scholarly journals Generic existence of solutions of nonconvex optimal control problems

2005 ◽  
Vol 2005 (4) ◽  
pp. 375-421 ◽  
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Optimal Control ◽  
Existence And Uniqueness ◽  
Optimal Control Problems ◽  
Existence Of Solutions ◽  
Integral Functional ◽  
Growth Conditions ◽  
Uniqueness Result ◽  
Control Problems ◽  
Convexity Condition ◽  
Generic Existence

The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrandsfwhich satisfy convexity and growth conditions. In 1996, the author obtained a generic existence and uniqueness result (with respect to variations of the integrand of the integral functional) without the convexity condition for a class of optimal control problems satisfying the Cesari growth condition. In this paper, we survey this result and its recent extensions, and establish several new results in this direction.

scholarly journals Existence of Solutions for Optimal Control Problems on Time Scales whose States are Absolutely Continuous

2016 ◽  
Vol 17 (1) ◽  
pp. 81
Author(s):  
Iguer L D Santos
Keyword(s):  
Optimal Control ◽  
Time Scales ◽  
Optimal Control Problems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Control Problems ◽  
Optimal Controls ◽  
Absolutely Continuous

This paper considers a class of optimal control problems on time scales described by dynamic equations on time scales. We have established sufficient conditions for theexistence of optimal controls.

scholarly journals Upper separated multifunctions in deterministic and stochastic optimal control

2017 ◽  
Vol 2 (2) ◽  
pp. 479-484 ◽  
Author(s):  
Jerzy Motyl
Keyword(s):  
Banach Space ◽  
Optimal Control ◽  
Banach Lattice ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Existence Of Solutions ◽  
Control Problems

AbstractLet X be a Banach space while (Y,⪯) a Banach lattice. We consider the class of “upper separated” set-valued functions F : X → 2Y and investigate the problem of the existence of order-convex selections of F. First, we present results on the existence of the Carathéodory-convex type selections of upper separated multifunctions and apply them to investigation of the existence of solutions of differential and stochastic inclusions. We will discuss the applicability of obtained selection results to some deterministic and stochastic optimal control problems.

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