Related papers: Differentiability of the value function in control…
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…
In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together with previous…
An optimal control problem for a semilinear elliptic equation of divergence form is considered. Both the leading term and the semilinear term of the state equation contain the control. The well-known Pontryagin type maximum principle for…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
We show that infinitely differentiable solutions to parabolic and hyperbolic equations, whose right-hand sides are analytical in time, are also analytical in time at each fixed point of the space. These solutions are given in the form of…
In this paper, we are concerned with local controllability properties of degenerate parabolic equations in bounded domains that evolve in time. More precisely, we deal with the exact controllability to a positive trajectory of a…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
We study the optimal value function for control problems on Banach spaces that involve both continuous and discrete control decisions. For problems involving semilinear dynamics subject to mixed control inequality constraints, one can show…
In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to…
We study the problem of controlling the initial condition of a vibrating beam. The optimal control problem seeks to determine solutions of initial velocity that assure the approach of the state of the beam to a given target function in the…
In this article, we prove second-order necessary optimality conditions for the so-called time crisis problem that comes up within the context of viability theory. It consists in minimizing the time spent by solutions of a controlled…
A class of optimal control problems governed by semilinear parabolic equations with mixed constraints and a box constraint for control variable is considered. We show that if the separation condition is satisfied, then both optimality…
An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…
Given an optimal control problem on a heterogeneous body with a periodical structure of particles depending on a small parameter e, we study the asymptotic behavior, as e converges to zero, of the optimal control functional and the optimal…
In this article we study a controllability problem for a parabolic and a hyperbolic partial differential equations in which the control is the shape of the domain where the equation holds. The quantity to be controlled is the trace of the…
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…
In this note, we consider an optimal control problem associated to a differential equation driven by a H\"{o}lder continuous function g of index greater than 1/2. We split our study in two cases. If the coefficient of dg\_t does not depend…