arXiv subjects

Jin Gyu Lee

Publications and source records attributed to Jin Gyu Lee.

At least 19 recordsLinked to original sources

arXiv2026

On stability of a distributed observer over switching networks: The case of commutative coupling

Distributed state estimation algorithms have been extended to switching networks, which model unreliable communication networks. Yet existing results apply only to specific classes of systems, such as neutrally stable systems. In this paper, we analyze a distributed observer under the assumption that the system matrix commutes with the coupling matrices. This not only enables a refined analysis that leads to a necessary and sufficient condition for stability over switching networks, but also covers a broader class of systems than existing results, including unstable systems such as vehicular platoons.

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arXiv2026

A Note on Emergent Behavior in Multi-agent Systems Enabled by Neuro-spike Communication

In this note, we present a novel synchronization framework for heterogeneous multi-agent systems enabled by neuro-spike communication, which induces emergence. Unlike conventional synchronization strategies that require continuous transmission of full-state data packets, our approach utilizes a bio-inspired neuromorphic amplifier to achieve practical synchronization via intermittent, 1-bit Dirac delta pulses. The proposed method drastically improves communication efficiency in terms of bandwidth and energy by minimizing the information payload to a single bit, with intermittent and asynchronous communication. We provide a rigorous convergence analysis of the proposed method and validate the proposed scheme through numerical examples.

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arXiv2026

A note on input signal generators: A relaxation of Willems' fundamental lemma in the SISO case

We provide a practical relaxation of Willems' fundamental lemma for discrete-time linear time-invariant (single-input-single-output) systems. Instead of maintaining conventional Willems' persistency of excitation condition in the behavioral theory, we reformulate the problem in terms of signal generators, hence going back to the dynamical systems theory. We discuss the relationship between the persistency of excitation order and the dimension of the signal generator. Furthermore, we identify a necessary and sufficient condition on the signal generator that can generate informative input--output data for almost all systems and initial conditions. This formulation accommodates both a broad range of conventional persistently exciting input designs and a class of shorter inputs that violate Willems' condition, including sinusoidal sequences with fewer frequencies. Finally, the signal generator perspective allows a natural extension to continuous-time systems.

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arXiv2026

Emergent Behavior Is Robust to Communication Delays at the Cost of Slower System Evolution

Previous works have shown that strong coupling among heterogeneous agents enforces practical synchronization, leading to collective behavior governed by emergent dynamics. However, it remains an open question whether emergent behavior persists in the presence of communication delays, as high-gain methods are typically sensitive to delays. To address this problem, we instead slow down the agent dynamics, reproducing the synchronization mechanism of strong coupling on a slow time scale. As a result, the emergence of collective behavior is guaranteed despite arbitrary constant communication delays. This, however, comes at a cost: delays induce a derivative-like term, thereby scaling down the vector field of the emergent dynamics. The amount of the scaling is explicitly characterized as a function of the coupling weights and the delay lengths. We further suggest that this delay-induced slowdown, which is of independent interest, may be a general feature of diffusive coupling under suitable assumptions.

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arXiv2026

Steady-state response assignment for a given disturbance and reference: Sylvester equation rather than regulator equations

Conventionally, the concept of moment has been primarily employed in model order reduction to approximate system by matching the moment, which is merely the specific set of steady-state responses. In this paper, we propose a novel design framework that extends this concept from "moment matching" for approximation to "moment assignment" for the active control of steady-state. The key observation is that the closed-loop moment of an interconnected linear system can be decomposed into the open-loop moment and a term linearly parameterized by the moment of the compensator. Based on this observation, we provide necessary and sufficient conditions for the assignability of desired moment and a canonical form of the dynamic compensator, followed by constructive synthesis procedure of compensator. This covers both output regulation and closed-loop interpolation, and further suggests using only the Sylvester equation, rather than regulator equations.

