This article reviews the recent development of adaptive dynamic programming (ADP) with applications in control. First, its applications in optimal regulation are introduced, and some skilled and efficient algorithms are presented. Next, the use of ADP to solve game problems, mainly nonzero-sum game problems, is elaborated. It is followed by applications in large-scale systems. Note that although the functions presented in this article are based on continuous-time systems, various applications of ADP in discrete-time systems are also analyzed. Moreover, in each section, not only some existing techniques are discussed, but also possible directions for future work are pointed out. Finally, some overall prospects for the future are given, followed by conclusions of this article. Through a comprehensive and complete investigation of its applications in many existing fields, this article fully demonstrates that the ADP intelligent control method is promising in today’s artificial intelligence era. Furthermore, it also plays a significant role in promoting economic and social development.

This paper develops an event-triggered decentralized tracking control (DTC) approach for modular reconfigurable robots (MRRs) by using adaptive dynamic programming. By establishing a decentralized neural network (NN) observer, which uses local input-output data and desired states of coupling subsystems, the local dynamics of MRR subsystem can be obtained. In order to obtain the DTC, the tracking error subsystem is augmented by the exosystem with the desired trajectory. Based on the event-triggered mechanism and a modified local cost function, the DTC is derived by solving the local Hamilton-Jacobi-Bellman equation via a local critic NN with asymptotically stable structure. The stability of the entire closed-loop MRR system is analyzed by Lyapunov's direct method. The simulation of a two-degree of freedom MRR system ensures that the developed event-triggered DTC scheme is effective.

This article presents a novel reinforcement learning strategy that addresses an optimal stabilizing problem for unknown nonlinear systems subject to uncertain input constraints. The control algorithm is composed of two parts, i.e., online learning optimal control for the nominal system and feedforward neural networks (NNs) compensation for handling uncertain input constraints, which are considered as the saturation nonlinearities. Integrating the input-output data and recurrent NN, a Luenberger observer is established to approximate the unknown system dynamics. For nominal systems without input constraints, the online learning optimal control policy is derived by solving Hamilton-Jacobi-Bellman equation via a critic NN alone. By transforming the uncertain input constraints to saturation nonlinearities, the uncertain input constraints can be compensated by employing a feedforward NN compensator. The convergence of the closed-loop system is guaranteed to be uniformly ultimately bounded by using the Lyapunov stability analysis. Finally, the effectiveness of the developed stabilization scheme is illustrated by simulation studies.

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 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.