International Journal of Systems Science and Applied Mathematics
Volume 2, Issue 4, July 2017, Pages: 75-82
Received: May 18, 2017;
Accepted: May 27, 2017;
Published: Jul. 18, 2017
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Ying Shang, Department of Electrical and Computer Engineering, Southern Illinois University Edwardsville, Edwardsville, USA
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.
Biped Robot Modeling and Control Using Controlled Hybrid Automata, International Journal of Systems Science and Applied Mathematics.
Vol. 2, No. 4,
2017, pp. 75-82.
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