Local controllability and optimal control for a model of combined anticancer therapy with control delays

DOI10.3934/mbe.2017013zbMath1351.93018OpenAlexW2530601300WikidataQ50544120 ScholiaQ50544120MaRDI QIDQ335260

Jerzy Klamka, Helmut Maurer, Andrzej Swierniak

Publication date: 2 November 2016

Published in: Mathematical Biosciences and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mbe.2017013

zbMATH Keywords

discretizationoptimal controloptimality conditionsnonlinear programminglocal controllabilitycombined cancer therapycontrol delays

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Controllability (93B05) Applications of optimal control and differential games (49N90) Numerical methods based on nonlinear programming (49M37) Dynamical systems in biology (37N25) Medical applications (general) (92C50) Existence theories for optimal control problems involving ordinary differential equations (49J15) Control/observation systems governed by ordinary differential equations (93C15) Discrete approximations in optimal control (49M25) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items

Optimal control of a delayed HIV model ⋮ Modeling of tumor growth incorporating the effects of necrosis and the effect of Bevacizumab ⋮ Closed-loop control of tumor growth by means of anti-angiogenic administration ⋮ Optimal control problems with time delays: two case studies in biomedicine

Uses Software

• AMPL
• Ipopt

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal scheduling of radiotherapy and angiogenic inhibitors
• Theory and applications of optimal control problems with multiple time-delays
• Geometric optimal control. Theory, methods and examples
• Analysis of the Hopf bifurcation for the family of angiogenesis models
• On the optimality of singular controls for a class of mathematical models for tumor anti-angiogenesis
• On optimal delivery of combination therapy for tumors
• SQP-methods for solving optimal control problems with control and state constraints: Adjoint variables, sensitivity analysis and real-time control
• Chemotherapy of vascularised tumours: role of vessel density and the effect of vascular ``pruning
• Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis
• Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999)
• Constrained controllability of nonlinear systems
• Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy
• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
• Local Controllability of Models of Combined Anticancer Therapy with Delays in Control
• Comparison of six models of antiangiogenic therapy
• AntiAngiogenic Therapy in Cancer Treatment as an Optimal Control Problem
• Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment
• A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy
• Controllability in Linear Autonomous Systems with Positive Controllers
• Simple ODE models of tumor growth and anti-angiogenic or radiation treatment