Waseem Abbas

A tight lower bound on the controllability of networks with multiple leaders

In this paper we study the controllability of networked systems with static network topologies using tools from algebraic graph theory. Each agent in the network acts in a decentralized fashion by updating its state in accordance with a nearest-neighbor averaging rule. In order to control the system, external control inputs are injected into the so called leader nodes, and the influence is propagated throughout the network. Our main result is a tight lower bound on the rank of the controllability matrix associated with such systems. This bound is derived using the distances of nodes to the leaders, and valid for systems with arbitrary network topologies and possibly multiple leaders.

Distribution of agents in heterogeneous multiagent systems

Heterogeneous multiagent systems are useful for performing various complex distributed tasks. The effectiveness and scope of service such systems provide, can be attributed to the distribution of agents of different types through the network. This paper deals with the development of methods and techniques to analyse heterogeneity distributions in such networks, both qualitatively and quantitatively. These developed tools are used to establish information pertaining to the roles and significance of individual agents. Moreover, the notion of heterogeneity is formalized in terms of the underlying network topology.

Sensor placement for fault location identification in water networks

This paper focuses on the optimal sensor placement problem for the identification of pipe failure locations in large-scale urban water systems. The problem involves selecting the minimum number of sensors such that every pipe failure can be uniquely localized. This problem can be viewed as a minimum test cover (MTC) problem, which is NP-hard. We consider two approaches to obtain approximate solutions to this problem. In the first approach, we transform the MTC problem to a minimum set cover (MSC) problem and use the greedy algorithm that exploits the submodularity property of the MSC problem to compute the solution to the MTC problem. In the second approach, we develop a new augmented greedy algorithm for solving the MTC problem. This approach does not require the transformation of the MTC to MSC. Our augmented greedy algorithm provides in a significant computational improvement while guaranteeing the same approximation ratio as the first approach. We propose several metrics to evaluate the performance of the sensor placement designs. Finally, we present detailed computational experiments for a number of real water distribution networks.

Robust Graph Topologies for Networked Systems

Abstract Robustness of networked systems against noise corruption and structural changes in an underlying network topology is a critical issue for a reliable performance. In this paper, we investigate this issue of robustness in networked systems both from structural and functional viewpoints. Structural robustness deals with the effect of changes in a graph structure due to link or edge failures, while functional robustness addresses how well a system behaves in the presence of noise. We discuss that both of these aspects are inter-related, and can be measured through a common graph invariant. A graph process is introduced where edges are added to an existing graph in a step-wise manner to maximize robustness. Moreover, a relationship between the symmetry of an underlying network structure and robustness is also discussed.

Deploying Robots With Two Sensors in K1, 6-Free Graphs

Let G be a graph of minimum degree at least 2 with no induced subgraph isomorphic to K1, 6. We prove that if G is not isomorphic to one of eight exceptional graphs, then it is possible to assign two-element subsets of to the vertices of G in such a way that for every and every vertex the label i is assigned to v or one of its neighbors. It follows that G has fractional domatic number at least 5/2. This is motivated by a problem in robotics and generalizes a result of Fujita, Yamashita, and Kameda who proved that the same conclusion holds for all 3-regular graphs.

Securing multiagent systems against a sequence of intruder attacks

In this paper, we discuss the issue of security in multiagent systems in the context of their underlying graph structure that models the interconnections among agents. In particular, we investigate the minimum number of guards required to counter an infinite sequence of intruder attacks with a given sensing and response range of an individual guard. We relate this problem of eternal security in graphs to the domination theory in graphs, providing tight bounds on the number of guards required along with schemes for securing a multiagent system over a graph.

Graph Distances and Controllability of Networks

In this technical note, we study the controllability of diffusively coupled networks from a graph theoretic perspective. We consider leader-follower networks, where the external control inputs are injected to only some of the agents, namely the leaders. Our main result relates the controllability of such systems to the graph distances between the agents. More specifically, we present a graph topological lower bound on the rank of the controllability matrix. This lower bound is tight, and it is applicable to systems with arbitrary network topologies, coupling weights, and number of leaders. An algorithm for computing the lower bound is also provided. Furthermore, as a prominent application, we present how the proposed bound can be utilized to select a minimal set of leaders for achieving controllability, even when the coupling weights are unknown.

Scheduling Intrusion Detection Systems in Resource-Bounded Cyber-Physical Systems

In order to be resilient to attacks, a cyber-physical system (CPS) must be able to detect attacks before they can cause significant damage. To achieve this, \emph{intrusion detection systems} (IDS) may be deployed, which can detect attacks and alert human operators, who can then intervene. However, the resource-constrained nature of many CPS poses a challenge, since reliable IDS can be computationally expensive. Consequently, computational nodes may not be able to perform intrusion detection continuously, which means that we have to devise a schedule for performing intrusion detection. While a uniformly random schedule may be optimal in a purely cyber system, an optimal schedule for protecting CPS must also take into account the physical properties of the system, since the set of adversarial actions and their consequences depend on the physical systems. Here, in the context of water distribution networks, we study IDS scheduling problems in two settings and under the constraints on the available battery supplies. In the first problem, the objective is to design, for a given duration of time

Resilient consensus protocol in the presence of trusted nodes

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Hierarchical assembly of leader-asymmetric, single-leader networks

, scheduling schemes for IDS so that the probability of detecting an attack is maximized within that duration. We propose efficient heuristic algorithms for this general problem and evaluate them on various networks. In the second problem, our objective is to design scheduling schemes for IDS so that the overall lifetime of the network is maximized while ensuring that an intruder attack is always detected. Various strategies to deal with this problem are presented and evaluated for various networks.