Continuous output‐feedback finite‐time control for a class of second‐order nonlinear systems with disturbances

Abstract

Summary In this paper, a solution to the continuous output‐feedback finite‐time control problem is proposed for a class of second‐order MIMO nonlinear systems with disturbances. First, a continuous finite‐time controller is designed to stabilize system states at equilibrium points in finite time, which is proven correct by a constructive Lyapunov function. Next, because only the measured output is available for feedback, a continuous nonlinear observer is presented to reconstruct the total states in finite time and estimate the unknown disturbances. Then, a continuous output‐feedback finite‐time controller is proposed to track the desired trajectory accurately or alternatively converge to an arbitrarily small region in finite time. Finally, proposed methods are applied to robotic manipulators, and simulations are given to illustrate the applicability of the proposed control approach. Copyright © 2015 John Wiley & Sons, Ltd.

Free-chattering robust finite time tracking for connected double integrator nonlinear systems

“…A general form for a chain of connected double integrator nonlinear systems subject to bounded uncertainties and disturbances is given by (8). In fact, model (8) represents double integrator nonlinear systems having interactions with each other.…”

“…In fact, model (8) represents double integrator nonlinear systems having interactions with each other. (8) and…”

“…The finite time stabilizers have been exploited in many practical applications in the recent years [3]. The survey of relevant papers reveals that three main approaches containing direct Lyapunov method [4][5][6][7][8][9], geometric homogeneity based method [10,11], and terminal sliding mode control (TSMC) technique [12][13][14][15] have been proposed and exploited for finite time stabilization of different classes of nonlinear systems.…”

“…Most of the finite time control techniques based on this approach [4][5][6][7][8][9], have several shortcomings. As the first deficiency, these techniques are mostly applicable on special classes of single input-single output (SISO) nonlinear systems including double integrator system [2,5,8] and canonical high order nonlinear system [6,7,9]. As the second weakness, most of these methods have been designed the finite time control laws without considering uncertainties and external disturbances.…”

“…As the second weakness, most of these methods have been designed the finite time control laws without considering uncertainties and external disturbances. As the third shortcoming, finding an appropriate Lyapunov candidate function is a time-consuming, complex, and difficult process [4][5][6][7][8].…”