1. H. Zhang, B. Yalcin, J. Lavaei, and E.D. Sontag. Exact recovery guarantees for parameterized nonlinear system identification problem under sparse disturbances or semi-oblivious attacks. 2025. Note: Submitted. Abstract:

   In this work, we study the problem of learning a nonlinear dynamical system by parameterizing its dynamics using basis functions. We assume that disturbances occur at each time step with an arbitrary probability p, which models the sparsity level of the disturbance vectors over time. These disturbances are drawn from an arbitrary, unknown probability distribution, which may depend on past disturbances, provided that it satisfies a zero-mean assumption. The primary objective of this paper is to learn the system's dynamics within a f inite time and analyze the sample complexity as a function of p. To achieve this, we examine a LASSO-type non-smooth estimator and establish necessary and sufficient conditions for its well-specifiedness and the uniqueness of the global solution to the underlying optimization problem. We then provide exact recovery guarantees for the estimator under two distinct conditions: boundedness and Lipschitz continuity of the basis functions. We show that finite-time exact recovery is achieved with high probability, even when p approaches 1. Unlike prior works, which primarily focus on independent and identically distributed (i.i.d.) disturbances and provide only asymptotic guarantees for system learning, this study presents the first finite-time analysis of nonlinear dynamical systems under a highly general disturbance model. Our framework allows for possible temporal correlations in the disturbances and accommodates semi-oblivious adversarial attacks, significantly broadening the scope of existing theoretical results.

1. A.C.B de Olivera, M. Siami, and E.D. Sontag. Bilinear dynamical networks under malicious attack: an efficient edge protection method. In Proc. 2021 Automatic Control Conference, pages 1210-1216, 2021. [PDF] Keyword(s): Bilinear systems, adversarial attacks, robustness measures, supermodular optimization. Abstract:

   In large-scale networks, agents and links are often vulnerable to attacks. This paper focuses on continuous-time bilinear networks, where additive disturbances model attacks or uncertainties on agents/states (node disturbances), and multiplicative disturbances model attacks or uncertainties on couplings between agents/states (link disturbances). It investigates network robustness notion in terms of the underlying digraph of the network, and structure of exogenous uncertainties and attacks. Specifically, it defines a robustness measure using the $\mathcal H_2$-norm of the network and calculates it in terms of the reachability Gramian of the bilinear system. The main result is that under certain conditions, the measure is supermodular over the set of all possible attacked links. The supermodular property facilitates the efficient solution finding of the optimization problem. Examples illustrate how different structures can make the system more or less vulnerable to malicious attacks on links.




2. A.C.B de Olivera, M. Siami, and E.D. Sontag. Eminence in noisy bilinear networks. In Proc. 2021 60th IEEE Conference on Decision and Control (CDC), pages 4835-4840, 2021. [PDF] Keyword(s): Bilinear systems, H2 norm, centrality, adversarial attacks, robustness measures. Abstract:

   When measuring importance of nodes in a network, the interconnections and dynamics are often supposed to be perfectly known. In this paper, we consider networks of agents with both uncertain couplings and dynamics. Network uncertainty is modeled by structured additive stochastic disturbances on each agent's update dynamics and coupling weights. We then study how these uncertainties change the network's centralities. Disturbances on the couplings between agents resul in bilinear dynamics, and classical centrality indices from linear network theory need to be redefined. To do that, we first show that, similarly to its linear counterpart, the squared H2 norm of bilinear systems measures the trace of the steady-state error covariance matrix subject to stochastic disturbances. This makes the H2 norm a natural candidate for a performance metric of the system. We propose a centrality index for the agents based on the H2 norm, and show how it depends on the network topology and the noise structure. Finally, we simulate a few graphs to illustrate how uncertainties on different couplings affect the agents' centrality rankings compared to a linearized model of the same system.

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