DS, including RNNs, that refer to topological (qualitative) changes in a system's

The use of momentum in stochastic gradient methods has become a widespread practice in machine learning. Different variants of momentum, including heavy-ball momentum, Nesterov's accelerated gradient (NAG), and quasi-hyperbolic momentum (QHM), have demonstrated success on various tasks.

In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems -- especially in aerospace -- this region cannot be determined a priori and is often challenging to compute. One of the most common methods for computing the stability region is to identify a Lyapunov function. A Lyapunov function is a positive function whose time derivative along system trajectories is non-positive, which provides a sufficient condition for stability and characterizes an estimated stability region. However, existing methods of characterizing a stability region via a Lyapunov function often rely on explicit knowledge of the system governing equations. In this work, we present a new physics-informed machine learning method of characterizing an estimated stability region by inferring a Lyapunov function from system trajectory data that treats the dynamical system as a black box and does not require explicit knowledge of the system governing equations. In our presented Lyapunov function Inference method (LyapInf), we propose a quadratic form for the unknown Lyapunov function and fit the unknown quadratic operator to system trajectory data by minimizing the average residual of the Zubov equation, a first-order partial differential equation whose solution yields a Lyapunov function. The inferred quadratic Lyapunov function can then characterize an ellipsoidal estimate of the stability region. Numerical results on benchmark examples demonstrate that our physics-informed stability analysis method successfully characterizes a near-maximal ellipsoid of the system stability region associated with the inferred Lyapunov function without requiring knowledge of the system governing equations.

DS, including RNNs, that refer to topological (qualitative) changes in a system's

The use of momentum in stochastic gradient methods has become a widespread practice in machine learning. Different variants of momentum, including heavy-ball momentum, Nesterov's accelerated gradient (NAG), and quasi-hyperbolic momentum (QHM), have demonstrated success on various tasks.

In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the optimization procedure, it is necessary to employ a numerical scheme to integrate candidate dynamical systems and assess how their solutions fit the data. This paper reveals potentially serious effects of a chosen numerical scheme on the learning outcome. In particular, our analysis demonstrates that a damped oscillatory system may be incorrectly identified as having "anti-damping" and exhibiting a reversed oscillation direction, despite adequately fitting the given data points.

Random Recurrent Neural Networks (RRNN) are the simplest recurrent networks to model and extract features from sequential data. The simplicity however comes with a price; RRNN are known to be susceptible to diminishing/exploding gradient problem when trained with gradient-descent based optimization. To enhance robustness of RRNN, alternative training approaches have been proposed. Specifically, FORCE learning approach proposed a recursive least squares alternative to train RRNN and was shown to be applicable even for the challenging task of target-learning, where the network is tasked with generating dynamic patterns with no guiding input. While FORCE training indicates that solving target-learning is possible, it appears to be effective only in a specific regime of network dynamics (edge-of-chaos). We thereby investigate whether initialization of RRNN connectivity according to a tailored distribution can guarantee robust FORCE learning. We are able to generate such distribution by inference of four generating principles constraining the spectrum of the network Jacobian to remain in stability region. This initialization along with FORCE learning provides a robust training method, i.e., Robust-FORCE (R-FORCE). We validate R-FORCE performance on various target functions for a wide range of network configurations and compare with alternative methods. Our experiments indicate that R-FORCE facilitates significantly more stable and accurate target-learning for a wide class of RRNN. Such stability becomes critical in modeling multi-dimensional sequences as we demonstrate on modeling time-series of human body joints during physical movements.

--Wireless Human-Machine Collaboration (WHMC) represents a critical advancement for Industry 5.0, enabling seamless interaction between humans and machines across geographically distributed systems. As the WHMC systems become increasingly important for achieving complex collaborative control tasks, ensuring their stability is essential for practical deployment and long-term operation. Stability analysis certifies how the closed-loop system will behave under model randomness, which is essential for systems operating with wireless communications. However, the fundamental stability analysis of the WHMC systems remains an unexplored challenge due to the intricate interplay between the stochastic nature of wireless communications, dynamic human operations, and the inherent complexities of control system dynamics. This paper establishes a fundamental WHMC model incorporating dual wireless loops for machine and human control. Our framework accounts for practical factors such as short-packet transmissions, fading channels, and advanced HARQ schemes. We model human control lag as a Markov process, which is crucial for capturing the stochastic nature of human interactions. Building on this model, we propose a stochastic cycle-cost-based approach to derive a stability condition for the WHMC system, expressed in terms of wireless channel statistics, human dynamics, and control parameters. Our findings are validated through extensive numerical simulations and a proof-of-concept experiment, where we developed and tested a novel wireless collaborative cart-pole control system. The results confirm the effectiveness of our approach and provide a robust framework for future research on WHMC systems in more complex environments. HE Fourth Industrial Revolution, known as Industry 4.0, envisions significantly increased automation and mechanization in manufacturing, driven by rapidly advancing cyber-physical systems (CPS) with minimal human intervention on the factory floor [1]. However, many dynamically changing and unforeseen control tasks in manufacturing, such as recon-figuring the production line, are challenging for autonomous machines to handle alone [2]. Therefore, humans are rein-troduced to the manufacturing process to collaborate with machines in the fifth industrial revolution, Industry 5.0 [3]. In the Industry 5.0 era, human-machine collaboration (HMC) emerges as a key enabling technology to boost productivity, efficiency, and sustainability by combining human's creativity, The work of W . Liu was supported by the Australian Research Council's Discovery Early Career Researcher A ward (DECRA) Project DE230100016.