Related papers: Inverse extremal problem for an anti-tumor therapy…
Adaptive therapy is a recent paradigm in cancer treatment aiming at indefinite, safe containment of the disease when cure is judged unattainable. In modeling this approach, inherent limitations arise due to the structure of the vector…
We study a model introduced by Perthame and Vauchelet that describes the growth of a tumor governed by Brinkman's Law, which takes into account friction between the tumor cells. We adopt the viscosity solution approach to establish an…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
The goal of cancer immunotherapy is to boost a patient's immune response to a tumor. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumor microenvironment,…
In this paper, we consider a stochastic recursive optimal control problem under model uncertainty. In this framework, the cost function is described by solutions of a family of backward stochastic differential equations. With the help of…
We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
We apply innovative mathematical tools coming from optimal control theory to improve theoretical and experimental techniques in Magnetic Resonance Imaging (MRI). This approach allows us to explore and to experimentally reach the physical…
We pursue a computational analysis of the biomedical problem on the identification of the cancerous tumor at an early stage of development based on the Electrical Impedance Tomography (EIT) and optimal control of elliptic partial…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…
This work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy as well as immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population…
An optimal control problem for the continuity equation is considered. The aim of a controller is to maximize the total mass within a target set at a given type moment. An iterative numerical algorithm for solving this problem is presented.
We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…
In the present work we investigate an optimal control problem related to the following chemotaxis-consumption model in a bounded domain $\Omega\subset \mathbb{R}^3$: $$\partial_t u - \Delta u = - \nabla \cdot (u \nabla v), \quad \partial_t…
This paper deals with the classic radiotherapy dose fractionation problem for cancer tumors concerning the following goals: a) To maximize the effect of radiation on the tumor, restricting the effect produced to the organs at risk (healing…
This paper addresses the inverse optimal control for the linear quadratic tracking problem with a fixed but unknown target state, which aims to estimate the possible triplets comprising the target state, the state weight matrix, and the…
Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address…
In this paper, we consider the inverse optimal control problem for the discrete-time linear quadratic regulator, over finite-time horizons. Given observations of the optimal trajectories, and optimal control inputs, to a linear…