相关论文: A uniform Tauberian theorem in optimal control

This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously…

We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the…

We consider a control system with dynamics which are affine in the (unbounded) derivative of the control $u$. We introduce a notion of generalized solution $x$ on $[0,T]$ for controls $u$ of bounded total variation on $[0,t]$ for every…

We consider a nonlinear control system depending on two controls u and v, with dynamics affine in the (unbounded) derivative of u, and v appearing initially only in the drift term. Recently, motivated by applications to optimization…

This paper is concerned with a linear quadratic (LQ, for short) optimal control problem with fixed terminal states and integral quadratic constraints. A Riccati equation with infinite terminal value is introduced, which is uniquely solvable…

The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this…

We establish the turnpike property for linear quadratic control problems for which the control operator is admissible and may be unbounded, under quite general and natural assumptions. The turnpike property has been well studied for bounded…

We investigate conditions of optimality for an infinite horizon control problem and consider their correspondence with the value function. Assuming Lipschitz continuity of the value function, we prove that sensitivity relations plus the…

We consider the Dirichlet problem u_t &= \Delta u + f(x, u, \nabla u)+ h(x, t),& \qquad &(x, t) \in \Omega \times (0, \infty), u &= 0, & \qquad &(x, t) \in \partial\Omega \times (0, \infty), on a bounded domain $\Omega \subset…

The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…

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…

This paper studies the long-time behavior of optimal solutions for a class of linear-convex optimal control problems. We focus on a partial exponential turnpike property, established without imposing controllability or stabilizability…

We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter $D$, the notions of $D$-compactness and of $D$-pseudocompactness…

In this paper we deal with infinite horizon optimal control problems. Basing on weak variations in an extremal problem in weighted function spaces we prove necessary conditions in form of the adjoint equation and a variational inequality.…

We consider the problem of finding a stopping time that minimises the $L^1$-distance to $\theta$, the time at which a L\'evy process attains its ultimate supremum. This problem was studied in [12] for a Brownian motion with drift and a…

In this paper we introduce the concept of universal stabilizability: the condition that every solution of a nonlinear system can be globally stabilized. We give sufficient conditions in terms of the existence of a control contraction…

For an $N \times T$ random matrix $X(\beta)$ with weakly dependent uniformly sub-Gaussian entries $x_{it}(\beta)$ that may depend on a possibly infinite-dimensional parameter $\beta\in \mathbf{B}$, we obtain a uniform bound on its operator…

We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general…

We first derive a general integral-turnpike property around a set for infinite-dimensional non-autonomous optimal control problems with any possible terminal state constraints, under some appropriate assumptions. Roughly speaking, the…

Let $\Delta$ be the Dirichlet Laplacian on the interval $(0,\pi)$, and let $T>0$. We prove a well-posedness results for the structurally damped beam equation $$u_{tt}+\Delta^2 u-\rho \Delta u_t=0, x\in (0,\pi),t>0$$ with various boundary…