Titlebook: Nonconvex Optimal Control and Variational Problems; Alexander J. Zaslavski Book 2013 Springer Science+Business Media New York 2013 Baire c

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Springer Optimization and Its Applicationshttp://image.papertrans.cn/n/image/667215.jpg

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https://doi.org/10.1007/978-1-4614-7378-7Baire category approach; Lavrentiev phenomenon; calculus of variations; nonconvex optimal control

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Introduction,Let ., . be a closed subset of the .-space .. and let .(.) denote its sections, that is . For every (.,.)∈. let .(.,.) be a given subset of the .-space .., ., ..

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Generic Nonoccurrence of the Lavrentiev Phenomenon,In this chapter we study nonoccurrence of the Lavrentiev phenomenon for a large class of nonconvex optimal control problems. We show that for most problems (in the sense of Baire category) the infimum on the full admissible class of trajectory-control pairs is equal to the infimum on a subclass of trajectory-control pairs with bounded controls.

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Uniform Boundedness of Approximate Solutions of Variational Problems,In this chapter, given an . we study the infinite horizon problem of minimizing the expression . as . grows to infinity where . satisfies the initial condition .(0) = ... We analyze the existence and properties of approximate solutions for every prescribed initial value ...

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The Turnpike Property for Approximate Solutions of Variational Problems,In this chapter we study the structure of approximate solutions of variational problems with continuous integrands . which belong to a complete metric space of functions .. We do not impose any convexity assumption and establish the existence of an everywhere dense ..-set . such that each integrand in . has the turnpike property.

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