Project number:
LPP-0092-07
Title of the project:
Model Predictive Control of Hybrid Systems
Project type:
APVV Research Projects
Project duration (start):
01.01.2008
Project duration (end):
31.12.2011
Principal investigator:
Miroslav Fikar
Investigators:
Michal Kvasnica

Date

2008-2011

Abstract

This postdoctoral project is concerned with research in the areas of modeling and predictive control of hybrid systems. This class of systems is appealing because it combines the elements of continuous dynamics with the discrete logic. One of the main problems in creation of suitable mathematical models of hybrid systems is their complexity. Therefore it is desirable to create a suitable modeling language, which creates the model automatically. Model Predictive Control (MPC) represents one of the most powerful methods for designing control policies for the class of hybrid systems. This method is based on solving an optimization problem, which takes the system model as well as the system constraints into account. The model used in the optimization problems allows MPC to "see" into the future and to optimize the input commands such that a certain goal is attained. Since MPC requires to solve the optimization problem on-line at each sampling instance, it is traditionally limited to slow processes only. In order to apply MPC to fast plants, the so-called parametric solutions to MPC problems can be obtained. In this approach the given MPC problem is solved for all admissible values of the initial condition. The resulting solution then takes a form of a look-up table, which can be implemented in real-time with low computational effort.

Objectives

The aim of this project is to extend the knowledge about parametric solutions to MPC problems for the class of hybrid systems. This involves, among other tasks, design of new algorithms for synthesis of robust control laws for the class of hybrid systems and new methods for state estimation for such systems. Modeling of compositional hybrid systems will be investigated as well. The goal is to create a software package which provides these algorithms to a broad range of users.

Project Code

LPP-0092-07

Solvers

M. Fikar, M. Kvasnica

Publications

2012

  1. M. KvasnicaM. Fikar: Clipping-Based Complexity Reduction in Explicit MPC. IEEE Transactions on Automatic Control, no. 7, vol. 57, pp. 1878–1883, 2012.

