Joint Centrality Distinguishes Optimal Leaders in Noisy Networks

We study the performance of a network of agents tasked with tracking an external unknown signal in the presence of stochastic disturbances and under the condition that only a limited subset of agents, known as leaders, can measure the signal directly. We investigate the optimal leader selection problem for a prescribed maximum number of leaders, where the optimal leader set minimizes total system error defined as steady-state variance about the external signal. In contrast to previously established greedy algorithms for optimal leader selection, our results rely on an expression of total system error in terms of properties of the underlying network graph. We demonstrate that the performance of any given set of leaders depends on their influence as determined by a new graph measure of centrality of a set. We define the $joint \; centrality$ of a set of nodes in a network graph such that a leader set with maximal joint centrality is an optimal leader set. In the case of a single leader, we prove that the optimal leader is the node with maximal information centrality. In the case of multiple leaders, we show that the nodes in the optimal leader set balance high information centrality with a coverage of the graph. For special cases of graphs, we solve explicitly for optimal leader sets. We illustrate with examples.Comment: Conditionally accepted to IEEE TCN

Graph Theoretic Analysis of Multi-Agent system Structural Properties

Ph.DDOCTOR OF PHILOSOPH

OPTIMAL LEADER-FOLLOWER FORMATION CONTROL USING DYNAMIC GAMES

Formation control is one of the salient features of multi-agent robotics. The main goal of this field is to develop distributed control methods for interconnected multi-robot systems so that robots will move with respect to each other in order to keep a formation throughout their joint mission. Numerous advantages and vast engineering applications have drawn a great deal of attention to the research in this field. Dynamic game theory is a powerful method to study dynamic interactions among intelligent, rational, and self-interested agents. Differential game is among the most important sub-classes of dynamic games, because many important problems in engineering can be modeled as differential games. The underlying goal of this research is to develop a reliable formation control algorithm for multi-robot systems based on differential games. The main idea is to benefit from powerful machinery provided by dynamic games, and design an improved formation control scheme with careful attention to practical control design requirements, namely state feedback, and computation costs associated to implementation. In this work, results from algebraic graph theory is used to develop a quasi-static optimal control for heterogeneous leader{follower formation problem. The simulations are provided to study capabilities as well as limitations associated to this approach. Based on the obtained results, a finite horizon open-loop Nash differential game is developed as adaptation of differential games methodology to formation control problems in multi-robot systems. The practical control design requirements dictate state-feedback; therefore, proposed controller is complimented by adding receding horizon approach to its algorithm. It leads to a closed loop state-feedback formation control. The simulation results are presented to show the effectiveness of proposed control scheme

Safe and Secure Control of Connected and Automated Vehicles

Evolution of Connected and Automated Vehicles (CAV), as an important class of Cyber-Physical Systems (CPS), plays a crucial role in providing innovative services in transport and traffic management. Vehicle platoons, as a set of CAV, forming a string of connected vehicles, have offered significant enhancements in traffic management, energy consumption, and safety in intelligent transportation systems. However, due to the existence of the cyber layer in these systems, subtle security related issues have been underlined and need to be taken into account with sufficient attention. In fact, despite the benefits brought by the platoons, they potentially suffer from insecure networks which provide the connectivity among the vehicles participating in the platoon which makes these systems prone to be under the risk of cyber attacks. One (or more) external intelligent intruder(s) might attack one (or more) of the vehicles participating in a platoon. In this respect, the need for a safe and secure driving experience is highly sensible and crucial. Hence, we will concentrate on improving the safety and security of CAVs in different scenarios by taking advantage of security related approaches and CAV control systems. In this thesis, we are going to focus on two main levels of platoon control, namely I) High level secure platoon control, and II) Low level secure platoon control. In particular, in the high level part, we consider platoons with arbitrary inter-vehicular communication topoloy whereby the vehicles are able to exchange their driving data with each other through DSRC-based environment. The whole platoon is modeled using graph-theoretic notions by denoting the vehicles as the nodes and the inter-vehicular communication quality as the edge weights. We study the security of the vehicle platoon exposed to cyber attacks using a novel game-theoretic approach. The platoon topologies under investigation are directed (called predecessor following) or undirected (bidirectional) weighted graphs. The attacker-detector game is defined as follows. The attacker targets some vehicles in the platoon to attack and the detector deploys monitoring sensors on the vehicles. The attacker's objective is to be as stealthy to the sensors as possible while the detector tries to place the monitoring sensors to detect the attack impact as much as he can. The existence of equilibrium strategies for this game is investigated based on which the detector can choose specific vehicles to put his sensors on and increase the security level of the system. Moreover, we study the effect of adding (or removing) communication links between vehicles on the game value. We then address the same problem while investigating the optimal actuator placement strategy needed by the defender to mitigate the effects of the attack. In this respect, the energy needed by the attacker to steer the consensus follower-leader dynamics of the system towards his desired direction is used as the game payoff. Simulation and experimental results conducted on a vehicle platoon setup using Robotic Operating System (ROS) demonstrate the effectiveness of our analyses. In the low level platoon control, we exploit novel secure model predictive controller algorithms to provide suitable countermeasure against a prevalent data availability attack, namely Denial-of-Service (DoS) attack. A DoS intruder can endanger the security of platoon by jamming the communication network among the vehicles which is responsible to transmit inter-vehicular data throughout the platoon. In other words, he may cause a failure in the network by jamming it or injecting a huge amount of delay, which in essence makes the outdated transferred data useless. This can potentially result in huge performance degradation or even hazardous collisions. We propose novel secure distributed nonlinear model predictive control algorithms for both static and dynamic nonlinear heterogeneous platoons which are capable of handling DoS attack performed on a platoon equipped by different communication topologies and at the same time they guarantee the desired formation control performance. Notably, in the dynamic case, our proposed method is capable of providing safe and secure control of the platoon in which arbitrary vehicles might perform cut-in and/or cut-out maneuvers. Convergence time analysis of the system are also investigated. Simulation results on a sample heterogeneous attacked platoon exploiting two-predecessor follower communication environment demonstrates the fruitfulness of the method

