Sliding mode control method having terminal convergence in finite time

摘要

Nonlinear control method is provided for a closed-loop trajectory in a control system of the form x=ƒ(x)+u through a sliding surface, s, chosen such that s=e+&lgr;e=, where e is the trajectory, and &lgr; is a positive constant using a control law of the form ##EQU1## which exploits terminal attractors of the form ##EQU2## where &agr; is a constant greater than zero, &bgr;.sub.n, &bgr;.sub.d =(2i+1), where i belongs to the set of positive integers chosen for &bgr;. sub.n and &bgr; .sub.d, and &bgr;.sub.d &bgr;.sub.n for convergence in finite time. For a system in which an initial S.sub.i is zero, a control law is used of the form ##EQU3## which yields a control equation ##EQU4## where . delta..sub.n, &dgr;.sub.d =(2i+1), wherein i belongs to the set of positive integers chosen for &dgr;.sub.n and &dgr;.sub.d, and &dgr;. sub.d &dgr;.sub.n for retaining convergence in finite time.