**Project number:** VEGA 1/0403/15

**Principal investigator:** M. Kvasnica

**Period:** 2015-2018

**Keywords:** Optimal control, process control, stability, real-time control

**Project summary:**

This research project is devoted to design, synthesis, and implementation of optimal control systems for process control applications which require rigorous guarantees that the control system will exhibit desired safety and economical properties. The parameters of safety and economical behavior are divided into theoretical properties (closed-loop stability, recursive feasibility and satisfaction of process constraints), and practical properties (guaranteed execution of the optimization algorithm on platforms with restricted computational resources, correct behavior of the control system under quantization and under failures of the communication channels). Nowadays, these properties are verified by extensive testing, which is time consuming and expensive. Therefore the main goal of the project is to develop a unified methodology which allows to design optimal control systems in which safety properties can be imposed and verified already at the design stage.

**Scientific goals:**

The main aim of the project is to develop novel methods and algorithms for synthesis of verifiably safe optimal control strategies. Such a synthesis must be tailored to specific hardware platform on which the control system is to be implemented, and must take into account parameters of the input/output channels, as well as properties of communication channels. The objective is to synthesize such optimization-based control strategies which satisfy these limits from the very beginning, abolishing the need to a-posteriori extensive verification. Achieving this objective requires solving three main tasks, which represent the particular goals of this project:

- Obtaining a rigorous certificate that a given optimization-based control strategy provides closed-loop stability and recursive feasibility even in the presence of the model-plant mismatch, and when measurements/control inputs are quantized or are subject to network communication.
- Synthesis of optimal control algorithms which are guaranteed to be executed correctly even on hardware platforms with prescribed constraints on computational power and available memory.
- Implementation and verification of verifiably safe optimal control systems under hard real-time constraints.

The main vision of the project is to provide a unified control design and verification methodology which will abolish the need of costly a-posteriori testing of safety properties. This will be achieved by synthesizing rigorous certificates of closed-loop stability and recursive feasibility in the form of Lyapunov functions and invariant sets. These certificates will be constructed using parametric and mixed-integer optimization. Results of this research project will be experimentally verified on a rich scale of chemical and biotechnological processes, as well as on mobile robotic platforms.

- J. Holaza – M. Klaučo – J. Drgoňa – J. Oravec – M. Kvasnica – M. Fikar:
**MPC-Based Reference Governor Control of a Continuous Stirred-Tank Reactor**.*Computers & Chemical Engineering*, vol.**108**, pp. 289–299, 2018.

