Non-zero set-point affine feedback control of impulsive systems with application to biomedical processes

ABSTRACT

Linear impulsive systems have been extensively studied in the last decades, mainly in the field of biomedical research. However, a proper characterisation of the equilibria of such a systems - when they are out of the origin - and its use by optimising control strategies is still a matter of discussion. In this work, a novel characterisation of the system equilibria and invariant regions - derived from the definition of two underlying discrete-time systems - is given, and based on this characterisation impulsive affine feedback control strategies for non-zero set-points are designed. The closed-loop performance and benefits of the strategies are assessed through two biomedical examples: the Lithium ions distribution in the human body and the HIV treatment.

KEYWORDS:

• Impulsive systems
• non-zero regulation
• feedback control
• impulsive invariant sets
• drug administration

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Pablo S. Rivadeneira http://orcid.org/0000-0001-8392-4556

Notes

1 We consider here, for simplicity, the fixed time interval $\mathcal{I}$ instead of $({\tau }_k,{\tau }_{k+1}]$ because ${\tau }_{k+1}-{\tau }_k=T$ for all $k\in \mathbb{N}$

Additional information

Notes on contributors

Pablo S. Rivadeneira

Pablo S. Rivadeneira was born in Ipiales, Colombia in 1981. He received the Control Engineering degree from the Universidad Nacional de Colombia, at Medellín, in 2005, and the doctorate in Chemical Technology from the Universidad del Litoral, at Santa Fe, Argentina in 2010. After that, he did a postdoctoral stage at IRRCyN, Nantes, France during 2010–2012. Now, he is assistant professor at Universidad Nacional de Colombia. His main research interests include aspects of nonlinear systems and control, with applications to industrial and biological processes.

Alejandro H. González

Alejandro H. González is a Titular Professor of Industrial Engineering at National University of Litoral (UNL), and Adjoint Researcher at the Argentine National Scientific and Technical Research Council (CONICET). After getting his Ph.D from UNL in 2006, he became Postdoctoral fellow at the Chemical Engineering Department at Universidade de São Paulo, São Paulo-Brazil, under the supervision of Prof. Darci Odloak (2007–2008) and, subsequently, at the “Departamento de Ingeniería y Automática de la Escuela Técnica Superior de Ingenieros de la Universidad de Sevilla, Seville-Spain (2010–2011). After concluding his Postdoctoral activities, he returned to Argentine to work as a researcher in the Process Control Group of INTEC (CONICET-UNL) and Professor at the University, as well as to supervise Ph.D. research projects and students at INTEC (CONICET-UNL). His research interests include Advanced Control, Model Predictive Control (MPC) design, Control of Constrained System and Invariant Sets for Linear Systems.