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...

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 paper we solve a finite-horizon partially observed risk-sensitive stochastic optimal control problem for discrete-time nonlinear systems and obtain small noise and small risk limits. The small noise limit is interpreted as a deterministic partially observed dynamic game, and new insights into the optimal solution of such game problems are obtained. Both the risk-sensitive stochastic con...

The notes derive the salient features of optimal control theory for an infinite horizon objective function. For concreteness, the necessary and sufficient conditions are derived with reference to the neoclassical model of growth. However, the ideas easily extend to other economic problems. The need for the exercise arises from the lack of a single source which students can access for a developm...