Related papers: Dimension reduction for large-scale stochastic sys…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
We explore the effect of stochastic resetting on the first-passage properties of space-dependent diffusion in presence of a constant bias. In our analytically tractable model system, a particle diffusing in a linear potential…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
We present a Stochastic Model Predictive Control (SMPC) framework for linear systems subject to Gaussian disturbances. In order to avoid feasibility issues, we employ a recent initialization strategy, optimizing over an interpolation of the…
Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order $1$ for Dirichlet boundary conditions and to order $1.5$ for Neumann and Robin boundary…
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…
This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…
Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…
In this paper, we study a multi-objective inverse initial problem with a Nash strategy constraint for forward stochastic reaction-diffusion equations with dynamic boundary conditions, where both the volume and surface equations are…
We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…
Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…
We present and analyze a first order least squares method for convection dominated diffusion problems, which provides robust L2 a priori error estimate for the scalar variable even if the given data f in L2 space. The novel theoretical…
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps $\Delta x$, $\Delta t$ in space and time, respectively. By applying large-deviation theory on the…
General distribution steering is intrinsically an infinite-dimensional problem, when the continuous distributions to steer are arbitrary. We put forward a moment representation of the primal system for control in [42]. However, the system…
Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling…
Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed…