Attitude stabilization of unmanned aerial vehicles in uncertain environments presents significant challenges due to nonlinear dynamics, parameter variations, and sensor limitations. This paper presents a comparative study of $\mathcal{H}_\infty$ and classical PID controllers for multi-rotor attitude regulation in the presence of wind disturbances and gyroscope noise. The flight dynamics are modeled using a linear parameter-varying (LPV) framework, where nonlinearities and parameter variations are systematically represented as structured uncertainties within a linear fractional transformation formulation. A robust controller based on $\mathcal{H}_\infty$ formulation is designed using only gyroscope measurements to ensure guaranteed performance bounds. Nonlinear simulation results demonstrate the effectiveness of the robust controllers compared to classical PID control, showing significant improvement in attitude regulation under severe wind disturbances.

Online continual learning (OCL), which enables AI systems to adaptively learn from non-stationary data streams, is commonly achieved using experience replay (ER)-based methods that retain knowledge by replaying stored past during training. However, these methods face challenges of prediction bias, stemming from deviations in parameter update directions during task transitions. This paper identifies parameter variation imbalance as a critical factor contributing to prediction bias in ER-based OCL. Specifically, using the proposed parameter variation evaluation method, we highlight two types of imbalance: correlation-induced imbalance, where certain parameters are disproportionately updated across tasks, and layer-wise imbalance, where output layer parameters update faster than those in preceding layers. To mitigate the above imbalances, we propose the Parameter Variation Balancing Framework (PVBF), which incorporates: 1) a novel method to compute parameter correlations with previous tasks based on parameter variations, 2) an encourage-and-consolidate (E&C) method utilizing parameter correlations to perform gradient adjustments across all parameters during training, 3) a dual-layer copy weights with reinit (D-CWR) strategy to slowly update output layer parameters for frequently occuring sample categories. Experiments on short and long task sequences demonstrate that PVBF significantly reduces prediction bias and improves OCL performance, achieving up to 47\% higher accuracy compared to existing ER-based methods.

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods to analyze non-stationary processes, and yet most time-series analysis methods that are used in practice, on important problems across science and industry, make the simplifying assumption of stationarity. One important problem in the analysis of non-stationary systems is the problem class that we refer to as Parameter Inference from a Non-stationary Unknown Process (PINUP). Given an observed time series, this involves inferring the parameters that drive non-stationarity of the time series, without requiring knowledge or inference of a mathematical model of the underlying system. Here we review and unify a diverse literature of algorithms for PINUP. We formulate the problem, and categorize the various algorithmic contributions. This synthesis will allow researchers to identify gaps in the literature and will enable systematic comparisons of different methods. We also demonstrate that the most common systems that existing methods are tested on - notably the non-stationary Lorenz process and logistic map - are surprisingly easy to perform well on using simple statistical features like windowed mean and variance, undermining the practice of using good performance on these systems as evidence of algorithmic performance. We then identify more challenging problems that many existing methods perform poorly on and which can be used to drive methodological advances in the field. Our results unify disjoint scientific contributions to analyzing non-stationary systems and suggest new directions for progress on the PINUP problem and the broader study of non-stationary phenomena.

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state observation of the underlying system and tacitly assume adiabatic changes in the parameter. Formulating an inverse problem and exploiting reservoir computing, we develop a model-free and fully data-driven framework to accurately track time-varying parameters from partial state observation in real time. In particular, with training data from a subset of the dynamical variables of the system for a small number of known parameter values, the framework is able to accurately predict the parameter variations in time. Low- and high-dimensional, Markovian and non-Markovian nonlinear dynamical systems are used to demonstrate the power of the machine-learning based parameter-tracking framework. Pertinent issues affecting the tracking performance are addressed.