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Split-Merge Dynamics for Shapley-Fair Coalition Formation Shapley-Fair联盟形成的分裂合并动力学
IFAC-PapersOnLine Pub Date : 2026-01-01 Epub Date: 2026-10-09 DOI: 10.1016/j.ifacol.2026.09.026
Quanyan Zhu, Zhengye Han
{"title":"Split-Merge Dynamics for Shapley-Fair Coalition Formation","authors":"Quanyan Zhu,&nbsp;Zhengye Han","doi":"10.1016/j.ifacol.2026.09.026","DOIUrl":"10.1016/j.ifacol.2026.09.026","url":null,"abstract":"<div><div>Coalition formation is often modeled as a static equilibrium problem, neglecting the dynamic processes governing how agents self-organize. This paper proposes a dynamic split-and-merge framework that balances two conflicting economic forces: individual fairness and collective efficiency. We introduce a control-theoretic mechanism where topological operations are driven by distinct signals: splits are triggered by fairness violations (specifically, negative Shapley values representing “agent-responsible inefficiency”), while merges are driven by strict surplus improvements (superadditivity). We prove that these dynamics converge in finite time to a specific class of steady states termed Shapley-Fair and Merge-Stable (SFMS) partitions. Convergence is established via a vector Lyapunov function tracking aggregate fairness deficits and system surplus, leveraging a discrete-time LaSalle invariance principle. Numerical case studies on a 10-player game demonstrate the algorithm’s ability to resolve fairness tensions and reach stable configurations, providing a rigorous foundation for endogenous coalition formation in dynamic environments.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"60 1","pages":"Pages 151-156"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Input-to-state stability and admissibility in integral norms for linear distributed parameter systems⁎ 线性分布参数系统积分范数的输入-状态稳定性和可容许性
IFAC-PapersOnLine Pub Date : 2026-01-01 Epub Date: 2026-10-09 DOI: 10.1016/j.ifacol.2026.09.021
Sahiba Arora, Andrii Mironchenko
{"title":"Input-to-state stability and admissibility in integral norms for linear distributed parameter systems⁎","authors":"Sahiba Arora,&nbsp;Andrii Mironchenko","doi":"10.1016/j.ifacol.2026.09.021","DOIUrl":"10.1016/j.ifacol.2026.09.021","url":null,"abstract":"<div><div>We investigate input-to-state stability (ISS) for infinite-dimensional linear systems with inputs and trajectories in Lp-spaces. We begin by developing the corresponding admissibility theory for linear systems with unbounded input operators. We show that ISS in integral norms cannot be in general characterized by exponential stability together with finite-time admissibility, in contrast to classical ISS theory. For analytic semigroups, we derive a precise characterization based on maximal regularity theory. Finally, we establish direct Lyapunov theorems and construct Lyapunov functions for L<sup>p</sup>-L<sup>q</sup>-ISS systems. We illustrate the results with examples, including diagonal systems and diffusion equations.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"60 1","pages":"Pages 121-126"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the stabilization of Timoshenko beams using boundary torque control⁎ 边界转矩控制下Timoshenko梁的稳定研究[j]
IFAC-PapersOnLine Pub Date : 2026-01-01 Epub Date: 2026-10-09 DOI: 10.1016/j.ifacol.2026.09.022
Jean Auriol, Yongxin Wu, Yann Le Gorrec, Hector Ramirez
{"title":"On the stabilization of Timoshenko beams using boundary torque control⁎","authors":"Jean Auriol,&nbsp;Yongxin Wu,&nbsp;Yann Le Gorrec,&nbsp;Hector Ramirez","doi":"10.1016/j.ifacol.2026.09.022","DOIUrl":"10.1016/j.ifacol.2026.09.022","url":null,"abstract":"<div><div>This study investigates the stabilization of a Timoshenko beam driven by a single torque actuator. Our approach begins by reformulating the system in Riemann coordinates, yielding a 2 × 2 hyperbolic system of balance laws. Due to the presence of a single actuator, the system is inherently underactuated. To address this limitation, we apply backstepping transformations to recast the system into an Integral Difference Equation with distributed actuation. Leveraging an approximate controllability condition, we then design a stabilizing controller featuring an auto-regressive structure. This controller relies on integrals of the system state and input history over a fixed-length time window. Finally, we validate the theoretical results through simulations, demonstrating the effectiveness of the proposed control strategy.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"60 1","pages":"Pages 127-132"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lyapunov criterion for boundedness of reachability sets⁎ 可达集有界性的Lyapunov准则
IFAC-PapersOnLine Pub Date : 2026-01-01 Epub Date: 2026-10-09 DOI: 10.1016/j.ifacol.2026.09.035