2011

  1. M. Kvasnica: Multi-Parametric Toolbox, In Selected Topics on Constrained and Nonlinear Control. Workbook, STU Bratislava - NTNU Trondheim, pp. 101–170, 2011.
  2. M. KvasnicaM. FikarĽ. Čirka – M. Herceg: Complexity Reduction in Explicit Model Predictive Control, In Selected Topics on Constrained and Nonlinear Control. Textbook, STU Bratislava - NTNU Trondheim, pp. 241–288, 2011.
  3. M. Kvasnica – M. Herceg – Ľ. ČirkaM. Fikar: Explicit Minimum-Time Controllers for Fuzzy Systems. In Selected Topics on Constrained and Nonlinear Control. Preprints, STU Bratislava - NTNU Trondheim, pp. 287–292, 2011.
  4. M. Kvasnica – M. Herceg – Ľ. ČirkaM. Fikar: Robust Explicit Time-Optimal Control of PWA Systems with Parametric Uncertainties. In Selected Topics on Constrained and Nonlinear Control. Preprints, STU Bratislava - NTNU Trondheim, pp. 295–300, 2011.
  5. M. Kvasnica – J. Löfberg – M. Fikar: Stabilizing polynomial approximation of explicit MPC. Automatica, no. 10, vol. 47, pp. 2292–2297, 2011.
  6. M. Kvasnica – I. Rauová – M. Fikar: Real-Time Implementation of Model Predictive Control Using Automatic Code Generation. In Selected Topics on Constrained and Nonlinear Control. Preprints, STU Bratislava - NTNU Trondheim, pp. 311–316, 2011.
  7. M. Kvasnica – I. Rauová – M. Fikar: Separation Functions used in Simplification of Explicit MPC Feedback Laws. In Selected Topics on Constrained and Nonlinear Control. Preprints, STU Bratislava - NTNU Trondheim, pp. 303–308, 2011.
  8. M. Kvasnica – I. Rauová – M. Fikar: Simplification of Explicit MPC Feedback Laws via Separation Functions. In Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011, pp. 5383–5388, 2011.
  9. M. Kvasnica – I. Rauová – Š. Gyurki – M. Fikar: Least Invasive Stabilizing Correction of Arbitrary Controllers, In Selected Topics in Modelling and Control, Editor(s): J. Mikleš, V. Veselý, Slovak University of Technology Press Bratislava, no. 7, pp. 13–15, 2011.
  10. M. Kvasnica – A. Szűcs – M. Fikar: Automated Piecewise Affine Approximation of Nonlinear Systems. In Selected Topics on Constrained and Nonlinear Control. Preprints, STU Bratislava - NTNU Trondheim, pp. 319–326, 2011.
  11. M. Kvasnica – A. Szűcs – M. Fikar: Automatic Derivation of Optimal Piecewise Affine Approximations of Nonlinear Systems. In Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011, pp. 8675–8680, 2011.
  12. M. Paulovič – M. Kvasnica – A. Szűcs – M. Fikar: Safety Verification of Rule-Based Controllers. Editor(s): Fikar, M., Kvasnica. M., In Proceedings of the 18th International Conference on Process Control, Slovak University of Technology in Bratislava, Tatranská Lomnica, Slovakia, pp. 278–283, 2011.
  13. I. Rauová – M. KvasnicaM. Fikar: Separating Functions for Complexity Reduction of Explicit Model Predictive Control. Editor(s): Fikar, M., Kvasnica. M., In Proceedings of the 18th International Conference on Process Control, Slovak University of Technology in Bratislava, Tatranská Lomnica, Slovakia, pp. 427–433, 2011.
  14. A. Szűcs – M. KvasnicaM. Fikar: MATLAB Toolbox for Automatic Approximation of Nonlinear Functions. Editor(s): Fikar, M., Kvasnica. M., In Proceedings of the 18th International Conference on Process Control, Slovak University of Technology in Bratislava, Tatranská Lomnica, Slovakia, pp. 119–124, 2011.
  15. A. Szűcs – M. KvasnicaM. Fikar: Data Compression Techniques for Complexity Reduction in Explicit MPC, In Selected Topics in Modelling and Control, Editor(s): J. Mikleš, V. Veselý, Slovak University of Technology Press Bratislava, no. 7, pp. 18–23, 2011.
  16. A. Szűcs – M. KvasnicaM. Fikar: A Memory-Efficient Representation of Explicit MPC Solutions. In Proceedings of the 50th CDC and ECC, Orlando, Florida, pp. 1916–1921, 2011.

2010

  1. M. KvasnicaM. Fikar: Performance-Lossless Complexity Reduction in Explicit MPC. 2010.
  2. M. KvasnicaM. Fikar: Advances in Real-Time Model Predictive Control. In Proceedings of the 9th International Scientific - Technical Conference Process Control 2010, University of Pardubice, Kouty nad Desnou, Czech Republic, pp. C012a-1–C012a-19, 2010.
  3. M. KvasnicaM. Fikar: Design and Implementation of Model Predictive Control using Multi-Parametric Toolbox and YALMIP. In Proceedings of the 2010 IEEE International Symposium on Computer-Aided Control System Design, Yokohama, Japan, pp. 999–1004, 2010.
  4. M. KvasnicaM. Fikar: Performance-Lossless Complexity Reduction in Explicit MPC. In Proceedings of the 49th IEEE Conference on Decision and Control 2010, pp. 5270–5275, 2010.
  5. M. Kvasnica – M. Herceg – Ľ. ČirkaM. Fikar: Model predictive control of a CSTR: A hybrid modeling approach. Chemical papers, no. 3, vol. 64, pp. 301–309, 2010.
  6. M. Kvasnica – F. J. Christophersen – M. Herceg – M. Fikar: Polynomial Approximation of Closed-Form MPC for Piecewise Affine Systems, In Selected Topics in Modelling and Control, Editor(s): Mikleš, J., Veselý, V., Slovak University of Technology Press, vol. 6, pp. 105–112, 2010.
  7. M. Kvasnica – J. Löfberg – M. Herceg – Ľ. ČirkaM. Fikar: Low-Complexity Polynomial Approximation of Explicit MPC via Linear Programming. In Proceedings of the American Control Conference, Baltimore, USA, pp. 4713–4718, 2010.
  8. M. Kvasnica – I. Rauová – M. Fikar: Real-time Implementation of MPC on Low-cost Hardware. In Proceedings of the 9th International Scientific - Technical Conference Process Control 2010, University of Pardubice, Kouty nad Desnou, Czech Republic, pp. C116a-1–C116a-11, 2010.
  9. M. Kvasnica – I. Rauová – M. Fikar: Automatic Code Generation for Real-Time Implementation of Model Predictive Control. In Proceedings of the 2010 IEEE International Symposium on Computer-Aided Control System Design, Yokohama, Japan, pp. 993–998, 2010.
  10. M. Kvasnica – A. Szűcs – M. Fikar: Optimization-Based Automatic Derivation of Hybrid Models. 2010.

