Lyapunov–schmidt Reduction for Optimal Control Problems
نویسندگان
چکیده
In this paper, we use the method of characteristics to study singularities in the flow of a parameterized family of extremals for an optimal control problem. By means of the Lyapunov–Schmidt reduction a characterization of fold and cusp points is given. Examples illustrate the local behaviors of the flow near these singular points. Singularities of fold type correspond to the typical conjugate points as they arise for the classical problem of minimum surfaces of revolution in the calculus of variations and local optimality of trajectories ceases at fold points. Simple cusp points, on the other hand, generate a cut-locus that limits the optimality of close-by trajectories globally to times prior to the conjugate points.
منابع مشابه
LYAPACK - A MATLAB Toolbox for Large Lyapunov and Riccati Equations, Model Reduction Problems, and Linear-Quadratic Optimal Control Problems - Users' Guide (Version 1.0)
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