SIAM Journal on Control and Optimization

We consider a problem of optimal distribution of conductivities in a system governed by a nonlocal diffusion law. The problem stems from applications in optimal design and more specifically topology optimization. We propose a novel parametrization of ...

We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game. We place ourselves ...

We address a long-standing open problem in risk theory, namely finding the optimal strategy to pay out dividends from an insurance surplus process if the dividends are paid according to a dividend rate that is not allowed to decrease. The optimality ...

A classical problem in stochastic ergodic control consists of studying the limit behavior of the optimal value of a discounted integral in infinite horizon (the so called Abel mean of an integral cost) as the discount factor $\lambda$ tends to zero ...

This paper examines the Root solution of the Skorokhod embedding problem given full marginals on some compact time interval. Our results are obtained by limiting arguments based on the finitely many marginals Root solution of Cox, Obłój, and Touzi [...

We show in this article how perturbative approaches from N. Burq and M. Hitrik [Math. Res. Lett., 14 (2007), pp. 35--47] and the black box strategy from N. Burq and M. Zworski [J. Amer. Math. Soc., 17 (2004), pp. 443--471] allow us to obtain decay rates for ...

We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path dependency is the novelty of the model and leads to an ...

In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the total energy of solutions can be controlled by the energy localized in a ...

An optimal control problem for a semilinear elliptic equation is discussed, where the control appears nonlinearly in the state equation but is not included in the objective functional. The existence of optimal controls is proved by a measurable selection ...

This paper explores the design problem of consensus algorithms in a class of convex geometric metric spaces. Using the techniques of convex analysis and possibility analysis, a simple assumption for designing consensus algorithms in a strict max-convex ...

Regularized approaches have been successfully applied to linear system identification in recent years; many of them model unknown impulse responses exploiting the so-called Reproducing Kernel Hilbert Spaces (RKHSs) that enjoy the notable property of being in ...

This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous- and discrete-time filters for stochastic dynamic systems with nonlinear state dynamics and linear measurements under certain strong ...

In this paper we study an Ergodic Markovian BSDE involving a forward process $X$ that solves an infinite dimensional forward stochastic evolution equation with multiplicative and possibly degenerate diffusion coefficient. A concavity assumption on the ...

We analyze linear McKean--Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-...

Unlike output-controllability of linear systems which is a consequence of controllability, the output-controllability problems of nonlinear systems can be much more difficult than the controllability problems. Thus, it is a challenging task to derive ...

The proportional-integral (PI) boundary stabilization of nonlinear hyperbolic systems of balance laws is investigated for the $H^2$-norm, in which the control and output measurements are all located at the boundaries. The boundary conditions of the system ...

In this paper, we obtain the maximum principle for optimal controls of stochastic systems with jumps by introducing a new method of variation. The control is allowed to enter both diffusion and jump terms and the control domain need not be convex.

In this paper, we establish spectral inequalities on measurable sets of positive Lebesgue measure for the Stokes operator, as well as observability inequalities on space-time measurable sets of positive measure for nonstationary Stokes system. The latter ...

The aim of this work is to study an optimal control problem with state constraints where the state is given by an age-structured, abstract parabolic differential equation. We prove the existence and uniqueness of solution for the state equation and ...

This paper deals with the optimal control of an obstacle problem where the control variable is the obstacle. The state system is described by a class of quasilinear elliptic variational inequalities with nonmonotone and nonsmooth perturbations. The cost ...

In this paper, we propose a novel space semidiscretized finite difference scheme for approximation of the one-dimensional wave equation under boundary feedback. This scheme, referred to as the order reduction finite difference scheme, does not use numerical ...

In optimal control problems, often initial data are required that are not known exactly in practice. In order to take into account this uncertainty, we consider optimal control problems for a system with an uncertain initial state. A finite terminal time is ...

An ergodic Bellman's (Hamilton--Jacobi--Bellman) equation is proved for a uniformly ergodic one-dimensional controlled diffusion with variable diffusion and drift coefficients both depending on control; convergence of the values provided by Howard's ...

We present an emergent stochastic flocking dynamics of the Cucker--Smale (CS) ensemble under randomly switching network topologies. The evolution of the CS ensemble with randomly switching topologies involves two random components (switching times and ...

Penalization of Dirichlet boundary controlled nonstationary magneto-hydrodynamic equations is considered. Asymptotic behavior of solutions of a penalized control problem with respect to the penalty parameter is investigated. It is proved that solutions of ...

We here consider optimal control problems governed by nonlinear stochastic equations on a Hilbert space $H$ with nonconvex payoff, which is rewritten as a deterministic optimal control problem governed by a Kolmogorov equation in $H$. We prove the existence ...

This paper is concerned with the study of local decay rates of the energy associated to a semilinear wave equation in an inhomogeneous medium with frictional localized damping. The problem is considered in $\Omega\subset \mathbb{R}^n$, an open, bounded, ...

In this paper we consider long-run risk-sensitive average cost impulse control applied to a continuous-time Feller--Markov process. Using the probabilistic approach, we show how to get the solution to a suitable continuous-time Bellman equation and link it ...

We consider average-cost Markov decision processes (MDPs) with Borel state and action spaces and universally measurable policies. For the nonnegative cost model and an unbounded cost model with a Lyapunov-type stability character, we introduce a set of ...

We introduce and solve a new type of quadratic backward stochastic differential equation (BSDE) systems defined in an infinite time horizon, called ergodic BSDE systems. Such systems arise naturally as candidate solutions to characterize forward performance ...