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Creators/Authors contains: "Siami, Milad"

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  1. Free, publicly-accessible full text available June 26, 2024
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  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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  5. 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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  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. In this paper, we investigate the problem of actuator selection for linear dynamical systems. We develop a framework to design a sparse actuator schedule for a given large-scale linear system with guaranteed performance bounds using deterministic polynomial-time and randomized approximately linear-time algorithms. First, we introduce systemic controllability metrics for linear dynamical systems that are monotone and homogeneous with respect to the controllability Gramian. We show that several popular and widely used optimization criteria in the literature belong to this class of controllability metrics. Our main result is to provide a polynomial-time actuator schedule that on average selects only a constant number of actuators at each time step, independent of the dimension, to furnish a guaranteed approximation of the controllability metrics in comparison to when all actuators are in use. Our results naturally apply to the dual problem of sensor selection, in which we provide a guaranteed approximation to the observability Gramian. We illustrate the effectiveness of our theoretical findings via several numerical simulations using benchmark examples. 
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