2021 |
Aneel Tawani / Hyungbo Shim Lyapunov Functions for Singularly Perturbed Hybrid Systems with Frequent Jump Dynamics Proceedings Article In: Proc. of 2021 IEEE 60th Conference on Decision and Control, pp. 5382-5387, IEEE, Austin, Texas, USA, 2021. Abstract | Links | BibTeX | Tags: Hybrid system, Lyapunov function, Singular perturbation @inproceedings{nokey, This article considers the stability analysis for a class of hybrid systems with the focus being on the frequently occurring jump dynamics. The system class is modelled as a singularly perturbed hybrid system where the singular perturbation parameter governs the frequency of jumps. Consequently, this results in a quasi steady-state system modeled by a differential equation without any jumps, and the boundary-layer system described by purely discrete dynamics. By imposing appropriate assumptions on the quasi steady-state system and the boundary-layer system, we derive results showing practical convergence to a compact attractor when the jumps occur frequently often. Our system class is motivated by the control design problem in a network of second-order continuous-time coupled oscillators, where each agent communicates the information about its position to the neighbors at discrete times. As a corollary to our main result, we show that if the information exchange between the agents and their neighbors is frequent enough, then the oscillators achieve practical consensus. |
2020 |
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. |
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. |
2017 |
Hyeonjun Yun / Hyungbo Shim / H. J. Chang Singular Perturbation for Sampled-Data Systems With Fast Subsystems Proceedings Article In: Proc. of the 20th World Congress, pp. 8475-8480, IFAC Toulouse, France, 2017. Abstract | Links | BibTeX | Tags: Singular perturbation @inproceedings{YunShimChang17, We present a sampled-data version of the well-known Tikhonov’s theorem on singular perturbation theory. In particular, we claim that the nonlinear sampled-data systems with fast subsystems can be treated as a singularly perturbed system in a discrete-time sense. In this case, we show that the sampling period can be considered as a singular perturbation parameter. Following the nomenclature of the singular perturbation theory, we define the degenerate (DG) system and the boundary-layer (BL) system and obtain the solution of the sampled-data system as an approximation of the solutions of the lower-order subsystems. Finally, a simple example, sampled-data implementation of disturbance observer, is included to validate the theory. |
List of English Publication
2021 |
Lyapunov Functions for Singularly Perturbed Hybrid Systems with Frequent Jump Dynamics Proceedings Article In: Proc. of 2021 IEEE 60th Conference on Decision and Control, pp. 5382-5387, IEEE, Austin, Texas, USA, 2021. |
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. |
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. |
2017 |
Singular Perturbation for Sampled-Data Systems With Fast Subsystems Proceedings Article In: Proc. of the 20th World Congress, pp. 8475-8480, IFAC Toulouse, France, 2017. |