Related papers: Neural ODE Control for Trajectory Approximation of…
We propose a numerical method to approximate the exact averaged boundary control of a family of wave equations depending on an unknown parameter sigma. More precisely the control, independent of sigma, that drives an initial data to a…
This the text of a proceeding accepted for the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). We present some results of an ongoing research on the controllability problem of an abstract bilinear…
We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique…
The widespread adoption of deep learning models places demands on their robustness. In this paper, we consider the robustness of deep neural networks on videos, which comprise both the spatial features of individual frames extracted by a…
Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…
We propose a novel Branch-and-Bound method for reachability analysis of neural networks in both open-loop and closed-loop settings. Our idea is to first compute accurate bounds on the Lipschitz constant of the neural network in certain…
We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objects, but its computational cost becomes prohibitive when the…
Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…
Robust control problems have significant practical implications since external disturbances can significantly impact the performance of control methods. Existing robust control methods excel at control-affine systems but fail at neural…
We consider the motion of several rigid bodies immersed in a two-dimensional incompressible perfect fluid. The motion of the rigid bodies is given by the Newton laws with forces due to the fluid pressure and the fluid motion is described by…
In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In…
Optimal Control (OC) is the process of determining control and state trajectories for a dynamic system, over a period of time, in order to optimize a given performance index. With the increasing of variables and complexity, OC problems can…
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…
Existing algorithms for the optimal control of quantum observables are based on locally optimal steps in the space of control fields, or as in the case of genetic algorithms, operate on the basis of heuristics that do not explicitly take…
We consider the internal control of linear parabolic equations through on-off shape controls, i.e., controls of the form $M(t)\chi_{\omega(t)}$ with $M(t) \geq 0$ and $\omega(t)$ with a prescribed maximal measure. We establish small-time…
This paper studies the internal control of the Korteweg-de Vries-Burgers (KdVB) equation on a bounded domain. The diffusion coefficient is time-dependent and the boundary conditions are mixed in the sense that homogeneous Dirichlet and…
Suspensions of rodlike objects in a liquid are encountered in many areas of science and technology and the need to orientate them is extremely important to enhance or inhibit certain chemical reactions between them, other chemicals or with…
We study a property of dynamic optimization (DO) problems (as those encountered in model predictive control and moving horizon estimation) that is known as exponential decay of sensitivity (EDS). This property indicates that the sensitivity…
Many normalizing flow architectures impose regularity constraints, yet their distributional approximation properties are not fully characterized. We study the expressivity of bi-Lipschitz normalizing flows through the lens of score-based…
This paper addresses the study of the hierarchical control for the one-dimensional wave equation in intervals with a moving boundary. This equation models the motion of a string where an endpoint is fixed and the other one is moving. When…