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

In this paper, we give an overview of interval arithmetic techniques for both the offline and online verification of robust control strategies. Part 1 of the paper mainly addresses basic interval techniques focusing on offline applications while the focus of Part 2 is their online application. For offline applications, we aim at computing the sets of all admissible control strategies. Admissibility is defined in terms of constraints on, for example, the trajectories of the state variables, the range of control inputs, and the frequency response or eigenvalue regions of linear closed-loop control systems. In contrast to the offline application, the foremost requirement for online applications is the verification of the admissibility of at least one control strategy and to determine a suitable approximate solution to a control task which is both feasible and optimal in some specified sense. In addition to open-loop as well as closed-loop control, the problem of state and parameter estimation is addressed.