Interval Techniques for Design of Optimal and Robust Control Strategies

In this paper, an interval arithmetic optimization procedure for both discrete-time and continuous-time systems is presented. Besides computation of control strategies for systems with nominal parameters, robustness requirements for systems with interval bounded uncertainties are considered. Considering these uncertainties, control laws are obtained which directly take into account the influence of disturbances and deviations of system parameters from their nominal values. Compared to Bellman´s discrete dynamic programming, errors resulting from gridding of state and control variable intervals as well as errors due to rounding to nearest grid points are avoided. Furthermore, the influence of time discretization errors is taken into account by validated integration of continuous-time state equations. Optimization results for a simplified model of a mechanical positioning system with switchings between models for both static and sliding friction demonstrate the efficiency of the suggested approach and its applicability to processes with state-dependent switching characteristics.