Linear Dynamical Systems
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Related Articles from SNS
SpectraLDS: Provable Distillation for Linear Dynamical Systems
arXiv:2505.17868v2 Announce Type: replace Abstract: We present the first provable method for identifying symmetric linear dynamical systems (LDS) with accuracy guarantees that are independent of the systems' state dimension or effective memory. Our approach builds upon recent work that represents symmetric LDSs as convolutions learnable via fixed spectral transformations. We show how to invert this representation, thereby recovering an LDS model from its spectral transform and yielding an...
Optimal Control and Dissipativity of Linear Hermitian Matrix-Valued Dynamical Systems
arXiv:2606.08856v1 Announce Type: cross Abstract: We develop a unified framework for linear-cost optimal control, finite-time optimal steering, dissipativity analysis, and zero-sum differential games for linear impulsive systems whose state is a Hermitian matrix evolving in $\mathbb{H}^{n+m}_{\succeq0}$, a class that encompasses continuous- and discrete-time linear systems and switched systems as degenerate cases, and includes the second-order moment dynamics of linear (stochastic) hybrid...
$H_2$ optimal model reduction of linear systems with multiple quadratic outputs
Announce Type: replace Abstract: In this work, we consider the $H_2$ optimal model reduction of dynamical systems that are linear in the state equation and up to quadratic nonlinearity in the output equation. As our primary theoretical contributions, we derive gradients of the squared $H_2$ system error with respect to the reduced model quantities and, from the stationary points of these gradients, introduce Gramian-based first-order necessary conditions for the $H_2$ optimal approximation...
$\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation
Announce Type: replace Abstract: This paper addresses the $\mathcal{H}_2$-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive interpolatory first-order optimality conditions for the linear quadratic-output $\mathcal{H}_2$ minimization problem.
LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification
arXiv:2412.12036v2 Announce Type: replace Abstract: System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of data-driven discovery in nonlinear dynamical systems, these methods have garnered significant attention. Among them, Sparse Identification of Nonlinear Dynamics (SINDy) has emerged as a transformative approach,...
Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling
Announce Type: replace Abstract: Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models. With a lot of hype and industrial demand in this field, it is not always clear how much progress there really is. To advance TS forecasting and analysis to the next level, here we argue that the field needs a dynamical systems (DS) perspective.
Competitive Instability in Judo: The Hidden Mechanism within an AI-Driven Non-Linear Dynamics Framework
Announce Type: new Abstract: This study presents a unified nonlinear dynamical framework for understanding, modelling, and teaching competitive judo. The Tori Uke dyad is formalised as a constrained multi body system whose behaviour emerges from symmetry breaking,coupling dynamics and transitions between attractor basins. Two fundamental instability archetypes rotational collapse Uchi mata type and gravitational lever collapse Seoi otoshi,suwari version, are identified as the core pathways...
Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions
arXiv:2502.03847v2 Announce Type: replace Abstract: A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order one to five in time. The error estimates are obtained by a consistency and stability analysis, based on an energy...
Notes on data-driven output-feedback control of linear MIMO systems
Announce Type: replace Abstract: Recent works have approached the data-driven design of dynamic output-feedback controllers for discrete-time LTI systems by constructing non-minimal state vectors composed of past inputs and outputs. Depending on the system's complexity (order $n$, lag $\ell$ and number of outputs $p$), it was observed in several works that such an approach presents significant limitations. In particular, many works require to restrict the class of LTI systems to those...
Efficient Coordination and Synchronization of Multi-Robot Systems Under Recurring Linear Temporal Logic
Announce Type: replace Abstract: We consider multi-robot systems under recurring tasks formalized as linear temporal logic (LTL) specifications. To solve the planning problem efficiently, we propose a bottom-up approach combining offline plan synthesis with online coordination, dynamically adjusting plans via real-time communication. To address action delays, we introduce a synchronization mechanism ensuring coordinated task execution, leading to a multi-agent coordination and...