Discontinuous feedback stabilization using guiding functions: the fire truck example

A novel, systematic approach to the construction of feedback control for stabilization of drift free systems is presented. The feedback controls are piece-wise constant and the method relies on the introduction of a set of guiding functions whose sum vanishes only at the origin. The guiding functions are not Lyapunov functions, however, a comparison of their values allows us to determine a desired direction of system motion and permits us to construct a sequence of controls such that the sum of the guiding functions decreases in an average sense