A Min-Max Approach to Set Point Stabilisation for a Class of Drift-Free Systems

Abstract

A new type of feedback strategy, for stabilisation to a point, for a class of drift-free systems, is presented. The approach is based on the construction of a cost function which is a maximum of a finite number of component functions. The stabilising control is defined in terms of a set of nested, discrete processes, whose task is to minimise the non-differentiable cost. Repeated application of these processes yields a sequence of points along the controlled trajectory. While the corresponding sequence of cost values is decreasing monotonically, the cost, as a continuous function of time, decays along the controlled system trajectories only asymptotically. Stabilising properties of the resulting feedback strategy are discussed, and its effectiveness and generality are confirmed by examples. Many well-known non-holonomic systems are members of the class of systems considered, and simulations show that convergence to set points is very fast.