Document Type : reviewed article

Authors

Iran university of science and technology

Abstract

Due to various and complex phenomena in hybrid dynamical systems, the control of these types of systems has faced a challenge. Space systems also have hybrid dynamics due to different missions and operational modes. Therefore, to deal with these systems, we must first familiarize ourselves with the standard examples that have been studied before. Consequently, in the field of hybrid control science, various examples have been reviewed and researched. In order to improve the performance comparison of control methods or to check their comprehensiveness, some of these examples are used as benchmark examples. Therefore, this article has been tried to collect benchmark examples with different characteristics in the hybrid control field and compare them with each other. It should be noted that benchmark examples were selected based on the number of repetitions and recognition. Therefore, the performance of the developing controllers can be examined on these examples and compared with the results of other controllers. As a result, the researchers can choose their desired benchmark more accurate and efficient with the investigation and design of the controller

Keywords

Main Subjects

##Bemporad and M. Morari, "Control of systems integrating logic, dynamics, and constraints," Automatica, vol. 35, no. 3, pp. 407-427, 1999.##
##A. Cuzzola and M. Morari, "An LMI approach for H∞ analysis and control of discrete-time piecewise affine systems," International Journal of Control, Article vol. 75, no. 16, pp. 1293-1301, 2002.##
##Baotić, F. J. Christophersen, and M. Morari, "Constrained optimal control of hybrid systems with a linear performance index," IEEE Transactions on Automatic Control, Article vol. 51, no. 12, pp. 1903-1919, 2006.##
##Chan and S. J. a. p. a. Mitra, "Verifying safety of an autonomous spacecraft rendezvous mission," in 4th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH), 2017.##
##Althoff et al., "Arch-comp19 category report: Continuous and hybrid systems with linear continuous dynamics," in 6th International Workshop on Applied Verification for Continuous and Hybrid systems (ARCH), 2019, vol. 61, pp. 14-40.##
##Lagerberg, "A Benchmark on Hybrid Control of an Automotive Powertrain with Backlash," Department of Signals and Systems, Chalmers University of Technology, Göteborg1403266X (ISSN), 2007, Available: http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-6031.##
##Althoff and B. H. Krogh, "Avoiding geometric intersection operations in reachability analysis of hybrid systems," in 15th ACM international conference on Hybrid Systems: Computation and Control, 2012, pp. 45-54##.
##Besselmann, P. Rostalski, M. Baric, A. Lagerberg, and M. Morari, "A Benchmark on Hybrid Control of a Mechanical System with Backlash," Automatic Control Laboratory, ETH, Zürich, 2007, Available: http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-6037.##
##V. Nguyen and T. T. Johnson, "Benchmark: DC-to-DC Switched-Mode Power Converters (Buck Converters, Boost Converters, and Buck-Boost Converters)," in 6th International Workshop on Applied Verification for Continuous and Hybrid systems (ARCH), 2014, pp. 19-24.##
##Geyer, G. Papafotiou, R. Frasca, and M. Morari, "Constrained optimal control of the step-down dc-dc converter," IEEE Transactions on Power Electronics, Article vol. 23, no. 5, pp. 2454-2464, 2008.##
##Geyer, G. Papafotiou, and M. Morari, "Hybrid model predictive control of the step-down DC-DC converter," IEEE Transactions on Control Systems Technology, Article vol. 16, no. 6, pp. 1112-1124, 2008.##
##A. F. Theunisse, J. Chai, R. G. Sanfelice, and W. P. M. H. Heemels, "Robust Global Stabilization of the DC-DC Boost Converter via Hybrid Control," IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 62, no. 4, pp. 1052-1061, 2015.##
##A. Beg, A. Davoudi, and T. T. Johnson, "Reachability Analysis of Transformer-Isolated DC-DC Converters (Benchmark Proposal)," in 4th International Workshop on Applied Verification for Continuous and Hybrid Systems Workshop (ARCH), 2017.##
##Fehnker and F. Ivančić, "Benchmarks for hybrid systems verification," in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) vol. 2993, R. Alur and G. J. Pappas, Eds., ed: Springer Verlag, 2004, pp. 326-341.##
##P. Maschuw, G. C. Keßler, and D. Abel, "LMI-based control of vehicle platoons for robust longitudinal guidance," IFAC Proceedings Volumes, vol. 41, no. 2, pp. 12111-12116, 2008.##
##B. Makhlouf, J. P. Maschuw, P. Hänsch, H. Diab, S. Kowalewski, and D. Abel, "Safety Verification of a Cooperative Vehicle Platoon with Uncertain Inputs Using Zonotopes*," IFAC Proceedings Volumes, vol. 44, no. 1, pp. 9769-9774, 2011.##
##B. Makhlouf, H. Diab, and S. Kowalewski, "Safety Verification of a Controlled Cooperative Platoon Under Loss of Communication Using Zonotopes," IFAC Proceedings Volumes, vol. 45, no. 9, pp. 333-338, 2012.##
##B. Makhlouf and S. Kowalewski, "Networked Cooperative Platoon of Vehicles for Testing Methods and Verification Tools," in 1st and 2nd International Workshop on Applied veRification for Continuous and Hybrid Systems (ARCH), 2014, pp. 37-42.##
