sliding mode dynamics (SMDs). Then, the control problem is transformed into an optimal control (OC) problem for the nominal form of the SMDs by constructing a modified local value function. To obtain the event-triggered OC law, a critic-only structure is applied to approximate the local optimal value function of the nominal subsystem for solving the event-triggered Hamilton–Jacobi–Bellman equation. An event-triggered ADP control method is developed to decrease the updating frequency of the OC law and to reduce the computational burden. In addition, an experience replay-based weight updating policy is presented to relax the persistence of excitation condition. Furthermore, we prove that the developed method can guarantee the closed-loop system to be asymptotically stable by using Lyapunov’s direct method. Finally, a numerical example and a practical system are employed for simulation to demonstrate the effectiveness of the proposed ETDISMC scheme.