Related papers: Homogenization Results for a Deterministic Multi-d…
In this paper we study homogenization of a class of control problems in a stationary and ergodic random environment. This problem has been mostly studied in the calculus of variations setting in connection to the homogenization of the…
A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…
This article is the starting point of a series of works whose aim is the study of deterministic control problems where the dynamic and the running cost can be completely different in two (or more) complementary domains of the space $\R^N$.…
We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function…
We consider the homogenization of an optimal control problem in which the control is placed on a part of the boundary and the spatial domain contains a thin layer of "small particles", very close to the controlling boundary, and a Robin…
To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…
We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
We revisit the pioneering work of Bressan \& Hong on deterministic control problems in stratified domains, i.e. control problems for which the dynamic and the cost may have discontinuities on submanifolds of R N . By using slightly…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…
We consider optimal control problems with integer-valued controls and a total variation regularization penalty in the objective on domains of dimension two or higher. The penalty yields that the feasible set is sequentially closed in the…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…
In optimal control problems defined on stratified domains, the dynamics and the running cost may have discontinuities on a finite union of submanifolds of RN. In [8, 5], the corresponding value function is characterized as the unique…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
Mean field optimal control problems are a class of optimization problems that arise from optimal control when applied to the many body setting. In the noisy case one has a set of controllable stochastic processes and a cost function that is…
This paper investigates a new class of homogeneous stochastic control problems with cone control constraints, extending the classical homogeneous stochastic linear-quadratic (LQ) framework to encompass nonlinear system dynamics and…