Adaptive quantised control of uncertain non‐linear systems with state constraints and time‐varying delays

Abstract

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.