- M. Bakošová – J. Oravec – A. Vasičkaninová – A. Mészáros:
**Neural-Network-Based and Robust Model-Based Predictive Control of a Tubular Heat Exchanger**.*Chemical Engineering Transactions*, no. 61, pp. 301–306, 2017. - J. Drgoňa – M. Klaučo – F. Janeček – M. Kvasnica:
**Optimal control of a laboratory binary distillation column via regionless explicit MPC**.*Computers & Chemical Engineering*, vol.**96**, pp. 139–148, 2017. - J. Drgoňa – Z. Takáč – M. Horňák – R. Valo – M. Kvasnica:
**Fuzzy Control of a Laboratory Binary Distillation Column**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 21st International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 120–125, 2017. - J. Holaza – M. Klaučo – M. Kvasnica:
**Solution Techniques for Multi-Layer MPC-Based Control Strategies**. In*Preprints of the 20th IFAC World Congress, Toulouse, France*, vol.**20**, 2017. - J. Holaza – R. Valo – M. Klaučo:
**A Novel Approach of Control Design of the pH in the Neutralization Reactor**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 21st International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 191–196, 2017. - D. Ingole – J. Drgoňa – M. Kalúz – M. Klaučo – M. Bakošová – M. Kvasnica:
**Model Predictive Control of a Combined Electrolyzer-Fuel Cell Educational Pilot Plant**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 21st International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 147–154, 2017. - D. Ingole – J. Drgoňa – M. Kvasnica:
**Offset-Free Hybrid Model Predictive Control of Bispectral Index in Anesthesia**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 21st International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 422–427, 2017. - F. Janeček – M. Klaučo – M. Kalúz – M. Kvasnica:
**OPTIPLAN: A Matlab Toolbox for Model Predictive Control with Obstacle Avoidance**. In*Preprints of the 20th IFAC World Congress, Toulouse, France*, vol.**20**, 2017. - F. Janeček – M. Klaučo – M. Kvasnica:
**Trajectory Planning and Following for UAVs with Nonlinear Dynamics**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 21st International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 333–338, 2017. - M. Klaučo – M. Kalúz – M. Kvasnica:
**Real-time implementation of an explicit MPC-based reference governor for control of a magnetic levitation system**.*Control Engineering Practice*, no. 60, pp. 99–105, 2017. - M. Klaučo – M. Kvasnica:
**Control of a boiler-turbine unit using MPC-based reference governors**.*Applied Thermal Engineering*, vol.**110**, pp. 1437–1447, 2017. - M. Klaučo – R. Valo – J. Drgoňa:
**Reflux control of a laboratory distillation column via MPC-based reference governor**.*Acta Chimica Slovaca*, no. 2, vol.**10**, pp. 139–143, 2017. - N. A. Nguyen – S. Olaru – P. Rodríguez-Ayerbe – M. Kvasnica:
**Convex liftings-based robust control design**.*Automatica*, no. March 2017, vol.**77**, pp. 206–213, 2017. - J. Oravec – M. Bakošová – P. Artzová:
**Advanced Process Control Design for a Distillation Column Using UniSim Design**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 21st International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 303–308, 2017. - J. Oravec – M. Bakošová – L. Hanulová – M. Horváthová:
**Design of Robust MPC with Integral Action for a Laboratory Continuous Stirred-Tank Reactor**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 21st International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 459–464, 2017. - J. Oravec – M. Bakošová – D. Pakšiová – N. Mikušová – K. Batárová:
**Advanced Robust MPC Design of a Heat Exchanger: Modeling and Experiments**. Editor(s): Antonio Espuña, Moisès Graells, Luis Puigjaner, In*27th European Symposium on Computer Aided Process Engineering*, Elsevier, Barcelona, Spain, pp. 1585–1590, 2017. - J. Oravec – Y. Jiang – B. Houska – M. Kvasnica:
**Parallel Explicit MPC for Hardware with Limited Memory**. In*Preprints of the 20th IFAC World Congress, Toulouse, France*, vol.**20**, pp. 3356–3361, 2017. - J. Oravec – M. Klaučo – M. Kvasnica – J. Löfberg:
**Computationally Tractable Formulations for Optimal Path Planning with Interception of Targets’ Neighborhoods**.*Journal of Guidance, Control, and Dynamics*, no. 5, vol.**40**, pp. 1221–1230, 2017. - J. Oravec – M. Kvasnica – M. Bakošová:
**Quasi-Non-Symmetric Input and Output Constraints in LMI-based Robust MPC**. In*Preprints of the 20th IFAC World Congress, Toulouse, France*, vol.**20**, pp. 11829–11834, 2017. - J. Oravec – M. Trafczynski – M. Bakošová – M. Markowski – A. Mészáros – K. Urbaniec:
**Robust Model Predictive Control of Heat Exchanger Network in the Presence of Fouling**.*Chemical Engineering Transactions*, no. 61, pp. 334–342, 2017. - D. Picard – J. Drgoňa – M. Kvasnica – L. Helsen:
**Impact of the controller model complexity on model predictive control performance for buildings**.*Energy and Buildings*, pp. 739–751, 2017.

- J. Drgoňa – F. Janeček – M. Klaučo – M. Kvasnica:
**Regionless Explicit MPC of a Distillation Column**. In*European Control Conference 2016*, Aalborg, Denmark, pp. 1568–1573, 2016. - D. Ingole – J. Drgoňa – M. Kalúz – M. Klaučo – M. Bakošová – M. Kvasnica:
**Explicit Model Predictive Control of a Fuel Cell**. In*The European Conference on Computational Optimization*, Leuven, Belgium, vol.**4**, 2016. - M. Kalúz – J. Holaza – F. Janeček – S. Blažek – M. Kvasnica:
**A Robotic Traffic Simulator for Teaching of Advanced Control Methods**. In*Preprints of the 11th IFAC Symposium on Advances in Control Education*, vol.**11**, pp. 338–343, 2016. - M. Klaučo – S. Blažek – M. Kvasnica:
**An Optimal Path Planning Problem for Heterogeneous Multi-Vehicle Systems**.*International Journal of Applied Mathematics and Computer Science*, no. 2, vol.**26**, pp. 297–308, 2016. - J. Oravec – M. Bakošová – A. Mészáros:
**Robust Model Predictive Control of Heat Exchangers in Series**.*Chemical Engineering Transactions*, no. 52, pp. 253–258, 2016. - D. Picard – J. Drgoňa – L. Helsen – M. Kvasnica:
**Impact of the controller model complexity on MPC performance evaluation for building climate control**. In*The European Conference on Computational Optimization*, Leuven, Belgium, vol.**4**, 2016. - B. Takács – J. Števek – R. Valo – M. Kvasnica:
**Python Code Generation for Explicit MPC in MPT**. In*European Control Conference 2016*, Aalborg, Denmark, pp. 1328–1333, 2016.

