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In this paper, a novel adaptive critic control method is designed to solve an optimal H ∞ tracking control problem for continuous nonlinear systems with nonzero equilibrium based on adaptive dynamic programming (ADP). To guarantee the finiteness of a cost function, traditional methods generally assume that the controlled system has a zero equilibrium point, which is not true in practical systems. In order to overcome such obstacle and realize H ∞ optimal tracking control, this paper proposes a novel cost function design with respect to disturbance, tracking error and the derivative of tracking error. Based on the designed cost function, the H ∞ control problem is formulated as two-player zero-sum differential games, and then a policy iteration (PI) algorithm is proposed to solve the corresponding Hamilton–Jacobi–Isaacs (HJI) equation. In order to obtain the online solution to the HJI equation, a single-critic neural network structure based on PI algorithm is established to learn the optimal control policy and the worst-case disturbance law. It is worth mentioning that the proposed adaptive critic control method can simplify the controller design process when the equilibrium of the systems is not zero. Finally, simulations are conducted to evaluate the tracking performance of the proposed control methods. [ABSTRACT FROM AUTHOR]

In this paper, the guidance system with unknown dynamics is modeled as a partially unknown zero-sum differential game system. Then, a periodic event-triggered optimal control algorithm is designed to interception target under a plug-n-play framework. To realize this algorithm, generalized fuzzy hyperbolic models are employed to construct the identifier-critic structure, where the online identifier is used to estimate unknown dynamics, meanwhile, the generalized fuzzy hyperbolic models-based critic network is utilized to approximate the cost function. Note that plug-n-play framework lets both the designed identifier and critic network work simultaneously, in other words, the prior system information is no longer required, which simplifies the network structure. Using the Lyapunov function method, the approximate optimal control strategy and corresponding weight updating laws are derived to guarantee that the closed-loop system and weight approximation errors are uniformly ultimately bounded, where an additional function is added to weight updating laws to release the requirement for admissible initial control. Finally, to compare the intercept effects and the utilization ratio of communication resources of the periodic event-triggered control algorithm and the common adaptive dynamic programming algorithm, the missile interception system is introduced as an example. • The guidance system with unknown dynamics is modeled as a partially unknown zero-sum differential game system. Then, the event-based optimal control strategy is designed to improve the utilization of data transmissions. • A GFHM-based identifier is proposed under a plug-n-play framework to approximate unknown nonlinear functions and eliminate the priori identification process. • This paper proposes the fuzzy ADP approach to design the optimal controller, where the single critic network is adopted to approximate the optimal performance index by using GFHMs. [ABSTRACT FROM AUTHOR]

In this paper, an adjustable Q-learning scheme is developed to solve the discrete-time nonlinear zero-sum game problem, which can accelerate the convergence rate of the iterative Q-function sequence. First, the monotonicity and convergence of the iterative Q-function sequence are analyzed under some conditions. Moreover, by employing neural networks, the model-free tracking control problem can be overcome for zero-sum games. Second, two practical algorithms are designed to guarantee the convergence with accelerated learning. In one algorithm, an adjustable acceleration phase is added to the iteration process of Q-learning, which can be adaptively terminated with convergence guarantee. In another algorithm, a novel acceleration function is developed, which can adjust the relaxation factor to ensure the convergence. Finally, through a simulation example with the practical physical background, the fantastic performance of the developed algorithm is demonstrated with neural networks. [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]

The paper addresses the problem of fault tolerant control (FTC) for reentry vehicles (RV) subject to actuator fault and perturbation. In contrast to the majority of papers assuming bounded and exogenous actuator fault effect, the adaptive dynamic programming (ADP) control algorithm has been considered here to tackle with the dependence of closed-loop states induced by the setup of an active FTC strategy. By this way, the FTC problem formulation takes theoretically into account the fact that an actuator fault can destabilize a closed-loop. First, the FTC problem in attitude tracking is transformed into an error-optimal control problem. Next, a cost function based on zero-sum game theory is considered to achieve tracking under the joint influence of state-dependent actuator faults and perturbations. Lyapunov theory has been next used to prove the stability of FTC architecture and the network weight convergence. Benefits of proposed ADP-FTC algorithm is finally highlighted on a numerical benchmark of RV. [ABSTRACT FROM AUTHOR]

This paper considers a new class of deterministic finite-time horizon, two-player, zero-sum differential games (DGs) in which the maximizing player is allowed to take continuous and impulse controls whereas the minimizing player is allowed to take impulse control only. We seek to approximate the value function, and to provide a verification theorem for this class of DGs. By means of dynamic programming principle (DPP) in viscosity solution (VS) framework, we first characterize the value function as the unique VS to the related Hamilton–Jacobi-Bellman–Isaacs (HJBI) double-obstacle equation. Next, we prove that an approximate value function exists, that it is the unique solution to an approximate HJBI double-obstacle equation, and converges locally uniformly towards the value function of each player when the time discretization step goes to zero. Moreover, we provide a verification theorem which characterizes a Nash-equilibrium (NE) for the DG control problem considered. Finally, by applying our results, we derive a new continuous-time portfolio optimization model, and we provide related computational algorithms and numerical results. [ABSTRACT FROM AUTHOR]