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We propose a game-theoretic framework for improving the resilience of the consensus algorithm, under the $\mathcal{H}_2$ performance metric, in the presence of an attacker. In this game, an attacker selects a subset of nodes to inject attack signals to maximize the $\mathcal{H}_2$ norm of the system from the attack signal to the output of the system. The defender improves the resilience of the system by adding self-feedback loops to certain nodes of the network to minimize the system's norm. We investigate the interplay between the equilibrium strategies of the game and the underlying connectivity graph, using the $\mathcal{H}_2$ performance metric as the game pay-off. The existence of a Nash equilibrium is studied under undirected and directed networks. For the cases where the attacker-defender game does not admit a Nash equilibrium, the Stackelberg equilibrium of the game is studied with the defender as the game leader. We show that the effective center of the graph, a new network centrality measure, captures the optimal location of defense nodes in undirected networks. In directed networks, the optimal locations of defenders are those nodes with small in-degrees. The theoretical results are applied to the design of a resilient formation of vehicle platoons., QC 20210323

To cope with the growing amount of debris in the Earth orbit, spacecraft collision avoidance capabilities are necessary. In this paper, we propose an approach to debris avoidance maneuvering based on the use of safe positively invariant sets in order to steer the spacecraft, under closed-loop control, around a piece of debris. A connectivity graph of forced equilibria is computed based on the overlap of these invariant sets, and a graph search algorithm is then implemented in order to find the shortest path around the debris. Fast growth distance computation is employed for on-board real-time applicability. Simulation results are presented that illustrate this approach., AAS/AIAA Space Flight Mechanics Meeting, Charleston, SC, January 2012, AAS-12-250. The original document contains color images.

This technology described a technique for spacecraft maneuver planning that uses positively-invariant sets in order to avoid collisions with debris, while adhering to specified thrust limits. The approach is based on hopping between neighborhoods of equilibria in a virtual net, and maintaining the spacecraft trajectory within a tube formed by safe positively-invariant sets. For the case where thrust limits can be specified as polyhedral norm bounds, we have shown that the thrust limit on the growth distance can be easily computed; it is, in fact, feasible to perform these computations onboard a spacecraft in order to account for thruster failure or degradation. We described an extension in the presence of moving debris using contractive constraint admissible sets in order to avoid collisions. Lastly, we illustrated that the approach can be extended to include unmeasured bounded disturbances., The original document contains color images.

Several protocols have been proposed to date to defend against wormhole attacks in wireless networks by adopting synchronized clocks, positioning devices, or directional antennas. These requirements and assumptions limit their applicability especially in the case of mobile networks where the degree of association and de-association between the nodes is relatively high. In this work, we present a novel lightweight countermeasure for the wormhole attack, called LDAC (Localized-Decentralized Algorithm for Countering wormholes). It is completely localized and works by looking for simple evidence that no attack is taking place, using only connectivity information, as implied by the underlying communication graph. LDAC is not confined to static networks but extends naturally to dynamic and even mobile ones. Rigorous arguments that prove the correctness of the algorithm are coupled with detailed performance evaluation along with an implementation on real sensor devices that demonstrates its efficiency in terms of memory requirements and processing overhead., QC 20150629

In this paper we study the output consensus problem for systems of agents with linear continuous, time invariant dynamics. We derive control laws with minimal energy that solves the problem, while using only relative information. Instead of considering a fixed communication topology for the agents, and derive the optimal control for that topology, we derive the optimal control law for any communication topology between the agents. We show that the optimal control uses only relative information but requires the connectivity graph to be complete and in general requires measurements of the state errors. We identify the cases where the optimal control is only based on output errors, and show that in the infinite time horizon case, the optimal controller can always be expressed as a dynamic controller that is only based on the output errors. Regarding the theoretic contributions of this paper, the control laws are derived using methods from linear vector space optimization and are given in closed form. To the authors knowledge these methods have not been used within this context before., QC 20140905