Continuous uniformly finite time exact disturbance observer based control for fixed-time stabilization of nonlinear systems with mismatched disturbances

Abstract

This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory, continuous fixed-time stable state feedback controller and Lyapunov functions are constructed to achieve global fixed-time system stabilization. The proposed control method extends the existing fixed-time stable control results to high order nonlinear systems with mismatched disturbances and achieves global fixed-time system stabilization. Besides, the proposed control scheme improves the disturbance rejection performance and achieves performance recovery of nominal system. Simulation results are provided to show the effectiveness, the superiority and the applicability of the proposed control scheme.

Robust adaptive finite-time tracking control of uncertain mechanical systems with input saturation and deadzone

“…However, in order to realize bounded time stabilization, the control laws of fixed-time control schemes are usually more complex than those of finite-time (non-fixed-time) control schemes. Unlike the results in Ni et al (2016, 2017a,b), model uncertainties and input constraints are considered in this paper, and thus the proposed results cannot be directly extended to the case of fixed-time control. In the future, the fixed-time control of system (1) with uncertainties and input constraints will be an important research issue.…”

“…From the analysis of proof procedure, we can see that the convergence time T of SGFTUUB stabilization is finite and dependent on the state value X ( t m ) . In recent works (Ni et al, 2016, 2017a,b), a special finite-time control problem called ‘fixed-time control’ was investigated. The convergence time of fixed-time control is independent of initial conditions and bounded by a constant.…”

Continuous fixed-time nonsingular terminal sliding mode control of second-order nonlinear systems with matched and mismatched disturbances

“…Therefore, during the recent years, only the following papers have been published in this regard. Ni and Liu [29] have firstly introduced a uniformly finite-time exact disturbance observer which is reconciliation between uniform finite-time high-order sliding mode differentiator of [30] and finite-time disturbance observer of [31]. Then, they have proposed a fixed-time observer-based state-feedback controller for stabilization of high-order nonlinear systems with mismatched and matched disturbances.…”

Event-Triggered Adaptive Control for Prescribed Performance Tracking of Constrained Uncertain Nonlinear Systems

“…In recent years, the output tracking problem for uncertain nonlinear systems has attracted much attention in the control theory community. Many modern nonlinear control techniques have been employed to handle this problem, such as sliding mode control [1]- [3], the observed-based control [3], [4], the dynamic surface control [5], [6], and so on. A main limitation in these works is that the states of the uncertain nonlinear systems are compelled to be unconstrained.…”