Abstract: 
Positive systems are dynamical systems whose response signals to nonnegative input signals are constrained to be nonnegative and have applications in pharmacology, epidemiology, population biology, multi-agent systems, and communication networks. In this talk, we consider the general problem of tuning the parameters of positive linear systems under the constraint on the budget for tuning parameters and the requirement on the system norm. We discuss how the problem reduces to a geometric program, which in turn can be exactly and efficiently solved by convex optimization. The class of system norms under consideration includes the H-2 norm, H-infinity norm, Hankel norm, and Schatten p-norm. We discuss further extensions to delayed positive linear systems. Numerical examples on the synthesis of buffer networks and epidemic spreading processes are presented.

​

Biography: 
Masaki Ogura is an Assistant Professor in the Division of Information Science at the Nara Institute of Science and Technology, Japan. He received his M.Sc. degree in Informatics from Kyoto University in 2009, and his Ph.D. in Mathematics from Texas Tech University in 2014. From 2014 to 2017, he was a Postdoctoral Researcher at the University of Pennsylvania. His research interests include complex networks, dynamical systems, and stochastic processes with applications in networked epidemiology, design engineering, and biological physics. He was a runner-up of the 2019 Best Paper Award by the IEEE Transactions on Network Science and Engineering and a recipient of the 2012 SICE Best Paper Award.