Related papers: Closed-loop control of a reaction-diffusion system
We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient…
In this paper, we explore the solvability and the optimal control problem for a compartmental model based on reaction-diffusion partial differential equations describing a transmissible disease. The nonlinear model takes into account the…
Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions…
We derive a stochastic partial differential equation that describes the fluctuating behaviour of reaction-diffusion systems of N particles, undergoing Markovian, unary reactions. This generalises the work of Dean [J. Phys. A: Math. and…
In this paper we are concerned with the approximate controllability of a multidimensional semilinear reaction-diffusion equation governed by a multiplicative control, which is locally distributed in the reaction term. For a given initial…
In this paper we present a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure. We view the nonlinear systems as composed of a finite number of ``pieces,'' which are interpolated by…
We consider a $n \times n$ nonlinear reaction-diffusion system posed on a smooth bounded domain $\Omega$ of $\mathbb{R}^N$. This system models reversible chemical reactions. We act on the system through $m$ controls ($1 \leq m < n$),…
Reaction-diffusion systems are ubiquitous in nature and in engineering applications, and are often modeled using a non-linear system of governing equations. While robust numerical methods exist to solve them, deep learning-based reduced…
A general result on the method of randomized stopping is proved. It is applied to optimal stopping of controlled diffusion processes with unbounded coefficients to reduce it to an optimal control problem without stopping. This is motivated…
In this paper, we present an approach to characterising fast-reaction limits of systems with nonlinear diffusion, when there are either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local…
Control of open quantum systems is an essential ingredient to the realization of contemporary quantum science and technology. We demonstrate such control by employing a thermodynamically consistent framework, taking into account the fact…
We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed…
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small nonequilibrium systems. While work and heat are equally important forms of energy exchange, fluctuation relations have not been experimentally…
The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data. Building on the recent development of the Koopman model…
Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical concentrations and cell biology. We present a space-time…
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…
We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the…
In this paper, we consider an expanding construction of a distributed control system, which is obtained by adding a new subsystem one after the other, until all $n$ subsystems, where $n \ge 2$, are included in the distributed control…
This note deals with the boundary control problem of a nonhomogeneous flexible wing evolving under unsteady aerodynamic loads. The wing is actuated at its tip by flaps and is modeled by a distributed parameter system consisting of two…