Conference article

Defining and Solving Hybrid Optimal Control Problems with Higher Index DAEs

Radoslaw Pytlak
Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland

Damian Suski
Institute of Automatic Control and Robotics, Warsaw University of Technology, Poland

Tomasz Tarnawski
Department of Quantitative Methods and Information Technology, Kozminski University, Poland

Tomasz Zawadzki
Research and Academic Computer Network (NASK), Poland

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Published in: Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017

Linköping Electronic Conference Proceedings 132:28, p. 265-273

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Published: 2017-07-04

ISBN: 978-91-7685-575-1

ISSN: 1650-3686 (print), 1650-3740 (online)


The paper deals with optimal control problems defined for hybrid systems described by higher index DAEs. We present a prototype solution that supports the whole process from defining such problem to solving it and presenting results. Problem’s definition is done with Dynamic Optimization Modeling Language (DOML) which is based directly on Modelica. The proposed numerical procedure for solving the problems of interest has the following features: 1) it is based on the appropriately defined adjoint equations formulated for the discretized equations being the result of the numerical integration of system equations by an implicit Runge–Kutta method; 2) initialization for higher index DAEs is performed with the help of Pantelides’ algorithm; 3) it does not require the system to be transformed to ODEs (through differentiation of some algebraic equations).

The paper presents numerical examples related to hybrid systems described by index three DAEs, showing the validity of the proposed approach. All software components needed to carry out the computations, i.e. the code editor, compiler, numerical libraries and GUI for presenting results are prepared as parts of a combined platform: Interactive Dynamic Optimization Server (IDOS).


hybrid systems, optimal control problems, higher index DAEs


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