Second-Order Sliding Mode Control for Nonlinear Uncertain Systems Bounded by Positive Functions

Abstract

This paper considers the second-order sliding (2-sliding) mode control design problem for nonlinear systems with uncertainties bounded by positive functions. Two different 2-sliding mode control algorithms are proposed, including a discontinuous one and a quasi-continuous one. The discontinuous algorithm is built based upon Lyapunov method, and the global finite-time Lyapunov stability rather than global finite-time convergence is established for the resulting closed-loop system by using the modified adding a power integrator technique. On this basis, a quasi-continuous 2-sliding mode algorithm is further developed, and the chattering problem can be considerably reduced.Simulation results show that the control strategies proposed in this paper are effective.Index Terms-Sliding mode control, finite-time stability, adding a power integrator.

Finite-time tracking control of multiple nonholonomic mobile robots with external disturbances

“…In this section, we will solve the finite-time tracking control problem for system (4). In other word, we will design control laws u ji (j = 1, 2, i ∈ Γ) such that system (11) can converge to zero in finite time.…”

“…On the other hand, stabilizer for nominal system can be designed. Recently DOBC approach as a robust control approach has widely found its applications in mechanical and electrical, dynamics and structure control areas [2,3,4,10,32]. A characteristic of DOBC is having simple structure, combining with different control laws according to different desire of control performance and very easily setting on line and engineering realization.…”

Advances in Disturbance/Uncertainty Estimation and Attenuation [Guest editors' introduction]

“…The work [14], authored by Ding et al, considers the second-order sliding mode control design for nonlienar systems with uncertainties bounded by positive functions. Two different second-order control algorithms are proposed including a discontinuous one and a quasi-continuous one.…”

A New Integral Second-Order Terminal Sliding Mode Control with Time Delay Estimation for an Exoskeleton Robot with Dynamics Uncertainties

“…Nevertheless, the second-time derivative of the sliding surface might produce instability of the system, a risk that the nonlinear uncertainties and external disturbances amplify. Recently, Second Order Terminal Sliding mode Control (SOTSMC) was introduced to provide a great control performance to deal with a chattering phenomenon and provide a finite time convergence [9,10]. So, to the best of our knowledge, no SOTSMC with integral action has been proposed before to solve the mentioned problems.…”