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In this paper, we present a Q-learning framework for solving finite-horizon zero-sum game problems involving the H ∞ control of linear system without knowing the dynamics. Research in the past mainly focused on solving problems in infinite horizon with completely measurable state. However, in the practical engineering, the system state is not always directly accessible, and it is difficult to solve the time-varying Riccati equation associated with the finite-horizon setting directly either. The main contribution of the proposed model-free algorithm is to determine the optimal output feedback policies without measurement state in finite-horizon setting. To achieve this goal, we first describe the Q-function caused by finite-horizon problems in the context of state feedback, then we parameterize the Q-functions as input–output vectors functions. Finally, the numerical examples on aircraft dynamics demonstrate the algorithm's efficiency. [ABSTRACT FROM AUTHOR]

In this paper, an event-triggered tracking optimization control method is proposed for nonlinear uncertain systems with H ∞ discounted cost. First, the linearization method using the infinite series expansion theorem is given. And the tracking control design problem is solved by appropriate state augment. Secondly, the zero sum differential game strategy is introduced to address the control design problem of uncertain systems with event-triggered inputs. The actor-critic-disturbance networks framework is used to approximate the optimization of event- triggered controller strategy, optimization costs, and the disturbance strategy, respectively. Due to the consideration of discrete time and continuous time dynamics, we put the impulsive system method to use and choose appropriate Lyapunov functions to prove stability and boundedness, at the same time, there will be no infinite triggering situation. Finally, the effectiveness of the proposed scheme is demonstrated by an example of a practical tractor system with n trailers through simulation compared with another typical design method. [ABSTRACT FROM AUTHOR]

In view of zero-sum differential games, this paper addresses the fault-tolerant tracking control (FTTC) problem for nonlinear systems with multiplicative actuator faults. By augmenting the nominal system, the trajectory tracking problem is transformed into an optimal regulation problem. A fault observer is designed to estimate the multiplicative actuator fault factor. In order to better reflect system performance, a comprehensive performance index function including the trajectory tracking error, the control input, and the multiplicative actuator fault is constructed. By considering the control input and the multiplicative actuator fault as two players in the zero-sum differential game (ZSDG), the FTTC problem is thus transformed into a ZSDG problem. Then, a fault-tolerant control based on ZSDG is designed by solving the Hamilton–Jacobi-Isaacs (HJI) equation. Since the HJI equation is difficult to solve, a critic neural network is constructed to obtain its approximation, which constitutes the Nash equilibrium of the ZSDG. The closed-loop faulty system is guaranteed to be uniformly ultimately bounded via the Lyapunov's direct method. The effectiveness of the developed FTTC method is demonstrated by two simulation examples. [ABSTRACT FROM AUTHOR]

This paper investigates the fuzzy approximation-based optimal consensus control problem for nonlinear multiagent systems with unknown perturbations. By constructing local error dynamics, the considered optimal consensus problem is reformulated as finding Nash-equilibrium solutions to zero-sum games. Then, by using sliding mode control technology and the concept of hierarchical design, a series of control signals are sequentially designed to regulate the consensus error and minimize the local value function. In addition, an identifier-critic architecture is developed by using generalized fuzzy hyperbolic models, where the identifier is employed to relax the requirement for complete system dynamics information, and the hierarchical sliding mode surface-based critic network is applied to approximate optimal control inputs. Finally, A simulation example is presented to illustrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a data-driven approximate neural network (NN) learning scheme is developed to solve the multi-player nonzero-sum (NZS) game problem with completely unknown system dynamics. An augmented NN identifier based on a new parameter estimation algorithm is first established to approximate the completely unknown system dynamics. Then approximated dynamic programming (ADP) with neural networks is constructed to approximate the optimal solutions of the coupled Hamilton-Jacobi equations for each player. The approximated NN value functions are then used to synchronously calculate the optimal control policies for every player. The identifier and ADP NN weights are online updated with the system input-output data based on a novel adaptive law, which could achieve a faster convergence speed. Moreover, the convergence of all NN weights and the stability of the closed-loop system are proved based on the Lyapunov approach. Finally, a dual-driven servo motor system and a three-player nonlinear game system are simulated to verify the feasibility of the developed methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we solve the zero-sum game problems for discrete-time affine nonlinear systems with known dynamics via iterative adaptive dynamic programming algorithm. First, a greedy heuristic dynamic programming iteration algorithm is developed to solve the zero-sum game problems, which can be used to solve the Hamilton–Jacobi–Isaacs equation associated with optimal regulation control problems. The convergence analysis in terms of value function and control policy is provided. To facilitate the implementation of the algorithm, three neural networks are used to approximate the control policy, the disturbance policy, and the value function, respectively. Then, we extend the algorithm to optimal tracking control problems through system transformation. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed scheme. [Copyright &y& Elsevier]