Positive Definiteness and Stability of Interval Matrices
SIAM Journal on Matrix Analysis and Applications
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Nonlinear Control Systems
Computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation
VALENCIA-IVP: A Comparison with Other Initial Value Problem Solvers
SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
Interval Techniques for Design of Optimal and Robust Control Strategies
SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
Reliable Implementation of Real Number Algorithms: Theory and Practice
Numerical Validation in Current Hardware Architectures
A Novel Interval Arithmetic Approach for Solving Differential-Algebraic Equations with ValEncIA-IVP
International Journal of Applied Mathematics and Computer Science - Verified Methods: Applications in Medicine and Engineering
International Journal of Applied Mathematics and Computer Science - Verified Methods: Applications in Medicine and Engineering
International Journal of Applied Mathematics and Computer Science - Verified Methods: Applications in Medicine and Engineering
Journal of Computer and Systems Sciences International
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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.