2024 |
Hyungbo Shim How Does a Swarm Exhibit Emergent Behavior Through Synchronization? Journal Article In: Journal of Institute of Control, Robotics and Systems, vol. 30, iss. 4, pp. 352, 2024, ISSN: 1976-5622. Abstract | Links | BibTeX | Tags: Blended dynamics, Multi-agent systems, Synchronization @article{nokey, A swarm of individuals often exhibits behaviors that are not possible for each individual. This phenomenon is called emergence, and this paper mathematically demonstrates that new dynamics can arise in swarm behavior that cannot be explained by the dynamics of individuals. In particular, we argue that emergence occurs when heterogeneity is coupled with synchronization. These two concepts may seem conflicting, as heterogeneity is the tendency to differ whereas synchronization is the tendency toward sameness. However, we show that emergent behavior arises from the interplay between the two. |
Jeong Woo Kim / Jin Gyu Lee / Donggil Lee / Hyungbo Shim A design method of distributed algorithms via discrete-time blended dynamics theorem Journal Article In: Automatica, vol. 159, pp. 111371, 2024, ISSN: 0005-1098. Abstract | Links | BibTeX | Tags: Blended dynamics, Discrete-time blended dynamics, Discrete-time heterogeneous multi-agent system, Multi-step coupling @article{Discrete-timeheterogeneousmulti-agentsystemMulti-stepcouplingBlendeddynamics, 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. |
2023 |
Jeong Mo Seong / Donggil Lee / Hyungbo Shim Exponential Synchronization of Heterogeneous Multi-agent Systems via Linear-signum-type Diffusive Coupling: Blended Dynamics Approach Proceedings Article In: International Conference on Control, Automation and Systems (ICCAS 2023), IEEE, Yeosu, Korea, Republic of, 2023. Abstract | Links | BibTeX | Tags: Blended dynamics, Exponential synchronization, Heterogeneous multi-agents @inproceedings{nokey, This paper investigates the behavior of heterogeneous agents that interact through diffusive coupling, resulting in emergent blended dynamics that may not be observed in the dynamics of individual agents. In particular, we propose a linear-signum-type diffusive coupling to achieve exponential synchronization among heterogeneous agents. This finding offers a notable advantage over previous research, which primarily focused on linear-type diffusive coupling with remaining steady-state error in synchronization. We provide conditions of both linear and signum coupling strengths for achieving the exponential synchronization and analyze the associated convergence rate. Furthermore, simulation results validate the effectiveness of the proposed approach. |
Jin Gyu Lee / Thomas Berger / Stephan Trenn / Hyungbo Shim Edge-wise funnel output synchronization of heterogeneous agents with relative degree one Journal Article In: Automatica, vol. 156, pp. 111204, 2023, ISSN: 0005-1098. Abstract | Links | BibTeX | Tags: Blended dynamics, Funnel control, Heterogeneous multi-agents, output synchronization @article{nokey, 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 |
Donggil Lee / Junsoo Kim / Hyungbo Shim Distributed Resilient Observer: Blended Dynamics Theory Meets ℓ1-Minimization Approach Journal Article In: IEEE Control Systems Letters, vol. 7, pp. 2083 - 2088, 2023, ISSN: 2475-1456. Abstract | Links | BibTeX | Tags: Blended dynamics, Blended Dynamics Approach, Distributed state estimation, Resilient state estimation @article{nokeyp, This paper presents a distributed resilient observer for continuous-time linear time-invariant plants that remains functional even under sensor attacks. The proposed method aims to determine the estimation outcome that matches the majority of sensor measurements, which is formulated as an ℓ1-minimization problem considering all the observable components of each sensor measurement. A distributed observer based on the blended dynamics theory is then proposed to solve the ℓ1-minimization problem in a distributed manner. As a result, the distributed resilient estimation is enabled for a broader class of systems compared to previous works. The design procedure is constructive with parameters obtained from a specified condition that is equivalent to the well-known null-space property. |
2020 |