- J. Drgoňa – M. Klaučo – M. Kvasnica:
**MPC-Based Reference Governors for Thermostatically Controlled Residential Buildings**. In*54th IEEE Conference on Decision and Control*, Osaka, Japan, vol.**54**, 2015. - M. Herceg – C. Jones – M. Kvasnica – M. Morari:
**Enumeration-based approach to solving parametric linear complementarity problems**.*Automatica*, no. 62, pp. 243–248, 2015. - J. Holaza – B. Takács – M. Kvasnica – S. Di Cairano:
**Safety Verification of Implicitly Defined MPC Feedback Laws**. In*European Control Conference 2015*, Linz, Austria, pp. 2552–2557, 2015. - D. Ingole – J. Holaza – B. Takács – M. Kvasnica:
**FPGA-Based Explicit Model Predictive Control for Closed-Loop Control of Intravenous Anesthesia**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 20th International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 42–47, 2015. - D. Ingole – M. Kvasnica:
**FPGA Implementation of Explicit Model Predictive Control for Closed Loop Control of Depth of Anesthesia**. In*Preprints of the 5th IFAC Conference on Nonlinear Model Predictive Control*, pp. 484–489, 2015. - M. Kvasnica – J. Holaza – B. Takács – D. Ingole:
**Design and Verification of Low-Complexity Explicit MPC Controllers in MPT3 (Extended version)**. 2015. - M. Kvasnica – J. Holaza – B. Takács – D. Ingole:
**Design and Verification of Low-Complexity Explicit MPC Controllers in MPT3**. In*European Control Conference 2015*, Linz, Austria, pp. 2600–2605, 2015. - M. Kvasnica – B. Takács – J. Holaza – S. Di Cairano:
**On Region-Free Explicit Model Predictive Control**. In*54th IEEE Conference on Decision and Control*, Osaka, Japan, vol.**54**, pp. 3669–3674, 2015. - M. Kvasnica – B. Takács – J. Holaza – D. Ingole:
**Reachability Analysis and Control Synthesis for Uncertain Linear Systems in MPT**. Editor(s): Fikar, M., In*Proceedings of the 8th IFAC Symposium on Robust Control Design*, Elsevier, Bratislava, Slovak Republic, no. 8, pp. 302–307, 2015. - M. Nehéz – D. Bernát – M. Klaučo:
**Comparison of Algorithms for Near-Optimal Dominating Sets Computation in Real-World Networks**. Editor(s): B. Rachev, A. Smrikarov, In*Proceedings of the 16th International Conference on Computer Systems and Technologies*, Association for Computing Machinery (ACM), Dublin, Ireland, pp. 199–206, 2015. - J. Oravec – M. Bakošová:
**Software for Efficient LMI-based Robust MPC Design**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 20th International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 272–277, 2015. - J. Oravec – M. Bakošová:
**Alternative LMI-based Robust MPC Design Approaches**. Editor(s): Fikar, M., In*Proceedings of the 8th IFAC Symposium on Robust Control Design*, Elsevier, Bratislava, Slovak Republic, no. 8, pp. 180–184, 2015. - J. Oravec – M. Bakošová:
**Robust Model Predictive Control Based on Nominal System Optimization and Control Input Saturation**. Editor(s): Fikar, M., In*Proceedings of the 8th IFAC Symposium on Robust Control Design*, Elsevier, Bratislava, Slovak Republic, no. 8, pp. 314–319, 2015. - J. Oravec – M. Klaučo – M. Kvasnica – J. Löfberg:
**Optimal Vehicle Routing with Interception of Targets’ Neighbourhoods**. In*European Control Conference 2015*, Linz, Austria, pp. 2538–2543, 2015. - B. Takács – J. Holaza – J. Števek – M. Kvasnica:
**Export of Explicit Model Predictive Control to Python**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 20th International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 78–83, 2015.