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In this paper, we design an adaptive neural network (NN) controller of uncertain ${n}$ -joint robotic systems with time-varying state constraints. By proposing a nonlinear mapping, the robotic systems are transformed into the multiple-input, multiple-output systems. Compared with constant constraints, the time-varying state constraints are more general in the real systems. To overcome the design challenge, the time-varying barrier Lyapunov function is introduced to ensure that the states of the robotic systems are bounded within the predetermined time-varying range. The NN approximations are employed to approximate the uncertain parametric and unknown functions in the robotic systems. Based on the Lyapunov analysis, it can be proved that all signals of robotic systems are bounded; the tracking errors of system output converge on a small neighborhood of zero and the time-varying state constraints are never violated. Finally, a simulation example is performed to demonstrate the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

We investigate state estimation for a class of discrete-time recurrent neural networks with leakage delay and time-varying delay. The design method for the state estimator to estimate the neuron states through available output measurements is given. A novel delay-dependent sufficient condition is obtained for the existence of state estimator such that the estimation error system is globally asymptotically stable. Based a novel double summation inequality and reciprocally convex approach, an improved stability criterion is obtained for the error-state system. Two numerical examples are given to demonstrate the effectiveness of the proposed design methods. The simulation results show that the leakage delay has a destabilizing influence on a neural network system. [ABSTRACT FROM AUTHOR]