Jin Gyu Lee

In this article, we present a scheme of fully distributed resilient state estimation for linear dynamical systems under sensor attacks. The proposed state observer consists of a network of local observers, where each of them utilizes local measurements and information transmitted from the neighbors. As a fully distributed scheme, it does not necessarily collect a majority of sensing data for the sake of attack identification, whereas the compromised sensors are eventually identified by the distr

The behavior of heterogeneous multi-agent systems is studied when the coupling matrices are possibly all different and/or singular, that is, its rank is less than the system dimension. Rank-deficient coupling allows exchange of limited state information, which is suitable for the study of multi-agent systems under output coupling. We present a coordinate change that transforms the heterogeneous multi-agent system into a singularly perturbed form. The slow dynamics is still a reduced-order multi-

In this paper, we introduce a nonlinear time-varying coupling law, which can be designed in a fully decentralized manner and achieves approximate synchronization with arbitrary precision, under only mild assumptions on the individual vector fields and the underlying (undirected) graph structure. The proposed coupling law is motivated by the so-called funnel control method studied in adaptive control under the observation that arbitrary precision synchronization can be achieved for heterogeneous

Funnel control is a powerful and simple method to solve the output tracking problem without the need of a good system model, without identification and without knowlegde how the reference signal is produced, but transient behavior as well as arbitrary good accuracy can be guaranteed. Until recently, it was believed that the price to pay for these very nice properties is that only practical tracking and not asymptotic tracking can be achieved. Surprisingly, this is not true! We will prove that fu

A new approach to distributed consensus optimization is studied in this paper. The cost function to be minimized is a sum of local cost functions which are not necessarily convex as long as their sum is convex. This benefit is obtained from a recent observation that, with a large gain in the diffusive coupling, heterogeneous multi-agent systems behave like a single dynamical system whose vector field is simply the average of all agents' vector fields. However, design of the large coupling gain r

When a group of heterogeneous node dynamics are diffusively coupled with a high coupling gain, the group exhibits a collective emergent behavior which is governed by a simple algebraic average of the node dynamics called the blended dynamics. This finding has been utilized for designing heterogeneous multi-agent systems by building the desired blended dynamics first and then splitting it into the node dynamics. However, to compute the magnitude of the coupling gain, each agent needs to know glob

In this letter, we review an existing distributed least-squares solver and share some new insights on it. Then, by the observation that an estimation of a constant vector under output noise can be translated into finding the least-squares solution, we present an algorithm for distributed estimation of the state of linear time-invariant systems under measurement noise. The proposed algorithm consists of a network of local observers, where each of them utilizes local measurements and information t

The behavior of a network of heterogeneous Van der Pol oscillators under output diffusive coupling is studied. By the intuition on strong coupling given by the series of `blended dynamics' research, we first show that under sufficiently strong coupling gain the network achieves practical synchronization among heterogeneous oscillators even when there is no common internal model. Then, a further analysis finds a necessary and sufficient condition for the network to achieve synchronous and oscilla

This paper investigates the problem of localizing a team of robots in an indoor environment while simultaneously keeping a robust formation and performing group motion. A distributed observer is proposed to estimate the positions of mobile robots as well as the landmarks under a common global frame. Every robot uses its available local relative measurements, as well as the estimated relative measurements to its neighbors in order to keep a robust formation. Simultaneously, each robot estimates t

Processible norbornene copolymers were realized by judiciously designing norbornene comonomers, which were themselves prepared by the Diels-Alder reaction of cyclopentadiene and benzoquinone followed by the isomerization and alkylation of alcohols. The norbornene copolymers containing these derivatized comonomers, prepared by [Pd(NCCH2CH3)4][SbF6]2 catalyst, exhibited excellent solubility in many organic solvents as well as good thermal stability, as evidenced by their high glass transition (Tg)

In this paper, to participate in the understanding of a biological system, we analyze the synchronous and oscillatory behavior of coupled Liénard systems. In particular, we will consider a network of heterogeneous Liénard systems under output diffusive coupling to take into account two fundamental characteristics of a biological system. The key idea in this work is to emphasize the role of a network, which introduces an emergent behavior that each individual element approximately follows, hence

The Riemann Hypothesis is not proved yet and this article gives a possible proof for the hypothesis which confirms that the only possible nontrivial zeros of the Riemann zeta-function has its real value equal to 1/2. From the result, the application of the Riemann Hypothesis will be certified, e.g. research on prime numbers.