An Improved N-Step Value Gradient Learning Adaptive Dynamic Programming Algorithm for Online Learning

Convergence and Stability of Optimal Regulation via Generalized N-Step Value Gradient Learning

In this article, the generalized N -step value gradient learning (GNSVGL) algorithm, which takes a long-term prediction parameter λ into account, is developed for infinite horizon discounted near-optimal control of discrete-time nonlinear systems. The proposed GNSVGL algorithm can accelerate the learning process of adaptive dynamic programming (ADP) and has a better performance by learning from more than one future reward. Compared with the traditional N -step value gradient learning (NSVGL) algorithm with zero initial functions, the proposed GNSVGL algorithm is initialized with positive definite functions. Considering different initial cost functions, the convergence analysis of the value-iteration-based algorithm is provided. The stability condition for the iterative control policy is established to determine the value of the iteration index, under which the control law can make the system asymptotically stable. Under such a condition, if the system is asymptotically stable at the current iteration, then the iterative control laws after this step are guaranteed to be stabilizing. Two critic neural networks and one action network are constructed to approximate the one-return costate function, the λ -return costate function, and the control law, respectively. It is emphasized that one-return and λ -return critic networks are combined to train the action neural network. Finally, via conducting simulation studies and comparisons, the superiority of the developed algorithm is confirmed.

Decentralized Control for Large-Scale Systems With Actuator Faults and External Disturbances: A Data-Driven Method

This article investigates optimal control for a class of large-scale systems using a data-driven method. The existing control methods for large-scale systems in this context separately consider disturbances, actuator faults, and uncertainties. In this article, we build on such methods by proposing an architecture that accommodates simultaneous consideration of all of these effects, and an optimization index is designed for the control problem. This diversifies the class of large-scale systems amenable to optimal control. We first establish a min-max optimization index based on the zero-sum differential game theory. Then, by integrating all the Nash equilibrium solutions of the isolated subsystems, the decentralized zero-sum differential game strategy is obtained to stabilize the large-scale system. Meanwhile, by designing adaptive parameters, the impact of actuator failure on the system performance is eliminated. Afterward, an adaptive dynamic programming (ADP) method is utilized to learn the solution of the Hamilton-Jacobi-Isaac (HJI) equation, which does not need the prior knowledge of system dynamics. A rigorous stability analysis shows that the proposed controller asymptotically stabilizes the large-scale system. Finally, a multipower system example is adopted to illustrate the effectiveness of the proposed protocols.

Stability and Admissibility Analysis for Zero-Sum Games Under General Value Iteration Formulation

In this article, the general value iteration (GVI) algorithm for discrete-time zero-sum games is investigated. The theoretical analysis focuses on stability properties of the systems and also the admissibility properties of the iterative policy pair. A new criterion is established to determine the admissibility of the current policy pair. Besides, based on the admissibility criterion, the improved GVI algorithm toward zero-sum games is developed to guarantee that all iterative policy pairs are admissible if the current policy pair satisfies the criterion. On the basis of the attraction domain, we demonstrate that the state trajectory will stay in the region using the fixed or the evolving policy pair if the initial state belongs to the domain. It is emphasized that the evolving policy pair can stabilize the controlled system. These theoretical results are applied to linear and nonlinear systems via offline and online critic control design.

Offline and Online Adaptive Critic Control Designs With Stability Guarantee Through Value Iteration

This article is concerned with the stability of the closed-loop system using various control policies generated by value iteration. Some stability properties involving admissibility criteria, the attraction domain, and so forth, are investigated. An offline integrated value iteration (VI) scheme with a stability guarantee is developed by combining the advantages of VI and policy iteration, which is convenient to obtain admissible control policies. Also, based on the concept of attraction domain, an online adaptive dynamic programming algorithm using immature control policies is developed. Remarkably, it is ensured that the state trajectory under the online algorithm converges to the origin. Particularly, for linear systems, the online ADP algorithm with a general scheme possesses more enhanced stability property. The theoretical results reveal that the stability of the linear system can be guaranteed even if the control policy sequence includes finite unstable elements. The numerical results verify the effectiveness of the present algorithms.

Evolving and Incremental Value Iteration Schemes for Nonlinear Discrete-Time Zero-Sum Games

In this article, evolving and incremental value iteration (VI) frameworks are constructed to address the discrete-time zero-sum game problem. First, the evolving scheme means that the closed-loop system is regulated by using the evolving policy pair. During the control stage, we are committed to establishing the stability criterion in order to guarantee the availability of evolving policy pairs. Second, a novel incremental VI algorithm, which takes the historical information of the iterative process into account, is developed to solve the regulation and tracking problems for the nonlinear zero-sum game. Via introducing different incremental factors, it is highlighted that we can adjust the convergence rate of the iterative cost function sequence. Finally, two simulation examples, including linear and nonlinear systems, are conducted to demonstrate the performance and the validity of the proposed evolving and incremental VI schemes.