We develop a dynamic optimal control model of a fashion designer’s challenge of maintaining brand image in the face of short-term pro…t opportunities through expanded sales that risk brand dilution in the longer-run. The key state variable is the brand’s reputation, and the key decision is sales volume. Depending on the brand’s capacity to command higher prices, one of two regimes is observed. ...

In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to...

The exchange between an elected politician, such as a president, prime minister or a local governor and interest groups is analyzed as an optimization problem. The optimal control model shows the conditions required from regulatory policy and resource investment in order to maximize the politician’s utility from the interest group’s support. Given one interest group, such a policy includes two ...

We study the problem of manipulation of the men-proposing Gale-Shapley algorithm by a single woman via permutation of her true preference list. Our contribution is threefold: First, we show that the matching induced by an optimal manipulation is stable with respect to the true preferences. Second, we identify a class of optimal manipulations called inconspicuous manipulations which, in addition...

This paper deals with multiobjective optimization techniques for a class of hybrid optimal control problems in mechanical systems. We deal with general nonlinear hybrid control systems described by boundary-value problems associated with hybrid-type Euler-Lagrange or Hamilton equations. The variational structure of the corresponding solutions makes it possible to reduce the original “mechanical...

In this article, we study the initial-boundary-value problem for a sixth-order Cahn-Hilliard type equation ut = D μ, μ = γDu− a(u)Du− a′(u) 2 |Du| + f(u) + kut, which describes the separation properties of oil-water mixtures, when a substance enforcing the mixing of the phases is added. The optimal control of the sixth order Cahn-Hilliard type equation under boundary condition is given and the ...

The purpose of this paper is to present the solution of time-optimal problem of the controlled object u x f y y x + = = ) ( , ! ! , u ≤ 1 and motion resistance function f x x f x A x ( ) , ( ) = ≤ = − > 0 0 0 if if where 0 1 ≤ < A . In the formula of f x ( ) there exists a value A= b A = 2 2 − that plays an essential role. Namely, if A≤ b A then the time-optimal control process is typical. For ...

The quite usual and often assumption in the theory of optimal control is the fixed or given initial state. Such assumption enables, at least on the primary stages, to simplify certain results. Anyhow, there exists a number of problems for which this assumption is not met. Let us mention the class of periodic problems having the direct dependence between initial and final states. Other examples ...

This paper deals with the boundary control problem of a nonhomogeneous flexible wing evolving under unsteady aerodynamic loads. The wing is actuated at its tip by flaps and is modeled by a distributed parameter system consisting in two coupled partial differential equations. Based on the proposed boundary control law, the well-posedness of the underlying Cauchy problem is first investigated by ...

In this article, we introduce a novel three-step approach for solving optimal control problems in space mission design. We demonstrate its potential by the example task of sending a group of spacecraft to a specific Earth L2 Halo orbit. In each of the three steps we make use of recently developed optimization methods and the result of one step serves as input data for the subsequent one. Firstl...