Grainger College of Engineering, All Events

Location & Time: CSLB02, 4:00-5:00PM. Refreshments and coffee outside B02 at 3:30.

Title: Minimax Linear Regulator Problems for Positive Systems with applications to multi-agent synchronization.

Abstract: The instances where explicit solutions to optimal control problems are obtainable are the exception. Of particular interest are the explicit solutions derived for minimax problems, as they provide a framework for addressing challenges involving adversarial conditions and uncertainties. This work presents explicit solutions to a novel class of minimax optimal control problems for positive linear systems with linear costs, elementwise linear constraints in the control policy, and worst-case disturbances. Using dynamic programming theory, explicit solutions are derived for both finite and infinite horizons in discrete and continuous-time. Necessary and sufficient conditions for minimizing the l1-induced gain of the system are derived and characterized by the disturbance penalty in the cost function of the minimax problem. A linear programming formulation of the minimax setting in the presence of nonnegative disturbances is also introduced, along with an analysis of the stability and detectability properties of the problem setting. Additionally, this work addresses the positive synchronization problem on undirected graphs, presenting a stabilizing feedback policy by solving the linear programming formulation of the introduced minimax optimal control problem class in the absence of disturbances. By leveraging explicit solutions to minimax optimal control and multi-agent synchronization problems, this framework provides a computationally efficient and scalable framework for controlling large-scale systems.

Bio: Alba Gurpegui Ramón received her B.Sc. degree in mathematics from La Universidad Complutense, Madrid, Spain in 2020, and her M.Sc. degree in mathematics from Lund University, Sweden in 2022. Since September 2022, she has been a Ph.D. student in the Department of Automatic Control at Lund University, Sweden, working with Anders Rantzer and Emma Tegling. This past semester she has been a visiting scholar at Purdue University. Her research interests include optimal and robust control of positive systems, and their applications to large-scale systems and network synchronization.