Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes three mathematical background areas (graphs, matrices and optimization) to solve problems in the biological sciences (in particular, dynamic analysis and controller design of QP and polynomial systems arising from predator-prey and biochemical models). The book puts a significant emphasis on applications, focusing on quasi-polynomial (QP, or generalized Lotka-Volterra) and kinetic systems (also called biochemical reaction networks or simply CRNs) since they are universal descriptors for smooth nonlinear systems and can represent all important dynamical phenomena that are present in biological (and also in general) dynamical systems.
- Describes and illustrates the relationship between the dynamical, algebraic and structural features of the quasi-polynomial (QP) and kinetic models
- Shows the applicability of kinetic and QP representation in biological modeling and control through examples and case studies
- Emphasizes the importance and applicability of quantitative models in understanding and influencing natural phenomena
1. Introduction 1. Dynamic models for describing biological phenomena 2. Kinetic systems 3. QP models
2. Basic Notions 1. General nonlinear system representation in the form of ODEs 2. Formal introduction of the QP model form 3. Introduction of kinetic models with mass action and rational reaction rates 4. Basic relations between kinetic and QP models
3. Model Transformations and Equivalence Classes 1. Alfine and linear positive diagonal transformations 2. Nonlinear diagonal transformations 3. Quasi-monomial transformation and the corresponding equivalence classes of QP systems 4. Embedding transformations and the relationship between classes of positive polynomial systems
4. Model analysis 1. Stability analysis of QP models 2. Stability of kinetic systems 3. Invariants (first integrals) for QP and kinetic systems 4. Relations between the Lyapunov functions of QP and kinetic models 5. Computational analysis of the structure of kinetic systems
5. Stabilizing feedback control design 1. Stabilizing control of QP systems by using optimization 2. Stabilizing state feedback control of nonnegative polynomial systems using special CRN realizations 3. Robustness issues and robust design for the stabilizing control of polynomial systems
6. Case studies 1. Optimization-based structural analysis and design of reaction networks 2. Computational distinguishability analysis of an uncertain kinetic model 3. Stability analysis and stabilizing control of fermentation processes in QP form
A. Notations and abbreviations B. Mathematical tools B.1. Directed graphs B.2. Matrices of key importance B.3. Basics of the applied computational tools B.4. Basic notions from systems and control theory
Gábor Szederkényi received the M.Eng degree in computer engineering (University of Veszprém, 1998), his PhD in information sciences (University of Veszprém, 2002), and the DSc title in engineering sciences (Hungarian Academy of Sciences, 2013). Currently, he is a full professor at PPKE and the head of the Analysis and Control of Dynamical Systems research group. His main research interest is the computational analysis and control of nonlinear systems with special emphasis on reaction networks and kinetic models. He is the co-author of one book, several book chapters, more than 40 journal papers, and more than 60 conference papers on the theory and applicaton of the analysis and control of nonlinear systems. His education record includes BSc and MSc level courses on linear systems theory, nonlinear control and its application in robotics and in biological systems.
The history of the scientific cooperation of the proposed three authors dates back to 2003. Since then, they have published more than 25 joint scientific papers in international journals and conference proceedings mostly related to the topic of the proposed book. The scientific background of the three authors are really complementary: Prof. Katalin Hangos is an internationally known expert in the modelling and control of thermodynamical and (bio)chemical systems, Dr. Attila Magyar has significant experience in the analysis, application and control of quasi-polynomial systems, while Prof. Gábor Szederkényi has results on the optimization-based structural analysis and synthesis of kinetic systems. Moreover, all three authors have had continuous education and supervising experience both on the MSc and PhD levels at different universities.
Attila Magyar received his MSc in computer science (University of Pannonia, 2004), his PhD in computer science (University of Pannonia, 2008), respectively. He is working at the Department of Electrical Engineering and Information Systems at University of Pannonia He is the member of the Research Laboratory of Intelligent Control Systems of the Faculty of Information Technology. His main research interests lie in nonlinear control, system identification and robotics.
Hangos, Katalin M.
Katalin Hangos received her MSc in chemistry (ELTE TTK, 1976), her BSc in computer science (ELTE TTK, 1980), DSc (1993), and habilitations (chemical engineering, 1994, engineering informatics, 2000), respectively. She is the Research and Education Head of the Department of Electrical Engineering and Information Systems at University of Pannonia and the Head of the Process Control Research Group of the Computer and Automation Research Institute of Hung. Acad. Sci. She is also the Head of the Research Laboratory of Intelligent Control Systems of the Faculty of Information Technology. She is one of the very few female professors in process systems and control, who has a strong interdisciplinary background in systems and control theory and computer science, as well.
Her main research interest lies in dynamic modelling of process systems for control and diagnostic purposes. She is a co-author of more than 100 papers on various aspects of modelling and control of process systems with nonlinear, stochastic, Petri net, qualitative and graph theory based models.