Abstract
The time mean of a smooth objective function along a phase trajectory of a controlled dynamical system is maximized. The simplest singularities of the dependence of the optimal mean value on the parameter in generic one-parameter families of controlled systems of this kind are listed. It turns out that the most common generic stable singularity is the discontinuity of the first or second derivative of the optimal mean value with respect to the parameter.
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Arnold, V.I. Optimization in Mean and Phase Transitions in Controlled Dynamical Systems. Functional Analysis and Its Applications 36, 83–92 (2002). https://doi.org/10.1023/A:1015655005114
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DOI: https://doi.org/10.1023/A:1015655005114