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This paper is concerned with a path-finding method proposed by H. J. Sussmann, known as the homotopy continuation method (HCM). Given a control system initialized at some state, the HCM can be used to find an admissible open-loop control that performs a desired state transfer. This is accomplished by lifting curves in the state space of the system to curves in the space of regular admissible controls...
Sufficient conditions for the state space trajectory of a system of ordinary differential equations (ODEs) to be arbitrarily close to an equilibrium path and for the evolution of the system to be quasistationary are proved using basic topology and mathematical analysis concepts. The conditions are less conservative than previously derived ones based on Lyapunov functions.
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