Dynamic Matrix Control
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Related Articles from SNS
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...
Input-to-State Stable Bundle Koopman Neural ODEs for Learning Controlled Dynamics under Environmental Constraints
Announce Type: new Abstract: We propose ISS-BKNO, a unified framework that integrates Koopman operator identification, Neural ordinary differential equations (ODEs), fiber bundle geometry, and input-to-state stability (ISS) certification. Unlike prior approaches that address stability, extrinsic inputs, or environmental constraints in isolation, the proposed framework simultaneously learns controlled nonlinear dynamics while guaranteeing global convergence and a computable ISS gain. The...
Steering Fractional-Order Network Dynamics via Joint Parameter and State Control
arXiv:2605.31270v1 Announce Type: new Abstract: This paper studies the control of discrete-time linear fractional-order networks, a flexible modeling framework for systems with long-range memory such as power grids, biological networks, and neuronal circuits. In contrast to the common view that fractional exponents (time-scales) are fixed parameters, we show that they can be systematically steered, together with the network coupling matrix, by appropriately designed input sequences. We first...
Geometric scaling limits of phase-only control in multimode coherent systems
arXiv:2606.04288v1 Announce Type: new Abstract: Control of coherent waves is often restricted to phase-only actuation in multimode systems, yet the resulting physical limits remain poorly understood. Here, we show that restricting control to relative phases confines dynamics to a compact manifold whose geometry produces isolated stationary interference basins with robustness governed by local curvature. Imperfections act as smooth perturbations that soften basin structure without eliminating...
Unlocking feedforward capabilities in Model Predictive Control algorithms to deal with measurable disturbances
Announce Type: new Abstract: Disturbance rejection is a central objective in process control, particularly when measurable disturbances can be exploited through feedforward action. Although Model Predictive Control (MPC) naturally incorporates disturbance models and prediction capabilities, standard formulations cannot achieve complete disturbance rejection since the cost function penalises control effort.
CoMoL: Efficient Mixture of LoRA Experts via Dynamic Core Space Merging
arXiv:2603.00573v2 Announce Type: replace Abstract: Large language models (LLMs) achieve remarkable performance on diverse downstream and domain-specific tasks via parameter-efficient fine-tuning (PEFT). However, existing PEFT methods, particularly MoE-LoRA architectures, suffer from limited parameter efficiency and coarse-grained adaptation due to the proliferation of LoRA experts and instance-level routing. To address these issues, we propose Core Space Mixture of LoRA (\textbf{CoMoL}), a...
SALAAD: Sparse And Low-Rank Adaptation via ADMM for Large Language Model Inference
arXiv:2602.00942v3 Announce Type: replace Abstract: Modern large language models are increasingly deployed under compute and memory constraints, making flexible control of model capacity a central challenge. While sparse and low-rank structures naturally trade off capacity and performance, existing approaches often rely on heuristic designs that ignore layer and matrix heterogeneity or require model-specific architectural modifications. We propose SALAAD, a plug-and-play framework applicable...
The Spectral Dynamics and Noise Geometry of Muon
arXiv:2606.08388v1 Announce Type: new Abstract: Muon replaces a matrix gradient $G=U\Sigma V^\top$ by its polar factor $UV^\top$. This keeps the singular directions selected by the gradient, but makes the update spectrum flat. We study the optimization bias created by this operation. Under explicit alignment assumptions, we prove that the polar update is the one-step entropy-maximizing choice among bounded updates that use the gradient singular directions and do not adapt to the current...
FOAM: Frequency and Operator Error-Based Adaptive Damping Method for Reducing Staleness-Oriented Error for Shampoo
Announce Type: new Abstract: Shampoo is attracting considerable attention for its superior performance on large-scale optimization benchmarks; yet it faces a significant practical bottleneck: the prohibitive computational overhead of matrix inversion. To mitigate this, practitioners typically rely on stale preconditioner updates, creating a fundamental trade-off between computational efficiency and optimization fidelity. In this work, we provide a theoretical study of staleness through the...
Complex-gauge control of anomalous Floquet corner responses in a non-Hermitian physical-synthetic photonic lattice
Announce Type: cross Abstract: We propose a non-Hermitian Floquet photonic lattice formed by a physical resonator coordinate and a synthetic frequency coordinate. A two-step modulation protocol realizes a chiral walk in this physical-synthetic plane, with a real synthetic flux controlling loop interference and imaginary gauge fields controlling non-reciprocal envelopes. We show that anomalous corner pairs at quasienergies zero and \(\pi/T\) exhibit three distinct layers of physics.