Related papers: Controlled Occupied Processes and Viscosity Soluti…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…
In this paper, we consider the wave equation with both a viscous Kelvin-Voigt and frictional damping as a model of viscoelasticity in which we incorporate an internal control with a moving support. We prove the null controllability when the…
We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded…
This paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A…
We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…
The master equation is a type of PDE whose state variable involves the distribution of certain underlying state process. It is a powerful tool for studying the limit behavior of large interacting systems, including mean field games and…
This paper presents a linear programming approach for the optimal control of nonlinear switched systems where the control is the switching sequence. This is done by introducing modal occupation measures, which allow to relax the problem as…
Inverse Optimal Control (IOC) seeks to recover an unknown cost from expert demonstrations, and it provides a systematic way of modeling experts' decision mechanisms while considering the prior information of the cost functions.…
Obtaining initial conditions and parameterizations leading to a model consistent with available measurements or safety specifications is important for many applications. Examples include model (in-)validation, prediction, fault diagnosis,…
In this paper, we consider the Cauchy problem for an inviscid compressible Oldroyd-B model in three dimensions. The global well posedness of strong solutions and the associated time-decay estimates in Sobolev spaces are established near an…
In this paper, we present a convex formulation of $H_{\infty}$-optimal control problem for coupled linear ODE-PDE systems with one spatial dimension. First, we reformulate the coupled ODE-PDE system as a Partial Integral Equation (PIE)…
In this paper, we consider the problem of optimizing the worst-case behavior of a partially observed system. All uncontrolled disturbances are modeled as finite-valued uncertain variables. Using the theory of cost distributions, we present…
The theory of dissipativity has been primarily developed for controllable systems/behaviors. For various reasons, in the context of uncontrollable systems/behaviors, a more appropriate definition of dissipativity is in terms of the…
In this paper, we aim to develop the theory of optimal stochastic control for branching diffusion processes where both the movement and the reproduction of the particles depend on the control. More precisely, we study the problem of…
This paper presents an intrinsic approach for addressing control problems with systems governed by linear ordinary differential equations (ODEs). We use computer algebra to constrain a Gaussian Process on solutions of ODEs. We obtain…
In this work, we consider the local Cahn-Hilliard-Navier-Stokes equation with regular potential in two dimensional bounded domain. We formulate distributed optimal control problem as the minimization of a suitable cost functional subject to…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…
Finite-dimensional observer-based controller design for PDEs is a challenging problem. Recently, such controllers were introduced for the 1D heat equation, under the assumption that one of the observation or control operators is bounded.…