© 2015

Optimal Control for Mathematical Models of Cancer Therapies

An Application of Geometric Methods

  • Applies geometric optimal control to real life problems arising in cancer research, for the first time published in book form

  • Combines rigorous mathematical analysis with biomedical background and interpretations

  • Detailed complete solutions of optimal control problems for mathematically challenging, up-to-date biomedical models

  • Outcomes of elaborate constructions of solutions provide insights into design of optimal protocols and at the same time are great illustrations of the power of geometric methods


Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 42)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Heinz Schättler, Urszula Ledzewicz
    Pages 1-40
  3. Heinz Schättler, Urszula Ledzewicz
    Pages 41-114
  4. Heinz Schättler, Urszula Ledzewicz
    Pages 171-235
  5. Heinz Schättler, Urszula Ledzewicz
    Pages 237-274
  6. Heinz Schättler, Urszula Ledzewicz
    Pages 275-316
  7. Heinz Schättler, Urszula Ledzewicz
    Pages 317-380
  8. Heinz Schättler, Urszula Ledzewicz
    Pages 381-383
  9. Back Matter
    Pages 385-496

About this book


This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.


Optimal control anti-angiogenic treatment geometric optimal control mathematical models mathematical models forcancer therapies optimal protocols

Authors and affiliations

  1. 1.Electrical and Systems EngineeringWashington UniversitySt. LouisUSA
  2. 2.Mathematics and StatisticsSouthern Illinois University EdwardsvillEdwardsvilleUSA

About the authors

Heinz Schättler is a Professor of Electrical and Systems Engineering at Washington University in St. Louis. He holds a Master's degree in Mathematics from the University of Würzburg in Germany and a Ph.D. in Mathematics from Rutgers University. His main research area is optimal control theory where he has published extensively on applications of methods and tools from optimal control and dynamical systems theory to problems motivated by real life applications. Besides the medical topics that are the focus of this text, these include electric power systems as well as models in economics, physics and electronics.

Urszula Ledzewicz is a Distinguished Research Professor in the Department of Mathematics and Statistics at Southern Illinois University Edwardsville. She specialized in optimal control theory at the University of Lodz, Poland, where she received a master’s and doctorate in Applied Mathematics. Her research interests include optimal control and optimization, mathematical modeling and analysis of systems in biomedicine with special emphasis on mathematical models for cancer growth and treatments. She has been active in the field as an Associate Editor of numerous scientific journals focused on nonlinear analysis, dynamical systems and mathematical biosciences.

The authors also have published the text Geometric Optimal Control – Theory, Methods and Examples (Springer, 2012) and were co-editors for Mathematical Methods and Models in Biomedicine (Springer, 2012).

Bibliographic information


“The book is a self-contained monograph on the application of tools and techniques of optimal control theory to a wide class of problems arising in oncology. … All considerations are presented in a rigorous mathematical language, but the authors do their best to be understandable also for researchers involved in systems biology with a moderate mathematical background.” (Andrzej Świerniak, zbMATH 1331.92008, 2016)