2009

  1. M. Herceg – M. KvasnicaM. Fikar: Parametric Approach to Nonlinear Model Predictive Control, In Nonlinear Model Predictive Control, Editor(s): Magni, L. and Raimondo, D. M. and Allgoewer, F., Springer Berlin / Heidelberg, pp. 381–389, 2009.
  2. M. Herceg – M. KvasnicaM. Fikar: Minimum-time predictive control of a servo engine with deadzone. Control Engineering Practice, no. 60, pp. 1349–1357, 2009.
  3. M. Herceg – M. KvasnicaM. FikarĽ. Čirka: Real-Time Control of a Thermo-Optical Device Using Polynomial Approximation of MPC Scheme. Editor(s): Fikar, M., Kvasnica, M., In Proceedings of the 17th International Conference on Process Control ’09, Slovak University of Technology in Bratislava, Štrbské Pleso, Slovakia, pp. 332–340, 2009.
  4. M. Herceg – M. KvasnicaM. FikarĽ. Čirka: Real-time Control of a Thermo-Optical Device Using Polynomial Approximation of MPC Scheme. AT&P Journal Plus, no. 2, pp. 36–42, 2009.
  5. M. Kvasnica: Real-Time Model Predictive Control via Multi-Parametric Programming: Theory and Tools, VDM Verlag, Saarbruecken, 2009.
  6. M. Kvasnica – M. Herceg – Ľ. ČirkaM. Fikar: Time Optimal Control of Fuzzy Systems: a Parametric Programming Approach. In Proceedings of the 28th IASTED Conference on Modelling, Identification and Control, pp. 640-805.pdf, 2009.
  7. M. Kvasnica – M. Herceg – Ľ. ČirkaM. Fikar: Model Predictive Control of a CSTR. 2009.
  8. M. Kvasnica – M. Herceg – Ľ. ČirkaM. Fikar: Time-Optimal Control of Takagi-Sugeno Fuzzy Systems. In Proceedings of the 10th European Control Conference, Budapest, Hungary, pp. 916–921, 2009.
  9. M. Kvasnica – M. Herceg – Ľ. ČirkaM. Fikar: Robust Adaptive Minimum-Time Control of Piecewise Affine Systems. In Proceedings of the 48th IEEE Conference on Decision and Control, pp. 2454–2459, 2009.
  10. I. Rauová – M. KvasnicaĽ. ČirkaM. Fikar: Real-Time Model Predictive Control of a Laboratory Liquid Tanks System. Editor(s): Fikar, M., Kvasnica, M., In Proceedings of the 17th International Conference on Process Control ’09, Slovak University of Technology in Bratislava, Štrbské Pleso, Slovakia, pp. 304–308, 2009.

2008

  1. M. Kvasnica – M. Herceg – Ľ. ČirkaM. Fikar: Adaptive Model Predictive Control of Piecewise Affine Systems. Editor(s): L. Magni, D. Raimondo, F. Allgoewer, In International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, Pavia, Italy, pp. PIV3-1–PIV3-8, 2008.
  2. I. Rauová – M. KvasnicaĽ. ČirkaM. Fikar: Real-Time Model Predictive Control of a Laboratory Liquid Tanks System. In Proceedings of the 16th Annual Conference Technical Computing Prague 2008, Kongresové centrum ČVUT Praha, pp. 89–95, 2008.

Investigators

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