Hybrid Systems: Computation and Control.

Abstract

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A Hybrid-Control Approach to the Parking Problem of a Wheeled Vehicle Using Limited View-Angle Visual Feedback

“…To precisely describe this approach, and to prove that it indeed produces a solution to our problem, we formalize the system using tools from the recently developed theory of hybrid systems. In their most simple description, hybrid systems are dynamical systems comprised of a finite state automaton, whose states correspond to a continuous dynamic evolution, and whose transitions can be enabled by particular conditions ("guards" or "jumps") reached at by the continuous dynamics themselves (Branicky 1998;Henzinger and Sastry 1998;Schumacher and van der Schaft 1999).…”

On Invertibility of Switched Linear Systems

“…Switching can also be inherent by nature, such as when a physical plant has the capability of undergoing several operational modes (e.g., an aircraft during different thrust modes (Lygeros et al, 1999), a walking robot during leg impact and leg swing modes (Westervelt et al, 2003), different formations of a group of vehicles (Olfati-Saber and Murray, 2004)). Also, switched systems may be viewed as higher-level abstractions of hybrid systems (see, e.g., (Henzinger and Sastry, 1998) for hybrid system definitions), obtained by neglecting details of the discrete behavior and instead considering switching signals from a suitable class. Switched systems have attracted growing research interest recently and several important results for switched systems have been achieved, including various stability results (Agrachev and Liberzon, 2001;Branicky, 1998;Hespanha and Morse, 1999;Mancilla-Aguilar and Garcia, 2000), controllability and observability results (Sun et al, 2002;Xie and Wang, 2004;Vidal et al, 2002), and input-to-state properties (Hespanha, 2003;Xie et al, 2001;Vu et al, 2007) (see, e.g., (Liberzon, 2003) for other references on switched systems and switching control).…”