Lyapunov
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Related Articles from SNS
Dual Lyapunov-based Synchronization Control of R\"ossler System
Announce Type: cross Abstract: This paper proposes a novel approach for the synchronization problem of nonlinear dynamical systems, integrating dual Lyapunov stability analysis with polynomial optimization. A comprehensive review of the relevant scientific literature on synchronization methods is conducted, with a particular focus on classical Lyapunov-based methods for chaotic systems. In this study, the R\"ossler system is synchronized by employing dual Lyapunov-based closed-loop...
A Lyapunov-Based Small-Gain Theorem for Fixed-Time Stability
arXiv:2511.23474v2 Announce Type: replace Abstract: This paper introduces a novel Lyapunov-based small-gain methodology for establishing fixed-time stability (FxTS) guarantees in interconnected dynamical systems. Specifically, we consider interconnections in which each subsystem admits an individual fixed-time input-to-state stability (ISS) Lyapunov function that certifies FxT-ISS. We then show that if a nonlinear small-gain condition is satisfied, then the entire interconnected system is FxTS.
Optimal Initialization in Depth: Lyapunov Initialization and Limit Theorems for Deep Leaky ReLU Networks
Announce Type: replace-cross Abstract: Effective initialization in deep networks requires an understanding of random neural networks. In this work, a rigorous probabilistic analysis of deep bias-free random Leaky ReLU networks is provided. We prove a Law of Large Numbers and a Central Limit Theorem for the logarithm of the norm of network activations, establishing that, as the number of layers increases, their growth is governed by a parameter called the Lyapunov exponent.
Adaptive Artificial Time-Delay Control with Barrier Lyapunov Constraints for Euler-Lagrange Robots
Announce Type: new Abstract: This paper addresses the challenge of simultaneously compensating for state-dependent uncertainties and enforcing time-varying state constraints in Euler-Lagrange systems, a common requirement in robotics that remains underserved by existing control designs. A novel adaptive control framework is developed that combines an artificial time-delay-based uncertainty estimation strategy, also known as time-delay estimation, with a barrier Lyapunov function to enforce...
State-Dependent Lyapunov Analysis of Rank-1 Matrix Factorization
Announce Type: replace Abstract: We study gradient descent for rank-1 matrix factorization through a state-dependent Lyapunov perspective. The central object is a parameterized quadratic certificate $I(\delta;\,\cdot)$ whose boundary-inward property induces a monotone state parameter $\delta_t$, thereby certifying that the trajectory is confined to a shrinking family of level sets. For certified initializations below the critical step size, this mechanism proves convergence to global minimizers.
Non-Asymptotic Convergence of Stochastic Iterative Algorithms: A Lyapunov Framework
arXiv:2605.31309v1 Announce Type: new Abstract: We survey Lyapunov-based techniques for the finite-time analysis of stochastic iterative algorithms, also known as stochastic approximation (SA) algorithms, for solving fixed-point equations $\bar{F}(x)=x$, where the operator $\bar{F}(\cdot)$ can only be accessed through a noisy oracle. We first focus on the standard setting in which $\bar{F}(\cdot)$ is contractive with respect to some norm and the noise is i.i.d., and explain how generalized...
HALO: Learning Human-Robot Collaboration via Heterogeneous-Agent Lyapunov Policy Optimization
Announce Type: replace Abstract: To improve generalization and resilience in human-robot collaboration (HRC), robots must contend with diverse combinations of human behaviors and contexts, motivating multi-agent reinforcement learning (MARL). However, inherent heterogeneity between robots and humans creates a rationality gap (RG), where decentralized policy updates deviate from cooperative joint optimization. The resulting learning problem is a general-sum differentiable game, so independent...
LC-SAC: Lyapunov-Constrained Soft Actor-Critic via Koopman Operator Theory for Trajectory Tracking and Stabilization
arXiv:2602.04132v4 Announce Type: replace Abstract: Reinforcement Learning (RL) has achieved remarkable success in solving complex sequential decision-making problems. However, its application to safety-critical physical systems remains constrained by the lack of stability guarantees. Standard RL algorithms prioritize reward maximization, often yielding policies that may induce oscillations or unbounded state divergence.
Statistical Guarantees in Data-Driven Nonlinear Control: Conformal Robustness for Stability and Safety
arXiv:2506.06228v2 Announce Type: replace Abstract: We present a true-dynamics-agnostic, statistically rigorous framework for establishing exponential stability and safety guarantees of closed-loop, data-driven nonlinear control. Central to our approach is the novel concept of conformal robustness, which robustifies the Lyapunov and zeroing barrier certificates of data-driven dynamical systems against model prediction uncertainties using conformal prediction. It quantifies these...
Robust $\mathcal{H}_\infty$ Observer Design via Finsler's Lemma and IQCs
arXiv:2604.03989v3 Announce Type: replace-cross Abstract: This paper develops a Finsler-based LMI for robust $\mathcal{H}_\infty$ observer design with integral quadratic constraints (IQCs) and block-structured uncertainty. By introducing a slack variable that relaxes the coupling between the Lyapunov matrix, the observer gain, and the IQC multiplier, the formulation addresses two limitations of the standard block-diagonal approach: the LMI requirement $\mathrm{He}(PA) \prec 0$ (which fails...