Towards the Development of an Interval Arithmetic Environment for Validated Computer-Aided Design and Verification of Systems in Control Engineering

Abstract

Abstract. In this paper, an overview of the potential use of validated techniques for the analysis and design of controllers for linear and nonlinear dynamical systems with uncertainties is given. In addition to robust pole assignment for linear dynamical systems with parameter uncertainties, mathematical system models and computational techniques are considered in which constraints for both state and control variables are taken into account. For that purpose, the use of interval arithmetic routines for calculation of guaranteed enclosures of the solutions of sets of ordinary differential equations and for the calculation of validated sensitivity measures of state variables with respect to parameter variations are discussed. Simulation results as well as further steps towards the development of a general-purpose interval arithmetic framework for the design and verification of systems in control engineering are summarized.

Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems

“…At the implementation stage, it provides result verification for the kinematics and dynamics of various mechanical systems. Finally, the use of algorithmic differentiation and newly developed methods for sensitivity analysis (Rauh et al, 2009) identifies critical parameters and in this way makes the validation stage easier.…”

Detecting Unsolvability of Interval Linear Systems

“…One of the methods is the interval version of Gaussian elimination. We are not going to mention the verified LU decomposition, since the method is mathematically similar to Gaussian elimination (for references to verified LU decomposition see e.g., [13,19]). More detailed description of the interval Gaussian elimination can be found in [3] or [5].…”