Jiyeon Nam / Taekyoo Kim / Gyunghoon Park / Hyungbo Shim Weighted Averaged Behavior of Synchronization among Heterogeneous Agents in a Sampled-data Setting Proceedings Article In: Proc. of 2020 Annual American Control Conference (ACC), pp. 4405-4410, IEEE, Denver, CO, USA, 2020. Abstract | Links | BibTeX | Tags: Blended dynamics, Heterogeneous multi-agents, Sampled data system @inproceedings{NamKimParkShim20, In this paper, we address the problem of synchronization among heterogeneous agents in a sampled-data setting. The key observation is that the sample-and-hold process introduces additional node-wise weights on the Laplacian matrix in the discrete-time domain. We then show that in the sampled-data setting, all of the agents' states approach the state of the so-called weighted averaged dynamics, an auxiliary dynamics that represents the collective behavior of heterogeneous agents when they are synchronized. In addition, admissible ranges of the sampling period and the diffusive coupling gain are computed, with which the consensus among the agents is achieved in a practical sense. |
Jin Gyu Lee/ Hyungbo Shim A Tool for Analysis and Synthesis of Heterogeneous Multi-agent Systems under Rank-deficient Coupling Journal Article In: Automatica, vol. 117, pp. 108952, 2020, ISSN: 0005-1098. Abstract | Links | BibTeX | Tags: Blended dynamics, Heterogeneous multi-agents, Singular perturbation, Synchronization @article{Lee20, 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. |
Jin Gyu Lee / Junsoo Kim / Hyungbo Shim Fully distributed resilient state estimation based on distributed median solver Journal Article In: IEEE Transactions on Automatic Control, vol. 65, no. 9, pp. 3935-3942, 2020, ISSN: 0018-9286. Abstract | Links | BibTeX | Tags: Analytical redundancy, Attack detection, Attack resilience, Blended dynamics, Cyber-physical systems, Heterogeneous multi-agents, Resilient state estimation, Strong coupling @article{Lee20b, 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 distributed network and excluded from the observers. For this, the overall network (not the individual local observer) is assumed to have redundant sensors and assumed to be connected. The proposed scheme is based on a novel design of a distributed median solver, which approximately recovers the median value of local estimates. |
2019 |
Jin Gyu Lee / Hyungbo Shim Behavior of a network of heterogeneous Li´enard systems under strong output coupling Proceedings Article In: Proc. of 8th IFAC Symposium on Mechatronic Systems & 11th IFAC Symposium on Nonlinear Control Systems, pp. 256-261, IFAC, Vienna, Austria, 2019. Abstract | Links | BibTeX | Tags: Approximate synchronization, Blended dynamics, Heterogeneous multi-agents, Internal model principle, Lienard system, Oscillations, Singular perturbation, Strong coupling @inproceedings{LeeShim19b, 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 making elements approximately synchronize. The intuition comes from a series of developments recently made in the name of ‘blended dynamics,’ and thus, the common philosophy of ‘blended dynamics’ approach enables us to illustrate a biological phenomenon that collective behavior is preserved even when there are some malfunctioning elements. |
Seungjoon Lee / Hyungbo Shim Distributed Algorithm for Economic Dispatch Problem With Separable Losses Journal Article In: IEEE Control Systems Letters, vol. 3, no. 3, pp. 685-690, 2019. Links | BibTeX | Tags: Blended dynamics, Distributed optimization @article{LeeShim19, |
Hyeonjun Yun / Hyungbo Shim / Hyo-Sung Ahn Initialization-free Privacy-guaranteed Distributed Algorithm for Economic Dispatch Problem Journal Article In: Automatica, vol. 102, pp. 86-93, 2019. Abstract | Links | BibTeX | Tags: Blended dynamics, Synchronization @article{YunShimAhn19, This paper considers the economic dispatch problem for a network of power generators and customers. In particular, our aim is to minimize the total generation cost under the power supply-demand balance and the individual generation capacity constraints. This problem is solved in a distributed manner, i.e., a dual gradient-based continuous-time distributed algorithm is proposed in which only a single dual variable is communicated with the neighbors and no private information of the node is disclosed. The proposed algorithm is simple and no specific initialization is necessary, and this in turn allows on-line change of network structure, demand, generation constraints, and even the participating nodes. The algorithm also exhibits a special behavior when the problem becomes infeasible so that each node can detect over-demand or under-demand situation of the power network. Simulation results on IEEE 118 bus system confirm robustness against variations in power grids. |
2016 |
