Related papers: Trajectory stabilization of nonlocal continuity eq…
This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier-Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence…
The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
A new class of control problems is discussed - homeostasis control. Homeostasis control problems can be considered as control problems with a given target set, in particular, as a problem of stabilizing the values of some target function,…
Formation control deals with the design of decentralized control laws that stabilize mobile, autonomous agents at prescribed distances from each other. We call any configuration of the agents a target configuration if it satisfies the…
We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…
Feedback asymptotic stabilization of control systems is an important topic of control theory and applications. Broadly speaking, if the system $\dot{x} = f(x,u)$ is locally asymptotically stabilizable, then there exists a feedback control…
Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…
This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions.…
We consider the Navier-Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and…
We study the backstepping stabilization of higher order linear and nonlinear Schr\"odinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a…
This project investigates the approximate controllability of a class of stochastic integrodifferential equations in Hilbert space with non-local beginning conditions. In a departure from the conventional concerns expressed in the…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore,…
In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich…
The authors consider stochastic aspects of the stabilization problem for two and three-dimensional Oseen equations with help of feedback control defined on a part of the fluid boundary. Stochastic issues arise when inevitable unpredictable…
A fundamental control problem for autonomous vehicle formations is formation shape control, in which the agents must maintain a prescribed formation shape using only information measured or communicated from neighboring agents. While a…
The stabilization of nonlinear systems under zero-state-detectability assumption or its analogues is considered. The proposed supervisory control provides a finite time practical stabilization of output and it is based on uniting local and…