Failure Analysis in Multi-Agent Networks: A Graph-Theoretic Approach

A multi-agent network system consists of a group of dynamic control agents which interact according to a given information flow structure. Such cooperative dynamics over a network may be strongly affected by the removal of network nodes and communication links, thus potentially compromising the functionality of the overall system. The chief purpose of this thesis is to explore and address the challenges of multi-agent cooperative control under various fault and failure scenarios by analyzing the network graph-topology. In the first part, the agents are assumed to evolve according to the linear agreement protocol. Link failures in the network are characterized based on the ability to distinguish the agent dynamics before and after failures. Sufficient topological conditions are provided, under which dynamics of a given agent is distinguishable for distinct digraphs. The second part of this thesis is concerned with the preservation of structural controllability for a multi-agent network under simultaneous link and agent failures. To this end, the previously studied concepts of link and agent controllability degrees are first exploited to provide quantitative measures for the contribution of a particular link or agent to the controllability of the overall network. Next, the case when both communication links and agents in the network can fail simultaneously is considered, and graphical conditions for preservation of controllability are investigated

Adaptive Network Dynamics and Evolution of Leadership in Collective Migration

The evolution of leadership in migratory populations depends not only on costs and benefits of leadership investments but also on the opportunities for individuals to rely on cues from others through social interactions. We derive an analytically tractable adaptive dynamic network model of collective migration with fast timescale migration dynamics and slow timescale adaptive dynamics of individual leadership investment and social interaction. For large populations, our analysis of bifurcations with respect to investment cost explains the observed hysteretic effect associated with recovery of migration in fragmented environments. Further, we show a minimum connectivity threshold above which there is evolutionary branching into leader and follower populations. For small populations, we show how the topology of the underlying social interaction network influences the emergence and location of leaders in the adaptive system. Our model and analysis can describe other adaptive network dynamics involving collective tracking or collective learning of a noisy, unknown signal, and likewise can inform the design of robotic networks where agents use decentralized strategies that balance direct environmental measurements with agent interactions.Comment: Submitted to Physica D: Nonlinear Phenomen

Power network and smart grids analysis from a graph theoretic perspective

The growing size and complexity of power systems has given raise to the use of complex network theory in their modelling, analysis, and synthesis. Though most of the previous studies in this area have focused on distributed control through well established protocols like synchronization and consensus, recently, a few fundamental concepts from graph theory have also been applied, for example in symmetry-based cluster synchronization. Among the existing notions of graph theory, graph symmetry is the focus of this proposal. However, there are other development around some concepts from complex network theory such as graph clustering in the study. In spite of the widespread applications of symmetry concepts in many real world complex networks, one can rarely find an article exploiting the symmetry in power systems. In addition, no study has been conducted in analysing controllability and robustness for a power network employing graph symmetry. It has been verified that graph symmetry promotes robustness but impedes controllability. A largely absent work, even in other fields outside power systems, is the simultaneous investigation of the symmetry effect on controllability and robustness. The thesis can be divided into two section. The first section, including Chapters 2-3, establishes the major theoretical development around the applications of graph symmetry in power networks. A few important topics in power systems and smart grids such as controllability and robustness are addressed using the symmetry concept. These topics are directed toward solving specific problems in complex power networks. The controllability analysis will lead to new algorithms elaborating current controllability benchmarks such as the maximum matching and the minimum dominant set. The resulting algorithms will optimize the number of required driver nodes indicated as FACTS devices in power networks. The second topic, robustness, will be tackled by the symmetry analysis of the network to investigate three aspects of network robustness: robustness of controllability, disturbance decoupling, and fault tolerance against failure in a network element. In the second section, including Chapters 4-8, in addition to theoretical development, a few novel applications are proposed for the theoretical development proposed in both sections one and two. In Chapter 4, an application for the proposed approaches is introduced and developed. The placement of flexible AC transmission systems (FACTS) is investigated where the cybersecurity of the associated data exchange under the wide area power networks is also considered. A new notion of security, i.e. moderated-k-symmetry, is introduced to leverage on the symmetry characteristics of the network to obscure the network data from the adversary perspective. In chapters 5-8, the use of graph theory, and in particular, graph symmetry and centrality, are adapted for the complex network of charging stations. In Chapter 5, the placement and sizing of charging stations (CSs) of the network of electric vehicles are addressed by proposing a novel complex network model of the charging stations. The problems of placement and sizing are then reformulated in a control framework and the impact of symmetry on the number and locations of charging stations is also investigated. These results are developed in Chapters 6-7 to robust placement and sizing of charging stations for the Tesla network of Sydney where the problem of extending the capacity having a set of pre-existing CSs are addressed. The role of centrality in placement of CSs is investigated in Chapter 8. Finally, concluding remarks and future works are presented in Chapter 9

Laplacian Controllability for Graphs Obtained by Some Standard Products

Let LG be the Laplacian matrix of a graph G with n vertices, and let b be a binary vector of length n. The pair (LG, b) is said to be controllable (and we also say that G is Laplacian controllable for b) if LG has no eigenvector orthogonal to b. In this paper we study the Laplacian controllability of joins, Cartesian products, tensor products and strong products of two graphs. Besides some theoretical results, we give an iterative construction of infinite families of controllable pairs (LG, b)