Title: Invariant Properties of Distributed Averaging Algorithms and Application to Error Detection

Abstract: We consider the problem of average consensus in a distributed system comprising a set of nodes that can exchange information among themselves. We focus on a class of algorithms for solving such a problem whereby each node maintains a state and updates it iteratively as a linear combination of the states maintained by its in-neighbors, i.e., nodes from which it receives information directly. Averaging algorithms within this class can be thought of as discrete-time linear time-varying systems without external driving inputs and whose state matrix is column stochastic. As a result, the algorithms exhibit a global invariance property in that the sum of the state variables remains constant at all times. In this talk, we report on another invariance property for the aforementioned class of averaging algorithms. This property is local to each node and reflects the conservation of certain quantities capturing an aggregate of all the values received by a node from its in-neighbors and all the values sent by said node to its out-neighbors (i.e., nodes to which it sends information directly) throughout the execution of the averaging algorithm. We show how this newly-discovered invariant can be leveraged for detecting errors while executing the averaging algorithm.

Bio: Alejandro Domínguez-García is a Professor in the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign, where he is affiliated with the Power and Energy Systems area. He holds the M. Stanley Helm Professorship in Electrical and Computer Engineering. He is also a Research Professor in the Coordinated Science Laboratory and in the Information Trust Institute, both at the University of Illinois at Urbana-Champaign.

His research program aims at the development of technologies for providing a reliable and efficient supply of electricity—a key to ensuring societal welfare and sustainable economic growth. Specific activities within his program include work on: (i) control of distributed energy resources, (ii) grid data analytics, and (iii) reliability analysis.

Dr. Domínguez-García received the Ph.D. degree in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology, Cambridge, MA, in 2007, and the degree of “Ingeniero Industrial” from the University of Oviedo (Spain) in 2001.

Dr. Domínguez-García received the NSF CAREER Award in 2010, and the Young Engineer Award from the IEEE Power and Energy Society in 2012. In 2014, he was invited by the National Academy of Engineering to attend the US Frontiers of Engineering Symposium, and was selected by the U of I Provost to receive a Distinguished Promotion Award. In 2015, he received the U of I College of Engineering Dean’s Award for Excellence in Research. In 2023, he was elevated to IEEE Fellow for contributions to distributed control and uncertainty analysis of electrical energy systems.
 

Title: Invariant Properties of Distributed Averaging Algorithms and Application to Error Detection

Abstract: We consider the problem of average consensus in a distributed system comprising a set of nodes that can exchange information among themselves. We focus on a class of algorithms for solving such a problem whereby each node maintains a state and updates it iteratively as a linear combination of the states maintained by its in-neighbors, i.e., nodes from which it receives information directly. Averaging algorithms within this class can be thought of as discrete-time linear time-varying systems without external driving inputs and whose state matrix is column stochastic. As a result, the algorithms exhibit a global invariance property in that the sum of the state variables remains constant at all times. In this talk, we report on another invariance property for the aforementioned class of averaging algorithms. This property is local to each node and reflects the conservation of certain quantities capturing an aggregate of all the values received by a node from its in-neighbors and all the values sent by said node to its out-neighbors (i.e., nodes to which it sends information directly) throughout the execution of the averaging algorithm. We show how this newly-discovered invariant can be leveraged for detecting errors while executing the averaging algorithm.

Bio: Alejandro Domínguez-García is a Professor in the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign, where he is affiliated with the Power and Energy Systems area. He holds the M. Stanley Helm Professorship in Electrical and Computer Engineering. He is also a Research Professor in the Coordinated Science Laboratory and in the Information Trust Institute, both at the University of Illinois at Urbana-Champaign.

His research program aims at the development of technologies for providing a reliable and efficient supply of electricity—a key to ensuring societal welfare and sustainable economic growth. Specific activities within his program include work on: (i) control of distributed energy resources, (ii) grid data analytics, and (iii) reliability analysis.

Dr. Domínguez-García received the Ph.D. degree in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology, Cambridge, MA, in 2007, and the degree of “Ingeniero Industrial” from the University of Oviedo (Spain) in 2001.

Dr. Domínguez-García received the NSF CAREER Award in 2010, and the Young Engineer Award from the IEEE Power and Energy Society in 2012. In 2014, he was invited by the National Academy of Engineering to attend the US Frontiers of Engineering Symposium, and was selected by the U of I Provost to receive a Distinguished Promotion Award. In 2015, he received the U of I College of Engineering Dean’s Award for Excellence in Research. In 2023, he was elevated to IEEE Fellow for contributions to distributed control and uncertainty analysis of electrical energy systems.