Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics. II

Abstract

In this paper, we give an overview of interval arithmetic techniques for both the offline and online verification of robust control and observer strategies. In Part 1 of this paper, we have introduced basic interval arithmetic techniques focusing on offline applications while we deal with their online application in this Part 2. In contrast to the offline tasks considered in Part 1, in which guaranteed enclosures of all admissible solutions to a specific control problem are computed, real-time requirements have to be considered in online tasks. This means that we have to ensure to find a guaranteed admissible solution within a limited computing time. Therefore, the adapted goal in the online design of controllers and observers must be to determine at least one solution, and not necessarily all, such that feasibility under the influence of uncertainties is proven. After a summary of the basic computational procedures, first experimental results for the real-time application of interval tools for feedforward control and disturbance estimation are presented for the temperature control of a distributed heating system.