Related papers: The inverse problem for rough controlled different…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The…
We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
We study controlled differential equations driven by a rough path (in the sense of T. Lyons) with an additional, possibly unbounded drift term. We show that the equation induces a solution flow if the drift grows at most linearly.…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
The need to control the residual of a potentially nonlinear function $\mathcal{F}$ arises in several situations in mathematics. For example, computing the zeros of a given map, or the reduction of some cost function during an optimization…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…
We continue the approach in Part I \cite{duchong19} to study stationary states of controlled differential equations driven by rough paths, using the framework of random dynamical systems and random attractors. Part II deals with driving…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
Based on the notion of paracontrolled distributions, we provide existence and uniqueness results for rough Volterra equations of convolution type with potentially singular kernels and driven by the newly introduced class of convolutional…
Direct and inverse initial-boundary problems on a bounded interval for systems of quasilinear evolution equations with general nonlinearities are considered. In the case of inverse problems conditions of integral overdetermination are…
We study controlled differential equations with unbounded drift terms, where the driving paths is $\nu$ - H\"older continuous for $\nu \in (\frac{1}{3},\frac{1}{2})$, so that the rough integral are interpreted in the Gubinelli sense…
This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but…
Originating from the mathematical modelling of rainfall infiltration, we derive the solution of an initial-boundary value problem of a linear evolution partial differential equation, by using the Fokas method. We present numerical examples…
An extended quadratic function is a quadratic function plus the indicator function of an affine set, that is, a quadratic function with embedded linear equality constraints. We show that, under some technical conditions, random convex…