Related papers: Optimal control for the infinity obstacle problem
We study the turnpike phenomenon for optimal control problems with mean field dynamics that are obtained as the limit $N\rightarrow \infty$ of systems governed by a large number $N$ of ordinary differential equations. We show that the…
We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate…
We consider a system that is exactly controllable. For given initial state, terminal state and objective function, an optimal control is often well-defined. Such an optimal control has the disadvantage that although it works perfectly well…
We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present…
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…
An imbalanced rotor is considered. A system of moving balancing masses is given. We determine the optimal movement of the balancing masses to minimize the imbalance on the rotor. The optimal movement is given by an open-loop control solving…
In this paper we consider an optimal control problem (OCP) for the coupled system of a nonlinear monotone Dirichlet problem with matrix- valued non-smooth controls in coefficients and a nonlinear equation of Ham- merstein type. Since…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
The problems of optimizing the value of an arbitrary observable of the two-level system at both a fixed time and the shortest possible time is theoretically explored. Complete identification and classification along with comprehensive…
In this paper we discuss the obstacle problem for the $p$-Laplace operator. We prove optimal growth results for the solution. Of particular interest is the point-wise regularity of the solution at free boundary points. The most surprising…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of…
In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for…
We address Newton-type problems of minimal resistance from an optimal control perspective. It is proven that for Newton-type problems the Pontryagin maximum principle is a necessary and sufficient condition. Solutions are then computed for…
We consider an optimal control problem $\cQ$ governed by an elliptic quasivariational inequality with unilateral constraints. The existence of optimal pairs of the problem is a well known result, see \cite{SS}, for instance. We associate to…
This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…
In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set…
In optimal control theory, infimum gap means that there is a gap between the infimum values of a given minimum problem and an extended problem, obtained by enlarging the set of original solutions and controls. The gap phenomenon is somewhat…
We study a linear quadratic optimal control problem with stochastic coefficients and a terminal state constraint, which may be in force merely on a set with positive, but not necessarily full probability. Under such a partial terminal…
The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first…