Related papers: Analytical, Optimal, and Sparse Optimal Control of…
We consider the existence and first order conditions of optimality for a stochastic optimal control problem inspired by the celebrated FitzHugh-Nagumo model, with nonlinear diffusion term, perturbed by a linear multiplicative Brownian-type…
We present a method to control the position as a function of time of one-dimensional traveling wave solutions to reaction-diffusion systems according to a pre-specified protocol of motion. Given this protocol, the control function is found…
We investigate smooth and sparse optimal control problems for convective FitzHugh-Nagumo equation with travelling wave solutions in moving excitable media. The cost function includes distributed space-time and terminal observations or…
We consider the stability of position control of traveling waves in reaction-diffusion system as proposed in {[}J. L\"ober, H. Engel, arXiv:1304.2327{]}. Instead of analyzing the controlled reaction-diffusion system, stability is studied on…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
In various neurological disorders spatio-temporal excitation patterns constitute examples of excitable behavior emerging from pathological pathways. During migraine, seizure, and stroke an initially localized pathological state can…
This paper considers the problem of designing time-dependent, real-time control policies for controllable nonlinear diffusion processes, with the goal of obtaining maximally-informative observations about parameters of interest. More…
This paper is concerned with the well-posedness and optimal control problem of a reaction-diffusion system for an epidemic Susceptible-Infected-Recovered-Susceptible (SIRS) mathematical model in which the dynamics develops in a spatially…
In this work, we study the control constrained distributed optimal control of a stationary doubly diffusive flow model. For the control problem, we use a well-posedness analysis based on minimal assumptions on data and domain. We show the…
We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems. To solve proposed optimal control problems numerically, we…
We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A…
Travelling wave solutions of reaction-diffusion equations are widely used to model the spatial spread of populations and other phenomena in biology and physics. In this article, we reinterpret the classical variational principle approach…
We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal…
The Fitzhugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing to better understand the essential dynamics of the interaction of the membrane potential and the restoring force and to capture,…
Traveling localized spots represent an important class of self-organized two-dimensional patterns in reaction-diffusion systems. We study open-loop control intended to guide a stable spot along a desired trajectory with desired velocity.…
A distributed optimal control problem with final observation for a three- dimensional Lagrange averaged Navier-Stokes-? model is studied. The solvability of the optimal control problem is proved and the first-order optimality conditions are…
In the present paper we derive the existence and uniqueness of a solution for the optimal control problem determined by a stochastic FitzHugh-Nagumo equation with recovery variable. In particular due the cubic non-linearity in the drift…
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
Diffusion-based planning, learning, and control methods present a promising branch of powerful and expressive decision-making solutions. Given the growing interest, such methods have undergone numerous refinements over the past years.…