Patrick Bachmann, Andrii Mironchenko
{"title":"Lyapunov criterion for boundedness of reachability sets⁎","authors":"Patrick Bachmann,&nbsp;Andrii Mironchenko","doi":"10.1016/j.ifacol.2026.09.035","DOIUrl":"10.1016/j.ifacol.2026.09.035","url":null,"abstract":"<div><div>We provide a converse Lyapunov theorem for boundedness of reachability sets for a general class of control systems whose flow is Lipschitz continuous on compact intervals with respect to trajectory-dominated inputs. We show that this condition is satisfied by many semi-linear evolution equations. For ordinary differential equations, as a consequence of our results, we obtain a converse Lyapunov theorem for forward completeness, without a priori restrictions on the magnitude of inputs.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"60 1","pages":"Pages 205-210"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some extensions of the classical Laplace transform: Initial value theorem and inversion formula. 经典拉普拉斯变换的一些推广：初值定理和反演公式。
IFAC-PapersOnLine Pub Date : 2026-01-01 Epub Date: 2026-10-09 DOI: 10.1016/j.ifacol.2026.09.029
Erik I. Verriest
{"title":"Some extensions of the classical Laplace transform: Initial value theorem and inversion formula.","authors":"Erik I. Verriest","doi":"10.1016/j.ifacol.2026.09.029","DOIUrl":"10.1016/j.ifacol.2026.09.029","url":null,"abstract":"<div><div>The relation between the Fourier and Laplace transforms leads to an extension to a more general class of right-sided functions (and distributions). The initial value theorem, which classically enabled the computation of the initial value without explicit inversion, is generalized. With a precise notion of strict properness, it also generalizes to a <em>boundary value theorem</em>. In turn, novel <em>inversion formulas</em> are derived, avoiding the classical inversion formula, with its averaging as found in the Fejér theory. A Laplace-domain derivation is then given to characterize the instantaneous effect of impulsive inputs for linear time-invariant (LTI) systems.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"60 1","pages":"Pages 169-174"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exponential output-to-state stability of linear systems with bounded output operators⁎ 具有有界输出算子的线性系统的指数输出-状态稳定性
IFAC-PapersOnLine Pub Date : 2026-01-01 Epub Date: 2026-10-09 DOI: 10.1016/j.ifacol.2026.09.001
Qiaoling Chen, Andrii Mironchenko, Fabian Wirth
{"title":"Exponential output-to-state stability of linear systems with bounded output operators⁎","authors":"Qiaoling Chen,&nbsp;Andrii Mironchenko,&nbsp;Fabian Wirth","doi":"10.1016/j.ifacol.2026.09.001","DOIUrl":"10.1016/j.ifacol.2026.09.001","url":null,"abstract":"<div><div>For linear infinite-dimensional systems, exponential detectability is known to be stronger than exponential zero-detectability, and both these concepts are hard to extend to the nonlinear setting. In this work, we show that there is a broad hierarchy of detectability notions between these two concepts, centered around the concept of exponential output-to-state stability (eOSS). We study eOSS for linear infinite-dimensional systems with bounded output operators. It is shown that exponential detectability guarantees the existence of a coercive eOSS Lyapunov function and therefore eOSS. Several counterexamples demonstrate the fundamental differences between the detectability concepts employed in this work. However, if the system has only finitely many unstable eigenvalues, then all the concepts coincide. The results are illustrated with an example.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"60 1","pages":"Pages 1-6"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Data-Driven Network LQG Mean Field Games with Heterogeneous Populations via Integral Reinforcement Learning⁎ 基于积分强化学习的异构种群数据驱动网络LQG平均场博弈
IFAC-PapersOnLine Pub Date : 2026-01-01 Epub Date: 2026-10-09 DOI: 10.1016/j.ifacol.2026.09.033
Jean Zhu, Shuang Gao
{"title":"Data-Driven Network LQG Mean Field Games with Heterogeneous Populations via Integral Reinforcement Learning⁎","authors":"Jean Zhu,&nbsp;Shuang Gao","doi":"10.1016/j.ifacol.2026.09.033","DOIUrl":"10.1016/j.ifacol.2026.09.033","url":null,"abstract":"<div><div>This paper establishes a data-driven solution for infinite-horizon linear quadratic Gaussian Mean Field Games with network-coupled heterogeneous agent populations where the dynamics of the agents are unknown. The solution technique relies on Integral Reinforcement Learning and Kleinman’s iteration for solving algebraic Riccati equations (ARE). The resulting algorithm uses trajectory data to generate network-coupled MFG strategies for agents and does not require parameters of agents’ dynamics. Under technical conditions on the persistency of excitation and on the existence of unique stabilizing solution to the corresponding AREs, the learned network-coupled MFG strategies are shown to converge to their true values.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"60 1","pages":"Pages 193-198"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Observer Design for Systems with Unknown Dynamics and Limited Measurements⁎ 未知动力学和有限测量系统的观测器设计
