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.

Disturbance rejection design for repetitive control system with state delay based on equivalent input disturbance compensation

“…For instance, sliding mode control is an extensively used approach to suppress external disturbances. [11][12][13][14] In Yue and Li, 15 Xia et al, 16 Guan et al, 17 and Yang et al, 18 the adaptive controller is devised to address the unknown disturbances in the delay system by automatically adjusting the control parameters. The methods proposed in the above literatures are to passively suppress the disturbance by enhancing the overall control capabilities of the system, so they are difficult to achieve satisfactory results under strong disturbance or high tracking performance requirements.…”

SODO Based Reinforcement Learning Anti-Disturbance Fault Toler-Ant Control for a Class of Nonlinear Uncertain Systems With Matched and Mismatched Disturbances

“…In [13], taking the matched and mismatched disturbances into consideration, a trajectory linearization control method has been designed for the disturbed nonlinear systems. In [14], for a class of nonlinear systems with time-varying de-lay and state constraints, a novel quantitative adaptive control strategy has been established. In [15], for the miniature high-precision nonlinear system, a proportional integral-differential control method based on the dynamic hysteresis nonlinear model and inverse model has been pro-posed.…”

State prediction based control schemes for nonlinear systems with input delay and external disturbance

“…For various control issues of nonlinear systems with input delay, some results have been reported [8]- [14]. In [8], an adaptive quantised control method was proposed to tackle a class of uncertain nonlinear systems with state constraints and time-varying delays. Based on Laplace transformation and Taylor formula, a Pade approximation was used to transform time-delayed system into the delay-free one [13].…”

“…For various control issues of nonlinear systems with input delay, some results have been reported [8]- [14]. In [8], an adaptive quantised control method was proposed to tackle a class of uncertain nonlinear systems with state constraints and time-varying delays.…”