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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]

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]