Jaeyong Kim / Jongwook Yang / Hyungbo Shim / Jung-Su Kim / Jin Heon Seo Robustness of Synchronization of Heterogeneous Agents by Strong Coupling and a Large Number of Agents Journal Article In: IEEE Transactions on Automatic Control, vol. 61, no. 10, pp. 3096-3102, 2016. Abstract | Links | BibTeX | Tags: Blended dynamics, Heterogeneity, Multi-agent system, Synchronization @article{KimYangShimKimSeo16, This technical note studies robustness of synchronization against heterogeneity of multi-agent systems. Here, heterogeneity also includes uncertainties and external disturbances in each agent. In order to effectively deal with the heterogeneous agents, we introduce the concept of the averaged dynamics which is the average of all agents’ dynamics, and then claim that two sources enhance the robustness of synchronized behavior against heterogeneity of agents’ dynamics. First, in spite of the heterogeneity of agents’ dynamics, we show that strong coupling among agents makes the trajectories of all agents arbitrarily close to the averaged dynamics. Second, in the averaged dynamics, the effect of variations in each agent gets smaller as the number of agents increases. Simulation results confirm the claim that a large number of agents with strong couplings have robust synchronization. |
2015 |
Jaeyong Kim / Hyungbo Shim Robust Synchronization for High-Order Heterogeneous Multi-Agent Systems Proceedings Article In: Proc. of SWARM 2015: The First International Symposium on Swarm Behavior and Bio-Inspired Robotics, pp. 293-294, Kyoto, Japan, 2015. Abstract | BibTeX | Tags: Blended dynamics, Multi-agent system, Synchronization @inproceedings{KimShim15b, This paper studies robustness of synchronization for high-order heterogeneous multi-agent systems. Using the concept of the averaged dynamics, it is claimed that two sources enhance the robustness of synchronized behavior against heterogeneity of agents’ dynamics. First, strongly coupled network makes each behavior of heterogeneous agent close to that of the averaged dynamics. Second, we observe that the averaged dynamics becomes more robust against individual variation as the number of agents increases. Simulation result confirms our claim that a large number of agents with strong coupling have robust synchronization. |
List of English Publication
2024 |
How Does a Swarm Exhibit Emergent Behavior Through Synchronization? Journal Article In: Journal of Institute of Control, Robotics and Systems, vol. 30, iss. 4, pp. 352, 2024, ISSN: 1976-5622. |
A design method of distributed algorithms via discrete-time blended dynamics theorem Journal Article In: Automatica, vol. 159, pp. 111371, 2024, ISSN: 0005-1098. |
2023 |
Exponential Synchronization of Heterogeneous Multi-agent Systems via Linear-signum-type Diffusive Coupling: Blended Dynamics Approach Proceedings Article In: International Conference on Control, Automation and Systems (ICCAS 2023), IEEE, Yeosu, Korea, Republic of, 2023. |
Edge-wise funnel output synchronization of heterogeneous agents with relative degree one Journal Article In: Automatica, vol. 156, pp. 111204, 2023, ISSN: 0005-1098. |
Distributed Resilient Observer: Blended Dynamics Theory Meets ℓ1-Minimization Approach Journal Article In: IEEE Control Systems Letters, vol. 7, pp. 2083 - 2088, 2023, ISSN: 2475-1456. |
2020 |
Weighted Averaged Behavior of Synchronization among Heterogeneous Agents in a Sampled-data Setting Proceedings Article In: Proc. of 2020 Annual American Control Conference (ACC), pp. 4405-4410, IEEE, Denver, CO, USA, 2020. |
A Tool for Analysis and Synthesis of Heterogeneous Multi-agent Systems under Rank-deficient Coupling Journal Article In: Automatica, vol. 117, pp. 108952, 2020, ISSN: 0005-1098. |
Fully distributed resilient state estimation based on distributed median solver Journal Article In: IEEE Transactions on Automatic Control, vol. 65, no. 9, pp. 3935-3942, 2020, ISSN: 0018-9286. |
2019 |
Behavior of a network of heterogeneous Li´enard systems under strong output coupling Proceedings Article In: Proc. of 8th IFAC Symposium on Mechatronic Systems & 11th IFAC Symposium on Nonlinear Control Systems, pp. 256-261, IFAC, Vienna, Austria, 2019. |
Distributed Algorithm for Economic Dispatch Problem With Separable Losses Journal Article In: IEEE Control Systems Letters, vol. 3, no. 3, pp. 685-690, 2019. |
Initialization-free Privacy-guaranteed Distributed Algorithm for Economic Dispatch Problem Journal Article In: Automatica, vol. 102, pp. 86-93, 2019. |
2016 |
Robustness of Synchronization of Heterogeneous Agents by Strong Coupling and a Large Number of Agents Journal Article In: IEEE Transactions on Automatic Control, vol. 61, no. 10, pp. 3096-3102, 2016. |
2015 |
Robust Synchronization for High-Order Heterogeneous Multi-Agent Systems Proceedings Article In: Proc. of SWARM 2015: The First International Symposium on Swarm Behavior and Bio-Inspired Robotics, pp. 293-294, Kyoto, Japan, 2015. |