Generic Profit Singularities of One-Parameter Cyclic Processes with Discount
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On the circle for a smooth one-parameter family of controllable cyclic processes with discount, we classify generic singularities of time-average profit as a function of the parameter. The stability of these singularities with respect to small perturbations of generic families is proved.
KeywordsCyclic Process Double Point Switching Point Switching Function Optimal Motion
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- 1.V. I. Arnold, A. N. Varchenko, and S. M. Gusein-Sade, Singularities of Differentiable Maps, 1, Birkhäuser, Boston (1985).Google Scholar
- 5.A. A. Davydov, “Singularities of the maximum function over the preimage,” Banach Center Publ., 32, 167–181 (1995).Google Scholar
- 6.A. A. Davydov, “Generic profit singularities in Arnold’s model of cyclic processes,” Proc. Steklov Inst. Math., 250, 70–84 (2005).Google Scholar
- 7.A. A Davydov and H. Mena-Matos, “Singularity theory approach to time averaged optimization,” in: Singularities in Geometry and Topology, World Scientific Publ. (2007), pp. 598–628.Google Scholar
- 9.A. A. Davydov amd T. S. Shutkina, “Uniqueness of a cycle with discounting that is optimal with respect to the average time profit,” Tr. Inst. Mat., 17, No. 2 (2011).Google Scholar