Distributed Estimation over Directed Graphs Resilient to Sensor Spoofing
This paper addresses the problem of distributed estimation of an unknown dynamic parameter by a multi-agent system over a directed communication network in the presence of an adversarial attack on the agents' sensors. The mode of attack of the adversaries is to corrupt the sensor measurements of some of the agents, while the communication and information processing capabilities of those agents remain unaffected. To ensure that all the agents, both normal as well as those under attack, are able to correctly estimate the parameter value, the Resilient Estimation through Weight Balancing (REWB) algorithm is introduced. The only condition required for the REWB algorithm to guarantee resilient estimation is that at any given point in time, less than half of the total number of agents are under attack. The paper discusses the development of the REWB algorithm using the concepts of weight balancing of directed graphs, and the consensus+innovations approach for linear estimation. Numerical simulations are presented to illustrate the performance of our algorithm over directed graphs under different conditions of adversarial attacks.
Optimizing network topology for average controllability
We address the problem of identifying a network topology of a networked system for maximizing a controllability measure, the average controllability under constraints on the number of links in the network. We consider networked systems consisting of subsystems with higher-order discrete-time linear time-invariant dynamics. We show that the average controllability is a monotone increasing supermodular function of a set of links in the networked system. Since maximizing such a function with cardinality constraints is an NP-hard problem, we analyze the performance guarantees obtained from the greedy algorithm for maximizing non-submodular set functions in terms of supermodular curvature. We show that the lower bound obtained for the greedy algorithm becomes trivial as the number of subsystems in the networked system increases. Hence, we propose two heuristic algorithms to solve the optimization problem and numerically demonstrate the efficiency of the proposed heuristics in terms of computational complexity and performance improvement in average controllability.