Maximum-Volume Invariant Ellipsoid Approximating Attraction Domain in Stabilization Problem for Wheeled Robot

Abstract

AbstractThe path following problem for a wheeled robot with constrained control resource is studied. The problem is first reduced to that of stabilizing the zero solution of a system that admits feedback linearization. The attraction domain of the zero solution of the system with the synthesized feedback is approximated by an invariant ellipsoid. To take into account control constraints, an approach based on methods of absolute stability theory is used, in the framework of which construction of an approximating invariant ellipsoid reduces to solving a system of linear matrix inequalities. The problem of finding the best in the sense of volume invariant ellipsoid is posed. It is shown that the desired maximum-volume ellipsoid can be found by solving a standard constrained optimization problem for a function of two variables.