This paper joins some concepts that appear in Mechanics, Field Theory, Differential Geometry and Control Theory in order to solve multitime optimal control problems with area integral costs on boundary. Section 1 recalls the multitime maximum principle in the sense of the first author. The main results in Section 2 include the needle-shaped control variations, the adjoint PDEs, the behavior of ...

In this paper we show a simplified optimisation approach for free boundary problems in arbitrary space dimensions. This approach is mainly based on an extended operator splitting which allows a decoupling of the domain deformation and solving the remaining partial differential equation. First we give a short introduction to free boundary problems and the problems occurring in optimisation. Then...

Various optimal control problems of infinite dimensional systems with point and distributed delays were considered in [1], [2], [3], [5], [6], [7], [8], [9], [10] and [15]. In [15], optimal control problems for parabolic systems with Neumann boundary conditions involving constant time delays were considered. Such systems constitute in a linear approximation, a universal mathematical model for m...

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics, which describes the boundary conditions of the internal system. In other terms, we are concerned with non standard boundary conditi...

Perturbations in optimal control problems are discussed. Problems including those with state and/or control constraints and discontinuities are considered. The pcrturbations may appear in the functional, as well as in the dynamics, the boundary conditions or the inequality constraints. It is shown that an optimal solution of the disturbed control problem depending continuously differentiably up...

Temporal patterns for advertising include constant spending over time, decreasing spending over time and increasing spending over time. This research shows that all these spending patterns emerge at optimality for the same response function dynamics, due to differences in salvage value assumptions. I use these results to develop a methodology for determining the optimal planning horizon length ...

This paper derives linear quadratic regulator (LQR) results for boundary controlled parabolic partial differential equations (PDEs) via weak-variations. Research on optimal control of PDEs has a rich 40-year history. This body of knowledge relies heavily on operator and semigroup theory. Our research distinguishes itself by deriving existing LQR results from a more accessible set of mathematics...

We consider a generalized-Newtonian fluid with defective boundary conditions where only flow rates or mean pressures are prescribed on parts of boundary. The defect boundary condition problem is formulated as an optimal control problem in which a Neumann or Dirichlet boundary control is used for matching given flow rates or mean pressures. For the constrained optimization problem an optimality ...

A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the value function is C and its directional derivatives are the value functions of certain optimal stopping problems. Guided by the optimal stopping problem we then introduce the associated no-action region and the free boundary and show that, under appropriate conditions, an optimally contro...

In the paper we investigate solvability of nonlinear optimal Thermal and Diffusion processes control problems defined by semi-linear parabolic equations when the source function nonlinearly depends on the controlling parameters, and nonlinear integral criterion of quality is minimized. We obtained the sufficient conditions of uniqueness of the solution of the boundary value problem and the adjo...