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This paper studies an adaptive neural network (NN) tracking control method for a class of uncertain nonlinear strict-feedback systems with time-varying full-state constraints. As we all know, the states are inevitably constrained in the actual systems because of the safety and performance factors. The main contributions of this paper are that: 1) in order to ensure that the states do not violate the asymmetric time-varying constraint regions, an adaptive NN controller is constructed by introducing the asymmetric time-varying barrier Lyapunov function (TVBLF) and 2) the amount of the learning parameters is reduced by introducing a TVBLF at each step of the backstepping. Based on the Lyapunov stability analysis, it can be proven that all the signals in the closed-loop system are the semiglobal ultimately uniformly bounded and the time-varying full-state constraints are never violated. Finally, a numerical simulation is given, and the effectiveness of this adaptive control method can be verified. [ABSTRACT FROM AUTHOR]

In this paper, an optimal control algorithm is designed for uncertain nonlinear systems in discrete-time, which are in nonaffine form and with unknown dead-zone. The main contributions of this paper are that an optimal control algorithm is for the first time framed in this paper for nonlinear systems with nonaffine dead-zone, and the adaptive parameter law for dead-zone is calculated by using the gradient rules. The mean value theory is employed to deal with the nonaffine dead-zone input and the implicit function theory based on reinforcement learning is appropriately introduced to find an unknown ideal controller which is approximated by using the action network. Other neural networks are taken as the critic networks to approximate the strategic utility functions. Based on the Lyapunov stability analysis theory, we can prove the stability of systems, i.e., the optimal control laws can guarantee that all the signals in the closed-loop system are bounded and the tracking errors are converged to a small compact set. Finally, two simulation examples demonstrate the effectiveness of the design algorithm. [ABSTRACT FROM AUTHOR]

Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]