We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly known joint probability distribution of the extremal processes. We also delineate circumstances under which the value of a stopping problem induces directly this...

We study optimal boundary control problems for the two-dimensional Navier–Stokes equations in an unbounded domain. Control is effected through the Dirichlet boundary condition and is sought in a subset of the trace space of velocity fields with minimal regularity satisfying the energy estimates. An objective of interest is the drag functional. We first establish three important results for inho...

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework, where boundary heat flux and free boundary are components of the control vector, and optimality criteria consists of the minimization of the sum of L2-norm ...

in this paper, a new numerical method is presented for solvingthe optimal control problems of bang-bang type with free or xed terminaltime. the method is based on bezier polynomials which are presented inany interval as [t0; tf ]. the problems are reduced to a constrained problemswhich can be solved by using lagrangian method. the constraints ofthese problems are terminal state and conditions....

‎in this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎the equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

in the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. for this purpose, we replace the problem with an alternative optimal control problem in which the switching t...

in acceptance-sampling plans, the items of an incoming lot are inspected one by one. if the number of nonconforming items in sample is equal zero, the lot is accepted but if the number of nonconforming items is equal to one, then second sample is taken and the policy of zero acceptance number would be applied for the second sample. in this paper, a mathematical model is developed to design sing...

We consider the optimal control problem for a (finite-dimensional) quantum system with an energy-like cost. We explore the limit of small control amplitude and construct an approximation to the two-point boundary value problem resulting from the Maximum Principle. By solving the approximate two-point boundary value problem in two examples, we argue that this limit corresponds to the limit of la...