Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.29512

Dissipation Bounds and Hardness in Globally Asymptotically Stable Quadratic Systems

Subhransu S. Bhattacharjee
View original source ↗Read source document ↗Export metadata ↓

Abstract

Approximating the maximum retained energy fraction in globally asymptotically stable quadratic systems of growing dimension is NP-hard at every fixed positive additive error below $1/2$, even when strict quartic Lyapunov functions and strictness proofs are constructed in polynomial time and included in the input. Polynomial-factor approximation is also NP-hard for the least dissipated fraction, energy-halving time and structured coefficient distance to loss of asymptotic stability. For a partially damped family, minimum unit-sphere coupling norm equals that distance, with two-sided inverse-square halving-time bounds at distances in $(0,1/2]$ and explicit coefficient factors. Additive hardness persists under structured coefficient perturbations and direct damping, even with global exponential stability, a strict quadratic Lyapunov function and a Hurwitz Jacobian.

Explore related subjects

eess.SYcs.CCcs.SYmath.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Subhransu S. Bhattacharjee. 2026-10-22. Dissipation Bounds and Hardness in Globally Asymptotically Stable Quadratic Systems. https://arxiv.org/abs/2610.29512

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Opinion Dynamics in Social Multiplex Networks with Mono and Bi-directional Interactions in the Presence of Leaders

We delve into the dynamics of opinions within a multiplex network using coordination games, where agents communicate either through one-way or two-way interactions, and where a designated leader may be present. By employing graph theory and Markov chains, we illustrate that despite zero diagonal elements in transition probability matrices or decomposable layers, opinions converge under specific conditions on the layers, leading to a consensus, and we show by a counterexample that a spanning tree in the union of the layers does not suffice. We further scrutinize the convergence rates of opinion dynamics in networks with one-way versus two-way interactions. We find that in networks with a designated leader, opinions converge towards the initial opinion of the leader, whereas in networks without a designated leader, opinions converge to a convex combination of the opinions of agents. Moreover, we emphasize the crucial role of designated leaders in steering opinion convergence within the network. Paired experiments on 1,200 random multiplex networks show that a leader slows down convergence, and that two-way interactions slow it down in the presence of a leader but speed it up in its absence.

eess.SY↗
arXiv2026

Network-Aware Progressive Replacement Sequence Planning for Laser-Enhanced BeiDou Navigation Constellations

The early satellites of the third-generation BeiDou Navigation Satellite System (BDS-3) are approaching the end of their design lifetime, making progressive constellation replacement an inevitable engineering task. Meanwhile, laser inter-satellite links (LISLs) offer high-precision time transfer, ranging, and high-rate data forwarding, providing a promising upgrade path for future BeiDou satellites. This paper investigates the replacement-sequence planning problem for progressively replacing legacy microwave satellites with laser-enabled satellites from a networking perspective. Since practical replacement decisions remain constrained by legacy satellite lifetime, on-orbit condition, laser satellite manufacturing readiness, and launch scheduling, networking information is used as an auxiliary criterion in the actual engineering replacement process. An integer linear programming model is developed to evaluate the network value of intermediate laser--microwave hybrid states. Based on this common state evaluator, two complementary planning methods are developed. A priority-aware exact method supports round-wise network-assisted launch decisions, while a visibility-guided adaptive large-neighborhood search is used for full-sequence planning and provides a full-horizon network-oriented near-optimal reference. Simulations using the actual BDS-3 constellation show that stronger network participation leads to earlier and larger ground-connected laser subnetworks, fewer microwave-dependent satellites, better coordination between laser-backbone growth and high-rate ground access, and improved residual microwave-layer performance. These results provide a quantitative basis for incorporating network performance as an auxiliary criterion in future BeiDou replacement planning.

eess.SY↗
arXiv2026

Physically Constrained Agentic AI for Energy Scheduling

Agentic AI extends energy management beyond fixed-form interaction by translating natural-language requests into coordinated scheduling actions. We present a hierarchical ReAct Energy Management System (EMS) in which one orchestrator coordinates specialist agent types for shiftable appliances, EV charging, and thermal control. Physical authorization is separated from language generation: a deterministic critic reconstructs each integrated day-ahead candidate and checks its schema, appliance cycles, device power, thermal comfort, and, when active, the whole power feeder limit. Across Qwen 3.5 checkpoints, single-appliance mixed-integer schedules were feasible in 83.3 percent of runs. Localized feedback produced no accepted coupled schedule, whereas a multi-step policy authorized 6/6 current coupled runs: 3/3 for 27B and 3/3 for 35B-A3B. The standard occupied-window policy permits pre-conditioning, enforces comfort from 09:00-18:00. Every accepted schedule passed an independent final replay. Feasible costs were 2522.499 JPY for 27B and 1592.697 JPY for 35B-A3B, which are slightly higher than the mathematical optimization optimum of 1343.380 JPY. These results establish a fail-closed workflow for agentic MIP and MILP energy scheduling under the declared physical model.

eess.SY↗