This article presents an adaptive event-triggered dynamic surface control for pure-feedback systems with unknown input time-delay and quantized input.Event-triggered and quantized input are both of discontinuity, which will make their integral item nondifferentiable and the integral mean value theorem cannot be applied. In order to solve the design problem of input delay system with discontinuous input, an auxiliary tracking error, an auxiliary system and Lyapunov-Krasovskii functionals are well designed, which can effectively deal with the input delay and allows the time delay to be unknown. Moreover, the improved event-triggered quantized control can greatly reduce the amount of calculation of traditional quantized control and avoid unnecessary network access. The stability analysis shows that all signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the output constraint is not violated. A simulation example of practical control system is conducted to demonstrate the effectiveness of proposed control protocol.

This paper proposes an adaptive neural-network control design for a class of output-feedback nonlinear systems with input delay and unmodeled dynamics under the condition of an output constraint. A coordinate transformation with an input integral term and a Nussbaum function are combined to solve the problem of the input possessing both time delay and unknown control gain. By utilizing a barrier Lyapunov function and designing tuning functions, the adjustment of multiparameters is handled with a single adaptive law. The uncertainty of the system is approximated by dynamic signal and radial basis function neural networks (RBFNNs). Based on Lyapunov stability theory, an adaptive tracking control scheme is developed to guarantee all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded, and the output constraint is not violated. KEYWORDSinput delay, input integral term, output constraint, output feedback control, unmodeled dynamics 972

This study proposes an adaptive quantised fuzzy control strategy for a class of non-linear systems with time-varying delay, state constraints, and input unmodelled dynamics. Design difficulties focus on the fact that the input-quantised actuator possesses both unknown control gain and non-linear input unmodelled dynamics, and all the states are required to satisfy state constraints. To remove these obstacles, integral barrier Lyapunov functions combined with Nussbaum functions are designed to deal with the unknown control gains and state constraints, and a quantised controller combined with the normalised signal is developed to tackle the quantised input and input unmodelled dynamics. To avoid the chattering and reduce the quantisation error in a wide scope of the control volume, a novel logarithmic uniform hysteresis quantiser is employed, which has both advantages of the existing uniform quantiser and hysteresis quantiser. Two simulation examples of practical control systems are conducted to demonstrate the effectiveness of the proposed control protocol.

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