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arXiv2025

Adaptation of Parameters in Heterogeneous Multi-agent Systems

This paper proposes an adaptation mechanism for heterogeneous multi-agent systems to align the agents' internal parameters, based on enforced consensus through strong couplings. Unlike homogeneous systems, where exact consensus is attainable, the heterogeneity in node dynamics precludes perfect synchronization. Nonetheless, previous work has demonstrated that strong coupling can induce approximate consensus, whereby the agents exhibit emergent collective behavior governed by the so-called blended dynamics. Building on this observation, we introduce an adaptation law that gradually aligns the internal parameters of agents without requiring direct parameter communication. The proposed method reuses the same coupling signal employed for state synchronization, which may result in a biologically or sociologically plausible adaptation process. Under a persistent excitation condition, we prove that the linearly parametrized vector fields of the agents converge to each other, thereby making the dynamics asymptotically homogeneous, and leading to exact consensus of the state variables.

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arXiv2024

Node-wise monotone barrier coupling law for formation control

We study a node-wise monotone barrier coupling law, motivated by the synaptic coupling of neural central pattern generators. It is illustrated that this coupling imitates the desirable properties of neural central pattern generators. In particular, the coupling law 1) allows us to assign multiple central patterns on the circle and 2) allows for rapid switching between different patterns via simple `kicks'. In the end, we achieve full control by partitioning the state space by utilizing a barrier effect and assigning a unique steady-state behavior to each element of the resulting partition. We analyze the global behavior and study the viability of the design.

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arXiv2023

Rapid and robust synchronization via weak synaptic coupling Extended arXiv version

This paper examines how weak synaptic coupling can achieve rapid synchronization in heterogeneous networks. The assumptions aim at capturing the key mathematical properties that make this possible for biophysical networks. In particular, the combination of nodal excitability and synaptic coupling are shown to be essential to the phenomenon.

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arXiv2023

Complexity reduction for resilient state estimation of uniformly observable nonlinear systems

A resilient state estimation scheme for uniformly observable nonlinear systems, based on a method for local identification of sensor attacks, is presented. The estimation problem is combinatorial in nature, and so many methods require substantial computational and storage resources as the number of sensors increases. To reduce the complexity, the proposed method performs the attack identification with local subsets of the measurements, not with the set of all measurements. A condition for nonlinear attack identification is introduced as a relaxed version of existing redundant observability condition. It is shown that an attack identification can be performed even when the state cannot be recovered from the measurements. As a result, although a portion of measurements are compromised, they can be locally identified and excluded from the state estimation, and thus the true state can be recovered. Simulation results demonstrate the effectiveness of the proposed scheme.

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arXiv2023

Edge-wise funnel output synchronization of heterogeneous agents with relative degree one

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 global information such as the number of participating nodes, the graph structure, and so on, which prevents a fully decentralized design of the node dynamics in conjunction with the coupling laws. To resolve this issue, the idea of funnel control, which is a method for adaptive gain selection, can be exploited for a node-wise coupling, but the price to pay is that the collective emergent behavior is no longer governed by a simple average of the node dynamics. Our analysis reveals that this drawback can be avoided by an edge-wise design premise, which is the idea that we present in this paper. After all, we gain benefits such as a fully decentralized design without global information, collective emergent behavior being governed by the blended dynamics, and the plug-and-play operation based on edge-wise handshaking between two nodes.

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arXiv2022

A Design Method of Distributed Algorithms via Discrete-time Blended Dynamics Theorem

We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore, once we get a blended dynamics for a particular computational task, design idea of node dynamics for individual heterogeneous agents can easily occur. In the continuous-time case, prediction by blended dynamics was enabled by high coupling gain among neighboring agents. In the discrete-time case, we propose an equivalent action, which we call multi-step coupling in this paper. Compared to the continuous-time case, the blended dynamics can have more variety depending on the coupling matrix. This benefit is demonstrated with three applications; distributed estimation of network size, distributed computation of the PageRank, and distributed computation of the degree sequence of a graph, which correspond to the coupling by doubly-stochastic, column-stochastic, and row-stochastic matrices, respectively.

