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  1. Free, publicly-accessible full text available June 26, 2024
  2. Free, publicly-accessible full text available June 26, 2024
  3. Free, publicly-accessible full text available May 31, 2024
  4. We develop some basic principles for the design and robustness analysis of a continuous-time bilinear dynamical network, where an attacker can manipulate the strength of the interconnections/edges between some of the agents/nodes. We formulate the edge protection optimization problem of picking a limited number of attack-free edges and minimizing the impact of the attack over the bilinear dynamical network. In particular, the H2-norm of bilinear systems is known to capture robustness and performance properties analogous to its linear counterpart and provides valuable insights for identifying which edges are most sensitive to attacks. The exact optimization problem is combinatorial in the number of edges, and brute-force approaches show poor scalability. However, we show that the H2-norm as a cost function is supermodular and, therefore, allows for efficient greedy approximations of the optimal solution. We illustrate and compare the effectiveness of our theoretical findings via numerical simulation 
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    Free, publicly-accessible full text available April 1, 2024
  5. We consider the problems of asymptotic stability and robustness in large-scale second-order consensus networks and vehicle platoons in the discrete-time domain. First, we develop a graph-theoretic methodology to design the state feedback law for the second-order consensus networks and vehicle platoons in a discrete-time framework. We analyze the stability of such networks based on algebraic properties of the Laplacian matrices of underlying graphs and each vehicle’s update cycle (also known as the time step). We further provide a necessary and sufficient condition of stability of a linear second-order consensus network in the discrete-time domain. Moreover, we evaluate the robustness of the consensus networks by employing the expected value of the steady-state dispersion of the state of the entire network, also known as squared H2-norm, as a performance measure. We show the connection between performance measures with respect to network size, connectivity, and the update cycle. The main contribution of this work is that we provide a formal framework to quantify the relation between scaling performance measures and restrictions of the vehicles’ update cycles. Specifically, we show that denser networks (i.e., networks with more communications/edges) require faster agents (i.e., smaller update cycles) to outperform or achieve the same level of robustness as sparse networks (i.e., networks with fewer communications/edges). 
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  6. In this paper, we consider the problem of sensor selection for discrete-time linear dynamical networks. We develop a framework to design a sparse sensor schedule for a given large-scale linear system with guaranteed performance bounds using a learning-based algorithm. To sparsify the sensors in both time and space, we build our combinatorial optimization problems based on the notion of systemic controllability/observability metrics for linear dynamical networks with three properties: monotonicity, convexity, and homogeneity with respect to the controllability/observability Gramian matrix of the network. These combinatorial optimizations are inherently intractable and NP-hard. However, solving a continuous relaxation for each optimization is considered best practice. This is achievable since we constructed the objective based on the systemic metrics, which are convex. Furthermore, by leveraging recent advances in sparsification literature and regret minimization, we then round the fractional solution obtained by the continuous optimization to achieve a (1+epsilon) approximation sparse schedule that chooses on average a constant number of sensors at each time, to approximate all types of systemic metrics. 
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  7. Several sources of delay in an epidemic network might negatively affect the stability and robustness of the entire network. In this paper, a multi-delayed Susceptible-Infectious-Susceptible (SIS) model is applied on a metapopulation network, where the epidemic delays are categorized into local and global delays. While local delays result from intra-population lags such as symptom development duration or recovery period, global delays stem from inter-population lags, e.g., transition duration between subpopulations. The theoretical results for a network of subpopulations with identical linear SIS dynamics and different types of time-delay show that depending on the type of time-delay in the network, different eigenvalues of the underlying graph should be evaluated to obtain the feasible regions of stability. The delay-dependent stability of such epidemic networks has been analytically derived, which eliminates potentially expensive computations required by current algorithms. The effect of time-delay on the H2 norm-based performance of a class of epidemic networks with additive noise inputs and multiple delays is studied and the closed form of their performance measure is derived using the solution of delayed Lyapunov equations. As a case study, the theoretical findings are implemented on a network of United States’ busiest airports. 
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