Displaying similar documents to “Singularly perturbed set of periodic functional-differential equations arising in optimal control theory”

Periodic solutions of nth order delay Rayleigh equations

Gen-Qiang Wang, Sui Sun Cheng (2002)

Annales Polonici Mathematici

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A priori bounds are established for periodic solutions of an nth order Rayleigh equation with delay. From these bounds, existence theorems for periodic solutions are established by means of Mawhin's continuation theorem.

Periodic solutions for some delay differential equations appearing in models of power systems

Bingwen Liu, Lihong Huang (2005)

Annales Polonici Mathematici

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The authors use coincidence degree theory to establish some new results on the existence of T-periodic solutions for the delay differential equation x''(t) + a₁x'(t) + a₂(xⁿ(t))' + a₃x(t)+ a₄x(t-τ) + a₅xⁿ(t) + a₆xⁿ(t-τ) = f(t), which appears in a model of a power system. These results are of practical significance.

A notion of boundedness for hyperfunctions and Massera type theorems

Yasunori Okada (2012)

Banach Center Publications

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For some classes of periodic linear ordinary differential equations and functional equations, it is known that the existence of a bounded solution in the future implies the existence of a periodic solution. In order to think on such phenomena for hyperfunction solutions to linear functional equations, we introduced a notion of bounded hyperfunctions, and translated the problems into the problems on analytic solutions to some equations in complex domains. In this article,...

On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions

Denis Pennequin (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed...

On the Optimal Control of a Class of Time-Delay System

L. Boudjenah, M.F. Khelfi (2010)

Mathematical Modelling of Natural Phenomena

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In this work we study the optimal control problem for a class of nonlinear time-delay systems via paratingent equation with delayed argument. We use an equivalence theorem between solutions of differential inclusions with time-delay and solutions of paratingent equations with delayed argument. We study the problem of optimal control which minimizes a certain cost function. To show the existence of optimal control, we use the main topological...

On some topological methods in theory of neutral type operator differential inclusions with applications to control systems

Mikhail Kamenskii, Valeri Obukhovskii, Jen-Chih Yao (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.