Real-Time Application of Interval Methods for Robust Control of Dynamical Systems

The influence of bounded uncertainties in parameters and initial conditions of dynamical systems can be analyzed efficiently with the help of interval methods. In engineering, interval arithmetic tools are usually applied offline to verify, analyze, and design dynamical systems. In this contribution, we describe interval-based techniques for online model-predictive control of uncertain continuous-time dynamical systems. These techniques employ verified solution algorithms for sets of differential-algebraic equations which are implemented in the solver ValEncIA-IVP. Using ValEncIA-IVP, we derive procedures for feedforward control, trajectory planning, and guaranteed state and parameter estimation. The real-time applicability of these procedures is demonstrated by experimental results for a control-oriented, finite-dimensional model of a distributed heating system.