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 establishes an off-policy integral reinforcement learning (IRL) method to solve nonlinear continuous-time (CT) nonzero-sum (NZS) games with unknown system dynamics. The IRL algorithm is presented to obtain the iterative control and off-policy learning is used to allow the dynamics to be completely unknown. Off-policy IRL is designed to do policy evaluation and policy improvement in the policy iteration algorithm. Critic and action networks are used to obtain the performance index and control for each player. The gradient descent algorithm makes the update of critic and action weights simultaneously. The convergence analysis of the weights is given. The asymptotic stability of the closed-loop system and the existence of Nash equilibrium are proved. The simulation study demonstrates the effectiveness of the developed method for nonlinear CT NZS games with unknown system dynamics.

In this paper, a novel adaptive dynamic programming (ADP) algorithm, called “iterative zero-sum ADP algorithm,” is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method.

In this paper, convergence properties are established for the newly developed discrete-time local value iteration adaptive dynamic programming (ADP) algorithm. The present local iterative ADP algorithm permits an arbitrary positive semidefinite function to initialize the algorithm. Employing a state-dependent learning rate function, for the first time, the iterative value function and iterative control law can be updated in a subset of the state space instead of the whole state space, which effectively relaxes the computational burden. A new analysis method for the convergence property is developed to prove that the iterative value functions will converge to the optimum under some mild constraints. Monotonicity of the local value iteration ADP algorithm is presented, which shows that under some special conditions of the initial value function and the learning rate function, the iterative value function can monotonically converge to the optimum. Finally, three simulation examples and comparisons are given to illustrate the performance of the developed algorithm.

This paper utilizes parallel control to investigate the problem of event-triggered deep reinforcement learning and develops an event-triggered deep Q-network (ETDQN) for decision-making of autonomous driving, without training an explicit triggering condition . Based on the framework of parallel control, the developed ETDQN incorporates information of actions into the feedback and constructs a dynamic control policy. First, in the realization of the dynamic control policy, we integrate the current state and the previous action to construct the augmented state as well as the augmented Markov decision process. Meanwhile, it is shown theoretically that the goal of the developed dynamic control policy is to learn the variation rate of the action. The augmented state contains information of the current state and the previous action, which enables the developed ETDQN to directly design the immediate reward considering communication loss. Then, based on dueling double deep Q-network (dueling DDQN), we establish the augmented action-value, value, and advantage functions to directly learn the optimal event-triggered decision-making policy of autonomous driving without an explicit triggering condition. It is worth noticing that the developed ETDQN applies to various deep Q-networks (DQNs). Empirical results demonstrate that, in event-triggered control, the developed ETDQN outperforms dueling DDQN and reduces communication loss effectively. Source code of this paper is available at: https://github.com/lujingweihh/Event-triggered-deep-Q-network https://github.com/lujingweihh/Event-triggered-deep-Q-network.

In this article, an online adaptive optimal control algorithm based on adaptive dynamic programming is developed to solve the multiplayer nonzero-sum game (MP-NZSG) for discrete-time unknown nonlinear systems. First, a model-free coupled globalized dual-heuristic dynamic programming (GDHP) structure is designed to solve the MP-NZSG problem, in which there is no model network or identifier. Second, in order to relax the requirement of systems dynamics, an online adaptive learning algorithm is developed to solve the Hamilton-Jacobi equation using the system states of two adjacent time steps. Third, a series of critic networks and action networks are used to approximate value functions and optimal policies for all players. All the neural network (NN) weights are updated online based on real-time system states. Fourth, the uniformly ultimate boundedness analysis of the NN approximation errors is proved based on the Lyapunov approach. Finally, simulation results are given to demonstrate the effectiveness of the developed scheme.