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

Control and state estimation procedures need to be robust against imprecisely known parameters, uncertainty in initial conditions, and external disturbances. Interval methods and other set-based techniques form the basis for the implementation of powerful approaches that can be used to identify parameters of dynamic system models in the presence of the aforementioned types of uncertainty. Moreover, they are applicable to a verified feasibility and stability analysis of controllers and state estimators. In addition to these approaches which are typically used offline for analysis of system models designed with classical floating point procedures, interval and set-based methods have also been developed in recent years, which allow to directly solve the associated design tasks and to implement reliable techniques that are applicable online, i.e., during system operation. The latter approaches include set-based model predictive control, online parameter adaptation techniques for nonlinear variable-structure and backstepping controllers, interval observers, and fault diagnosis techniques. This paper provides an overview of the methodological background and reviews numerous practical applications for which interval and other set-valued approaches have been employed successfully.