Higher Order Sliding Mode Control Based Finite-time Constrained Stabilization

This paper addresses the problem of finite-time constrained stabilization of nonlinear systems with matched uncertainties. The constrained stabilization refers to designing of higher order finite-time control law such that the output σ of the system remains in some prescribed range, i.e., σε(-c,c), c is chosen as constant while all the higher derivative of the output σ satisfy, ˙σ=⋅⋅⋅==˙σn=0 in some finite interval of time. The above problem of relative degree n w.r.t. output σ cannot be directly solved by using higher order sliding mode control. Therefore, a new coordinate transformation has been proposed in this paper to reduce the relative degree of such systems by one in some pre-specified range of space. However, in the remaining space, the problem of stabilization can be solved by higher order sliding mode controller having the same relative degree. The segway application is considered as an example to demonstrate the efficacy of the proposed theory.