An interval arithmetic approach for discrete time non-smooth uncertain systems with application to an anti-locking system

In this paper, a global optimization technique using interval analysis applied to the simulation of an anti-locking control system with possible sensor tolerances is presented. The anti-locking system and the vehicle are described as an uncertain discrete time system with nonsmooth nonlinearities. Sensor tolerances can be modeled in a natural way by means of interval arithmetics which helps to achieve reliable results in the simulation. However, a simulation approach using merely natural interval extensions leads to overestimations rendering the result useless. Therefore, we employ a global optimization algorithm which allows the inclusion of the actual dynamic system behavior with a predefined and guaranteed overestimation limit. All algorithms are implemented in MATLAB.