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arXiv2022

Open-loop contraction design

Given a non-contracting trajectory of a nonlinear system, we consider the question of designing an input perturbation that makes the perturbed trajectory contracting. This paper stresses the analogy of this question with the classical question of feedback stabilization. In particular, it is shown that the existence of an output variable that ensures contraction of the inverse system facilitates the design of a contracting input perturbation. We illustrate the relevance of this question in parameter estimation.

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arXiv2022

Zeros of the Riemann Zeta Function

In this paper, we present a proof of the Riemann hypothesis. We show that zeros of the Riemann zeta function should be on the line with the real value 1/2, in the region where the real part of complex variable is between 0 and 1.

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arXiv2022

The Riemann Hypothesis and the possible proof

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.

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arXiv2021

Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling Extended arXiv version

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 multi-agent systems by a high-gain coupling; consequently we call our novel synchronization method `(node-wise) funnel coupling.' By adjusting the conventional proof technique in the funnel control study, we are even able to obtain asymptotic synchronization with the same funnel coupling law. Moreover, the emergent collective behavior that arises for a heterogeneous multi-agent system when enforcing arbitrary precision synchronization by the proposed funnel coupling law, is analyzed in this paper. In particular, we introduce a single scalar dynamics called `emergent dynamics' which describes the emergent synchronized behavior of the multi-agent system under funnel coupling. Characterization of the emergent dynamics is important because, for instance, one can design the emergent dynamics first such that the solution trajectory behaves as desired, and then, provide a design guideline to each agent so that the constructed vector fields yield the desired emergent dynamics. We illustrate this idea via the example of a distributed median solver based on funnel coupling.

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arXiv2021

Target formation on the circle by monotone system design

Positivity and Perron-Frobenius theory provide an elegant framework for the convergence analysis of linear consensus algorithms. Here we consider a generalization of these ideas to the analysis of nonlinear consensus algorithms on the circle and establish tools for the design of consensus protocols that monotonically converge to target formations on the circle.

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arXiv2021

Design of heterogeneous multi-agent system for distributed computation

A group behavior of a heterogeneous multi-agent system is studied which obeys an "average of individual vector fields" under strong couplings among the agents. Under stability of the averaged dynamics (not asking stability of individual agents), the behavior of heterogeneous multi-agent system can be estimated by the solution to the averaged dynamics. A following idea is to "design" individual agent's dynamics such that the averaged dynamics performs the desired task. A few applications are discussed including estimation of the number of agents in a network, distributed least-squares or median solver, distributed optimization, distributed state estimation, and robust synchronization of coupled oscillators. Since stability of the averaged dynamics makes the initial conditions forgotten as time goes on, these algorithms are initialization-free and suitable for plug-and-play operation. At last, nonlinear couplings are also considered, which potentially asserts that enforced synchronization gives rise to an emergent behavior of a heterogeneous multi-agent system.

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arXiv2021

A Tool for Analysis and Synthesis of Heterogeneous Multi-agent Systems under Rank-deficient Coupling

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-agent system consisting of a weighted average of the vector fields of all agents, and some sub-dynamics of agents. The weighted average is an emergent dynamics, which we call a blended dynamics. By analyzing or synthesizing the blended dynamics, one can predict or design the behavior of a heterogeneous multi-agent system when the coupling gain is sufficiently large. For this result, stability of the blended dynamics is required. Since stability of the individual agent is not asked, the stability of the blended dynamics is the outcome of trading off the stability among the agents. It can be seen that, under the stability of the blended dynamics, the initial conditions of the individual agents are forgotten as time goes on, and thus, the behavior of the synthesized multi-agent system is initialization-free and is suitable for plug-and-play operation. As a showcase, we apply the proposed tool to four application problems; distributed state estimation for linear systems, practical synchronization of heterogeneous Van der Pol oscillators, estimation of the number of nodes in a network, and a problem of distributed optimization.

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