报告摘要：Abstract—This talk concerns the delay robustness of PID control in stabilizing LTI systems subject to variable, unknown delays, with a particular emphasis on multi-agent systems (MASs) with inter-agent communication delays. The basic issue to be investigated addresses the question: What is the largest range of time delay within which there exists a single PID control protocol so that the MAS can achieve consensus robustly? Similar to the fundamental measure of delay margin (DM) for robust stabilization of single-loop systems against uncertain time delays, this problem concerns the delay consensus margin (DCM) of multi-agent systems subject to delays. In this talk, we discuss a frequency-domain approach, from the DM of low-order systems achievable by PID control to the DCM of low-order MAS by PID feedback protocols. Of particular interest is first-order unstable agents, with undirected and directed graphs. Surprisingly, in spite of the simplicity in the agent dynamics, the problem actually poses a rather difficult task, which in general constitutes a challenging non-smooth max-min problem. We show that the problem can be solved as a so-called unimodal optimization for undirected graphs, and by an iterative algorithm for directed graphs; in both cases, the problem can be solved using convex optimization or gradient-based methods. We also show that the DCM achieved by PID protocols coincides with that by PD protocols. Furthermore, the results show how the agent dynamics and graph connectivity may fundamentally limit the range of delay tolerable, so that consensus can or cannot be maintained with the variation of the delay, thus providing useful guidelines in the tuning and analytical design of PID controllers and PID feedback protocols.
Dan Ma received the Ph.D. degree from Northeastern University in 2007, Shenyang, China, in Control Theory and Control Engineering. Since 2006, she has been with School of Information Science and Engineering, Northeastern University, Shenyang, where she is appointed an Associate Professor. She was a Postdoctoral Fellow at Northeastern University from 2008 to 2010, a Guest Professor with Department of Electrical Engineering, University of Notre Dame, South Bend, Indiana, USA, in 2012, a Visiting Scholar at Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China, in 2016 and a Research Fellow at Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China, in 2017. Her main research interests include time-delay systems, PID control, multi-agent systems and network-based switched systems. She is a Senior Member ofIEEE, a Member of CAA Youth Committee. She is serving on an Associate Editor of IET Control Theory & Applications, a Publicity Co-Chair for the 2019 IEEE Conference on Control Technology and Applications (CCTA2019) and a number of conference Associate Editors and Program Committee Members.