Abstractions of Hamiltonian control systems
Postprint version. Published in Automatica, Volume 39, Issue 12, December 2003, pages 2025-2033.
Publisher URL: http://dx.doi.org/10.1016/S0005-1098(03)00235-8
Given a control system and a desired property, an abstracted system is a reduced system that preserves the property of interest while ignoring modeling detail. In previous work, abstractions of linear and nonlinear control systems were considered while preserving reachability properties. In this paper, we consider the abstraction problem for Hamiltonian control systems, where, in addition to the property of interest we also preserve the Hamiltonian structure of the control system. We show how the Hamiltonian structure of control systems can be exploited to simplify the abstraction process. We then focus on local accessibility preserving abstractions, and provide conditions under which local accessibility properties of the abstracted Hamiltonian system are equivalent to the local accessibility properties of the original Hamiltonian control system.
Paulo Tabuada and George J. Pappas. "Abstractions of Hamiltonian control systems" Departmental Papers (ESE) (2003).
Available at: http://works.bepress.com/george_pappas/173