Control synthesis of reaction–diffusion systems with varying parameters and varying delays

Abstract

In this paper, the analysis and state-feedback control synthesis for reaction–diffusion linear parameter-varying (LPV) systems with time delays and Robin boundary conditions are addressed. We explore the stability and ${\mathcal{L}}_2$ gain performance for reaction–diffusion LPV systems using parameter-dependent Lyapunov functionals. Both analysis and synthesis conditions are formulated in terms of linear matrix inequalities (LMIs) that can be solved via efficient convex optimisation solvers. A numerical example of automated blood pressure regulation via vasoactive drug infusion is explored to demonstrate the effectiveness of the proposed state-feedback control synthesis.

Keywords:

• LPV control synthesis
• reaction–diffusion systems
• delayed system with varying parameters
• blood pressure regulation
• Friedrichs' inequality

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Financial and in-kind support for this research was provided by the National Natural Science Foundation of China [grant number 61803303], the Aeronautical Science Foundation of China [grant number 2018ZD53045], and Natural Science Foundation of Shaanxi Province of China [grant number 2019JQ-342].

Notes on contributors

Guoyan Cao

Guoyan Cao received the BS degree in mechanical engineering from Beijing Institute of Technology, China, in 2008, the MSc degree and the PhD degree in mechanical engineering from University of Houston in 2011 and 2015, respectively. After working as a Data scientist in Panton company in Houston, he is currently an assistant professor in the School of Cybersecurity in Northwestern Polytechnical University in China. His research interests include linear parameter varying modeling and control of nonlinear systems, data science and cyber security.

Karolos M. Grigoriadis

Karolos M. Grigoriadis has focused on the development of systematic methods for control systems design subject to practical implementation limitations, such as time delays, controller order, saturation constraints, and fault accommodations. He has been involved in multiple research projects sponsored by the U.S. National Science Foundation, NASA, the U.S. Army, and aerospace and automotive companies. His work on aerospace controlled systems in collaboration with aerospace companies and NASA has been addressing microgravity vibration isolation, control of smart structures, fault-tolerant control of space systems, and integrated design of structural parameters and control gains. His research on automotive engine diagnostics/controls in collaboration with the U.S. federal agencies and automotive companies has been on the development of real-time optimizing controllers for engine and exhaust aftertreatment to meet future automotive fuel economy and exhaust emission objectives.

Puchen Liu

Puchen Liu received the MSc degree in applied mathematics from Ocean University of China, Qingdao, China in 2005, and received the PhD degree in applied mathematics from University of Houston in USA in 2013. He is currently working in the College of Arts and Sciences in Shanghai Polytechnic University. He is interested in a number of topics in applied mathematics including Steklov eigenproblems and optimization in partial differential equations, neuronal networks, stochastic processes, time series analysis, financial dynamics and statistical modeling.