Related papers: Optimal distributed control of a diffuse interface…
A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid…
We a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential…
The paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system. The operators appearing in the system equations were fractional…
In this paper, we study a phase-space analysis of a mathematical model of tumor growth with an immune response. Mathematical analysis of the model equations with multipoint initial condition, regarding to dissipativity, boundedness of…
In this paper, a tractable methodology is proposed to approximate stochastic optimal feedback treatment in the context of mixed immuno-chemo therapy of cancer. The method uses a fixed-point value iteration that approximately solves a…
The emergence of mutant lineages within a viral species has become a public health problem, as the existing treatments and drugs are usually more effective on the original lineages than in the mutant ones. The following manuscript presents…
This paper is concerned with the designing, analyzing and implementing linear and nonlinear discretization scheme for the distributed optimal control problem (OCP) with the Cahn-Hilliard (CH) equation as constrained. We propose three…
In this work we are interested in the modelling and control of opinion dynamics spreading on a time evolving network with scale-free asymptotic degree distribution. The mathematical model is formulated as a coupling of an opinion alignment…
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…
We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the…
This paper is concerned with a boundary control problem for the Cahn--Hilliard equation coupled with dynamic boundary conditions. In order to handle the control problem, we restrict our analysis to the case of regular potentials defined on…
We consider a one--spatial dimensional tumour growth model [2, 3, 4] that consists of three dependent variables of space and time: volume fraction of tumour cells, velocity of tumour cells, and nutrient concentration. The model variables…
The focus of this paper is directed towards optimal control of multi-agent systems consisting of one leader and a number of followers in the presence of noise. The dynamics of every agent is assumed to be linear, and the performance index…
Distributed optimization algorithms are used in a wide variety of problems involving complex network systems where the goal is for a set of agents in the network to solve a network-wide optimization problem via distributed update rules. In…
The spread of metastases is a crucial process in which some questions remain unanswered. In this work, we focus on tumor cells circulating in the bloodstream, the so-called Circulating Tumor Cells (CTCs). Our aim is to characterize their…
This study proposes an effective positive control design strategy for cancer treatment by resorting to the combination of immunotherapy and chemotherapy. The treatment objective is to transfer the initial number of tumor cells and…
The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev and Zubik-Kowal (2011). The model is described by a system composed of four partial differential equations that represent the evolution of the…
Controlled one-dimensional diffusion processes, with infinitesimal variance (instead of the infinitesimal mean) depending on the control variable, are considered in an interval located on the positive half-line. The process is controlled…
The paper treats the problem of optimal distributed control of a Cahn-Hilliard-Oono system in $\mathbb{R}^d$, $1\leq d\leq 3$, with the control located in the mass term and admitting general potentials that include both the case of a…
Achieving global optimality in nonlinear model predictive control (NMPC) is challenging due to the non-convex nature of the underlying optimization problem. Since commonly employed local optimization techniques depend on carefully chosen…