Abstract The uncertain production-inventory problem with deteriorating items is investigated and an optimal control model developed in the present paper. perturbed by canonical process. Based on uncertainty theory, optimistic-value optimal-based established. study aims to find optimistic value of revenue at a certain confidence level. theory used obtain equation optimality. Using Hamilton–Jacob...

We explore the approximation of feedback control integro-differential equations containing a fractional Laplacian term. To obtain for state variable this nonlocal equation, we use Hamilton–Jacobi–Bellman equation. It is well known that approach suffers from curse dimensionality, and to mitigate problem couple semi-Lagrangian schemes discretization dynamic programming principle with Shepard appr...

We develop a theory for continuous-time non-Markovian stochastic control problems which are inherently time-inconsistent. Their distinguishing feature is that the classical Bellman optimality principle no longer holds. Our formulation cast within framework of controlled forward differential equation, and general objective functional setting. adopt game-theoretic approach to study such problems,...

This morphism sends probability calculus into optimal control problems. Therefore almost of the concepts introduced in probability calculus have an optimization counterpart. The purpose of this paper is to make a presentation of known and new results of optimal control with this morphism in mind. The emphasis of this talk is i) on the trajectory point of view by opposition to the cost point of ...

Inthispaper,wesolveHamilton-Jocobi-Bellman(HJB)equationsarisinginoptimalcontrolproblems usingHomotopyPerturbationTransformMethod(HPTM).Theproposedmethodisacombinedform oftheLaplaceTransformationMethodwiththeHomotopyPerturbationMethodtoproduceahighly effectivemethodtohandlemanyproblems. ApplyingtheHPTM,solutionprocedurebecomeseasier, simplerandmorestraightforward. Someillustrativeexamplesaregive...

<p style='text-indent:20px;'>This is a concise introduction to stochastic optimal control theory. We assume that the readers have basic knowledge of real analysis, functional elementary probability, ordinary differential equations and partial equations. will present following topics: (ⅰ) A brief presentation relevant results on analysis; (ⅱ) Formulation problems; (ⅲ) Variational method Po...

In this paper, we deal with a Cauchy problem for nonlinear fractional differential equation the Caputo derivative of order $$\alpha \in (0, 1)$$ . As initial data, consider pair consisting an point, which does not necessarily coincide inferior limit derivative, and function that determines values solution on interval from to point. We study differentiability properties functional associating da...