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Control and state estimation procedures need to be robust against impreciselyknown parameters, uncertainty in initial conditions, and external disturbances.Interval methods and other set-based techniques form the basis for theimplementation of powerful approaches that can be used to identify parametersof dynamic system models in the presence of the aforementioned types ofuncertainty. Moreover, they are applicable to a verified feasibility andstability analysis of controllers and state estimators. In addition to theseoffline approaches for analysis, interval and set-based methods have also beendeveloped in recent years, which allow to solve the associated design tasks andto implement reliable techniques that are applicable online. The latterapproaches include set-based model-predictive control, online parameteradaptation techniques for nonlinear variable-structure and backsteppingcontrollers, interval observers, and fault diagnosis techniques. This paperprovides an overview of the methodological background and reviews numerouspractical applications for which interval and other set-valued approaches havebeen employed successfully.

Offline and Online Use of Interval and Set-Based Approaches for Control  and State Estimation: A Review of Methodological Approaches and Their  Application