IFAC-PapersOnLine Pub Date : 2026-01-01 Epub Date: 2026-10-09 DOI: 10.1016/j.ifacol.2026.09.034
Joel Bartlett, Nicolas Hudon, Martin Guay
{"title":"Observer Design for Systems with Unknown Dynamics and Limited Measurements⁎","authors":"Joel Bartlett,&nbsp;Nicolas Hudon,&nbsp;Martin Guay","doi":"10.1016/j.ifacol.2026.09.034","DOIUrl":"10.1016/j.ifacol.2026.09.034","url":null,"abstract":"<div><div>We propose a method to design Kazantzis–Kravaris–Luenberger (KKL) observers for nonlinear systems with unknown dynamics using only output measurements. The order of the unknown dynamics is assumed to be known, and the system is assumed to be observable. The proposed approach first consists in approximating a model for the system from noise free output datasets using the SINDy algorithm. The obtained dynamics are then used to construct an approximate inverse of the KKL mapping using a SiLU neural network. Convergence of the proposed approach is demonstrated. A numerical example is provided to illustrate the approach and demonstrate its application for the observation of systems in the presence of measurement noise.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"60 1","pages":"Pages 199-204"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Set-Theoretic Output Feedback Tracking Control via Linear Programming 基于线性规划的集论输出反馈跟踪控制
IFAC-PapersOnLine Pub Date : 2026-01-01 Epub Date: 2026-10-09 DOI: 10.1016/j.ifacol.2026.09.030
Avaneet Kumar, Ashish Kothyari
{"title":"Set-Theoretic Output Feedback Tracking Control via Linear Programming","authors":"Avaneet Kumar,&nbsp;Ashish Kothyari","doi":"10.1016/j.ifacol.2026.09.030","DOIUrl":"10.1016/j.ifacol.2026.09.030","url":null,"abstract":"<div><div>This paper presents a set-theoretic framework for tracking a set-point reference signal in constrained discrete-time linear systems subject to bounded additive disturbances via output feedback. The proposed approach jointly synthesizes a stabilizing output-feedback controller and a robust control-invariant (RCI) set within the state and input constraints using zonotopic set representations. By exploiting zonotope inclusion properties, sufficient conditions for robust invariance are derived as tractable algebraic constraints, allowing the controller synthesis and RCI set computation to be formulated as a single linear program, thereby avoiding bilinear or nonconvex optimization, as is the case in state-of-the-art methods. Subsequently, a feedforward gain is designed to achieve robust set-point tracking. This feedforward gain also allows for computation of a set of admissible set-points. In addition, the explicit expressions for the steady-state tracking error bounds are derived, revealing their dependence on the disturbance set. The proposed method provides a computationally efficient and scalable solution for robust tracking control with guaranteed performance and constraint satisfaction. Finally, simulation results show the effectiveness of the proposed approach.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"60 1","pages":"Pages 175-180"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Solvability of Quasi-Regulator Equations in Non-smooth Output Regulation 非光滑输出调节中拟调节方程的可解性
IFAC-PapersOnLine Pub Date : 2026-01-01 Epub Date: 2026-10-09 DOI: 10.1016/j.ifacol.2026.09.028
Zirui Niu, Daniele Astolfi, Giordano Scarciotti
{"title":"On the Solvability of Quasi-Regulator Equations in Non-smooth Output Regulation","authors":"Zirui Niu,&nbsp;Daniele Astolfi,&nbsp;Giordano Scarciotti","doi":"10.1016/j.ifacol.2026.09.028","DOIUrl":"10.1016/j.ifacol.2026.09.028","url":null,"abstract":"<div><div>Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A fundamental prerequisite for solving this problem is the existence of solutions to the so-called “quasi-regulator equations”. In this paper, we investigate the solvability of these equations. To this end, we reformulate the quasi-regulator equations as differential-algebraic equations and highlight the critical role played by the system’s relative degree. We finally propose a “non-smooth non-resonance condition” that, under specific relative degree requirements, provides a necessary and sufficient characterization of the solvability of the quasi-regulator equations.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"60 1","pages":"Pages 163-168"},"PeriodicalIF":0.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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