scholarly journals Linear-quadratic control for a class of stochastic Volterra equations: Solvability and approximation

2021 ◽  
Vol 31 (5) ◽  
Author(s):  
Eduardo Abi Jaber ◽  
Enzo Miller ◽  
Huyên Pham
Keyword(s):  
Volterra Equations ◽  
Linear Quadratic Control ◽  
Linear Quadratic

scholarly journals Control and the Analysis of Cancer Growth Models

2018 ◽  
Author(s):  
Allen Tannenbaum ◽  
Tryphon Georgiou ◽  
Joseph Deasy ◽  
Larry Norton
Keyword(s):  
Tumor Cell ◽  
Growth Models ◽  
Point Of View ◽  
Cancer Growth ◽  
Volterra Equations ◽  
Linear Quadratic Control ◽  
Dynamical Models ◽  
Linear Quadratic ◽  
Tumor Cell Population ◽  
Theoretic Point

AbstractIn this note, we analyze two cancer dynamical models from a system-theoretic point of view. The first model is based upon stochastic controlled versions of the classical Lotka-Volterra equations. Here we consider from a controls point of view the utility of employing ultrahigh dose flashes in radiotherapy. The second is based on work of Norton-Simon-Massagué growth model that takes into account the heterogeneity of a tumor cell population. We indicate an optimal strategy based on linear quadratic control applied to a linear transformed model.

scholarly journals Optimal Control with Partial Information for Stochastic Volterra Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-25 ◽  
Author(s):  
Bernt øksendal ◽  
Tusheng Zhang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Problem ◽  
Partial Information ◽  
Volterra Equations ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Stochastic Delay ◽  
Stochastic Delay Equations ◽  
Linear Quadratic Control Problem

In the first part of the paper we obtain existence and characterizations of an optimal control for a linear quadratic control problem of linear stochastic Volterra equations. In the second part, using the Malliavin calculus approach, we deduce a general maximum principle for optimal control of general stochastic Volterra equations. The result is applied to solve some stochastic control problem for some stochastic delay equations.

Sign in / Sign up

Export Citation Format

Share Document