Higher order sliding mode control based on optimal linear quadratic control

In this paper, a new robust higher order sliding mode controller for uncertain minimum-phase nonlinear systems is designed. The problem is solved in three steps: a) the higher order sliding mode problem is formulated in input-output term; b) the problem is viewed in uncertain linear context by considering uncertain nonlinear functions as bounded non structured parametric uncertainties; c) following the optimal sliding-mode design for linear systems, a time varying manifold is designed through the minimization of a quadratic cost function over a finite time interval with a fixed final state. The control law which engenders the sliding on the time varying surface allows the establishment of an r^th order sliding mode. The designed controller is well-adapted to practical implementation and all the features of linear quadratic control can be used to synthesize the controller´s gain.