Hybrid systems are dynamical systems consisting of interacting discrete event and continuous state subsystems. A controlled hybrid automaton is a hybrid automaton whose continuous-state dynamics are described by inhomogeneous differential equations. This paper presents a sufficient condition for the existence of global non-terminating solutions in controlled hybrid automata. The condition is based on a recursive algorithm that can always terminate after a finite number of iterations to a limit set of states, i.e. the fixed point of the recursion. If the fixed point is non-empty, then there exists a measurable control under which the hybrid automaton generates a global non-terminating solution. The more important is that this result can also be used to infer the existence of global solutions to compositions of controlled hybrid automata, thereby providing a foundation for the analysis of large scale hybrid systems. The controlled hybrid automata model can be used for robotics system modeling and control. By solving the global non-terminating solution to controlled hybrid automata, the biped robots can be guaranteed to keep the walking gait without falling down.
| Published in | International Journal of Systems Science and Applied Mathematics (Volume 2, Issue 4) |
| DOI | 10.11648/j.ijssam.20170204.11 |
| Page(s) | 75-82 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
Hybrid Automata, Decidability Problem, Backward Reachability
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APA Style
Ying Shang. (2017). Biped Robot Modeling and Control Using Controlled Hybrid Automata. International Journal of Systems Science and Applied Mathematics, 2(4), 75-82. https://doi.org/10.11648/j.ijssam.20170204.11
ACS Style
Ying Shang. Biped Robot Modeling and Control Using Controlled Hybrid Automata. Int. J. Syst. Sci. Appl. Math. 2017, 2(4), 75-82. doi: 10.11648/j.ijssam.20170204.11
AMA Style
Ying Shang. Biped Robot Modeling and Control Using Controlled Hybrid Automata. Int J Syst Sci Appl Math. 2017;2(4):75-82. doi: 10.11648/j.ijssam.20170204.11
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Download@article{10.11648/j.ijssam.20170204.11,
author = {Ying Shang},
title = {Biped Robot Modeling and Control Using Controlled Hybrid Automata},
journal = {International Journal of Systems Science and Applied Mathematics},
volume = {2},
number = {4},
pages = {75-82},
doi = {10.11648/j.ijssam.20170204.11},
url = {https://doi.org/10.11648/j.ijssam.20170204.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20170204.11},
abstract = {Hybrid systems are dynamical systems consisting of interacting discrete event and continuous state subsystems. A controlled hybrid automaton is a hybrid automaton whose continuous-state dynamics are described by inhomogeneous differential equations. This paper presents a sufficient condition for the existence of global non-terminating solutions in controlled hybrid automata. The condition is based on a recursive algorithm that can always terminate after a finite number of iterations to a limit set of states, i.e. the fixed point of the recursion. If the fixed point is non-empty, then there exists a measurable control under which the hybrid automaton generates a global non-terminating solution. The more important is that this result can also be used to infer the existence of global solutions to compositions of controlled hybrid automata, thereby providing a foundation for the analysis of large scale hybrid systems. The controlled hybrid automata model can be used for robotics system modeling and control. By solving the global non-terminating solution to controlled hybrid automata, the biped robots can be guaranteed to keep the walking gait without falling down.},
year = {2017}
}
TY - JOUR T1 - Biped Robot Modeling and Control Using Controlled Hybrid Automata AU - Ying Shang Y1 - 2017/07/18 PY - 2017 N1 - https://doi.org/10.11648/j.ijssam.20170204.11 DO - 10.11648/j.ijssam.20170204.11 T2 - International Journal of Systems Science and Applied Mathematics JF - International Journal of Systems Science and Applied Mathematics JO - International Journal of Systems Science and Applied Mathematics SP - 75 EP - 82 PB - Science Publishing Group SN - 2575-5803 UR - https://doi.org/10.11648/j.ijssam.20170204.11 AB - Hybrid systems are dynamical systems consisting of interacting discrete event and continuous state subsystems. A controlled hybrid automaton is a hybrid automaton whose continuous-state dynamics are described by inhomogeneous differential equations. This paper presents a sufficient condition for the existence of global non-terminating solutions in controlled hybrid automata. The condition is based on a recursive algorithm that can always terminate after a finite number of iterations to a limit set of states, i.e. the fixed point of the recursion. If the fixed point is non-empty, then there exists a measurable control under which the hybrid automaton generates a global non-terminating solution. The more important is that this result can also be used to infer the existence of global solutions to compositions of controlled hybrid automata, thereby providing a foundation for the analysis of large scale hybrid systems. The controlled hybrid automata model can be used for robotics system modeling and control. By solving the global non-terminating solution to controlled hybrid automata, the biped robots can be guaranteed to keep the walking gait without falling down. VL - 2 IS - 4 ER -
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