Control and estimation of hybrid systems with mathematical optimization

Many practical systems consist of both continuous valued and discrete valued components. The term hybrid systems has been used to describe models, where both continuous and discrete aspects are considered within the same framework. This thesis presents theoretical results and experiments about the Mixed Logic Dynamical systems modelling framework for hybrid systems, introduced by Bemporad and Morari (1999a). The framework allows to model systems comprising interacting propositional logic, continuous dynamics and constraints. Besides their broad modelling capabilities, Mixed Logic Dynamical systems allow to systematically formulate and solve various analysis and synthesis problems using mathematical optimization techniques. The contributions of this thesis are: • We present systematic methods for the efficient and automatized derivation of models. Classical analytical approaches for the modelling of system components are compared to a geometrical approach. The proposed methods reduce the number of variables in the model. • Two practical systems are modelled in the Mixed Logic Dynamical systems framework: a three tank laboratory system and the outflow units of a hydroelectric power plant. Both systems illustrate the typical modeling capabilities of Mixed Logic Dynamical systems.

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