Geometry of Optimal Paths around Focal Singular Surfaces in Differential Games

Geometry of Optimal Paths around Focal Singular Surfaces in Differential Games We investigate a special type of singularity in non-smooth solutions of first-order partial differential equations, with emphasis on Isaacs’ equation. This type, called focal manifold, is characterized by the incoming trajectory fields on the two sides and a discontinuous gradient. We provide a complete set of constructive equations under various hypotheses on the singularity, culminating with the case where no a priori hypothesis on its geometry is known, and where the extremal trajectory fields need not be collinear. We show two examples of differential games exhibiting non-collinear fields of extremal trajectories on the focal manifold, one with a transversal approach and one with a tangential approach. Applied Mathematics and Optimization Springer Journals

Geometry of Optimal Paths around Focal Singular Surfaces in Differential Games

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Copyright © 2005 by Springer
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
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