Related papers: Cascading failures: dynamics, stability and contro…
Stability enforcement remains a challenge in data-driven control paradigms, where no parametrised model of the system is available. For instance, the system's instabilities can be estimated in order to enforce a closed-loop stability…
This paper studies the consequences of a human-initiated targeted attack on the national electric power system. We consider two kinds of attacks: ($i$) an attack by an adversary that uses a tactical weapon and destroys a large part of the…
Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions--the spread of ideas, beliefs, innovations--can lose or gain in momentum as they spread: ideas can get reinforced, beliefs…
Complex non-linear interactions between banks and assets we model by two time-dependent Erd\H{o}s Renyi network models where each node, representing bank, can invest either to a single asset (model I) or multiple assets (model II). We use…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
The dynamic network of relationships among corporations underlies cascading economic failures including the current economic crisis, and can be inferred from correlations in market value fluctuations. We analyze the time dependence of the…
Financial system being the place of metting capital flows (equality between saving and investment), a volatility of capital flows can destroy the robustness and good working of financial system, it means subvert financial stability. The…
In this work, it is demonstrated that the usual power system dynamic model exhibits a feedforward-feedback control structure. The distinct properties of the feedforward and feedback subsystems are identified and studied using respective…
We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…
The varied and complex dynamics of real-world systems challenge the formulation of a systematic strategy for designing a stabilizing feedback law. Rather than taking a universal approach, the control strategies developed thus far to handle…
The instability of the financial system as experienced in recent years and in previous periods is often linked to credit defaults, i.e., to the failure of obligors to make promised payments. Given the large number of credit contracts, this…
In this paper, we considered a design method of non-linear state feedback controller for input-affine non-linear system taking data losses into account. When data is lost in control system, control input is fixed to constant value or to the…
In this paper, we examine both stability and sustainability of a network-based model of natural resource consumption. Stability is studied from a dynamical systems perspective, though we argue that sustainability is a fundamentally…
We introduce a new microscopic model of the outages in transmission power grids. This model accounts for the automatic response of the grid to load fluctuations that take place on the scale of minutes, when the optimum power flow…
A system is called positive if the set of non-negative states is left invariant by the dynamics. Stability analysis and controller optimization are greatly simplified for such systems. For example, linear Lyapunov functions and storage…
Deep learning systems achieve remarkable empirical performance, yet the stability of the training process itself remains poorly understood. Training unfolds as a high-dimensional dynamical system in which small perturbations to…
We undertake a fundamental study of network equilibria modeled as solutions of fixed point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
A theoretical model of systemic-risk propagation of financial market is analyzed for stability. The state equation is an unsteady diffusion equation with a nonlinear logistic growth term, where the diffusion process captures the spread of…