##Corona and B. De Schutter, "Adaptive cruise control for a SMART car: A comparison benchmark for MPC-PWA control methods," IEEE Transactions on Control Systems Technology, vol. 16, no. 2, pp. 365-372, 2008.##
##Corona and B. De Schutter, "ADAPTIVE CRUISE CONTROLLER DESIGN: A COMPARATIVE ASSESSMENT FOR PWA SYSTEMS," IFAC Proceedings Volumes, vol. 39, no. 5, pp. 253-258, 2006.##
##Chen, S. Mitra, and G. Tian, "Motor-Transmission Drive System: a Benchmark Example for Safety Verification," in 1st and 2nd International Workshop on Applied Verification for Continuous and Hybrid Systems (ARCH), 2014, pp. 9-18.##
##Chen and S. Mitra, "Synthesis and verification of motor-transmission shift controller for electric vehicles," in International Conference on Cyber-Physical Systems (ICCPS), 2014, pp. 25-35.##
##M. Lopez et al., "Arch-comp19 category report: Artificial intelligence / neural network control systems (ainncs) for continuous and hybrid systems plants," in 6th International Workshop on Applied Verification for Continuous and Hybrid systems (ARCH), 2019, vol. 61, pp. 103-119.##
##Rodrigues and J. P. How, "Observer-based control of piecewise-affine systems," International Journal of Control, Article vol. 76, no. 5, pp. 459-477, 2003.##
##Safi and E. Khanmirza, "A Criticism of Position Control of the Inverted Pendulum with Biased Angle Measurements Using Double-Loop PID," in 2020 Advances in Science and Engineering Technology International Conferences (ASET), 2020, pp. 1-5.##
##Girard and S. Martin, "Synthesis for constrained nonlinear systems using hybridization and robust controllers on simplices," IEEE Transactions on Automatic Control, Article vol. 57, no. 4, pp. 1046-1051, 2012, Art. no. 6024442.##
##Takahashi, K. Furuta, S. Hatakeyama, S. Suzuki, and A. Sugiki, "SWING-UP CONTROL OF INVERTED PENDULUM BY PERIODIC INPUT," IFAC Proceedings Volumes, vol. 35, no. 1, pp. 283-286, 2002.##
##Heinz, J. Oehlerking, and M. Woehrle, "Benchmark: Reachability on a model with holes," in 1st and 2nd International Workshop on Applied veRification for Continuous and Hybrid Systems (ARCH), 2015, pp. 31-36.##
##Immler et al., "Arch-comp19 category report: Continuous and hybrid systems with nonlinear dynamics," in 6th International Workshop on Applied Verification for Continuous and Hybrid systems (ARCH), 2019, vol. 61, pp. 41-61.##
##J. Cruz, M. Oishi, and R. Fierro, "Lift of a cable-suspended load by a quadrotor: A hybrid system approach," in American Control Conference (ACC), 2015, pp. 1887-1892.##
##J. Cruz and R. Fierro, "Cable-suspended load lifting by a quadrotor UAV: hybrid model, trajectory generation, and control," (in English), Autonomous Robots, Article vol. 41, no. 8, pp. 1629-1643, 2017.##
##Parolini, S. Schuler, and A. Anta, "Benchmark problem: an air brake model for trains," in 1st and 2nd International Workshop on Applied veRification for Continuous and Hybrid Systems (ARCH), 2015, pp. 43-48.##
##Hariprasad and S. Bhartiya, "A computationally efficient robust tube based MPC for linear switched systems," Nonlinear Analysis: Hybrid Systems, vol. 19, pp. 60-76, 2016.##
##Heiming and J. Lunze, "Definition of the three-tank benchmark problem for controller reconfiguration," in European Control Conference (ECC), 1999, pp. 4030-4034, 1999.##
##H. Johansson and J. L. R. Nunes, "A multivariable laboratory process with an adjustable zero," in Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), vol. 4, pp. 2045-2049 vol.4.##
##Schürmann, R. Vignali, M. Prandini, and M. Althoff, "Set-based control for disturbed piecewise affine systems with state and actuation constraints," Nonlinear Analysis: Hybrid Systems, vol. 36, p. 100826, 2020.##
##A. Cengel and M. A. Boles, Thermodynamics: An Engineering Approach 6th Editon (SI Units). The McGraw-Hill Companies, Inc., New York, 2007.##
##F. S. Larsen, R. Izadi-Zamanabadi, and R. Wisniewski, "Supermarket refrigeration system - Benchmark for hybrid system control," in 9th European Control Conference (ECC), 2007, pp. 113-120: Institute of Electrical and Electronics Engineers Inc.##
##Lawrence Ricker, "Predictive hybrid control of the supermarket refrigeration benchmark process," (in English), Control Engineering Practice, Article vol. 18, no. 6, pp. 608-617, 2010.##
##S Sonntag, A. Devanathan, S. Engell, and O. Stursberg, "Hybrid nonlinear model-predictive control of a supermarket refrigeration system," in 2007 IEEE International Conference on Control Applications, 2007, pp. 1432-1437: IEEE.##
##Beg, A. Davoudi, and T. T. J. E. S. i. C. Johnson, "Charge Pump Phase-Locked Loops and Full Wave Rectifiers for Reachability Analysis," in 3rd International Workshop on Applied Verification for Continuous and Hybrid Systems (ARCH), 2017, vol. 43, pp. 27-35.##
##Althoff, S. Yaldiz, A. Rajhans, X. Li, B. H. Krogh, and L. Pileggi, "Formal verification of phase-locked loops using reachability analysis and continuization," in IEEE/ACM International Conference on Computer-Aided Design (ICCAD), 2011, pp. 659-666.##
##Balluchi, L. Benvenuti, M. D. Di Benedetto, T. Villa, and A. L. Sangiovanni-Vincentelli, "Idle speed control - a benchmark for hybrid system research," in Analysis and Design of Hybrid Systems 2006: Elsevier Ltd, 2006, pp. 259-264.##