Accurate trajectory tracking is an essential characteristic for the safe navigation of a quadrotor in cluttered or disturbed environments. In this paper, we present in detail two state-of-the-art model-based control frameworks for trajectory tracking: the Linear Model Predictive Controller (LMPC) and the Nonlinear Model Predictive Controller (NMPC). Additionally, the kinematic and dynamic models of the quadrotor are comprehensively described. Finally, a simulation system is implemented to verify feasibility, demonstrating the effectiveness of both controllers.

Intelligent aerial platforms such as Unmanned Aerial Vehicles (UAVs) are expected to revolutionize various fields, including transportation, traffic management, field monitoring, industrial production, and agricultural management. Among these, precise control is a critical task that determines the performance and capabilities of UAV systems. However, current research primarily focuses on trajectory tracking and minimizing flight errors, with limited attention to improving flight time. In this paper, we propose a Model Predictive Control (MPC) approach aimed at minimizing flight time while addressing the limitations of the commonly used classical MPC controllers. Furthermore, the MPC method and its application for UAV control are presented in detail. Finally, the results demonstrate that the proposed controller outperforms the standard MPC in terms of efficiency. Moreover, this approach shows potential to become a foundation for integrating intelligent algorithms into basic controllers.

The two-way flow of information and energy is an important feature of the Energy Internet. Data analytics is a powerful tool in the information flow that aims to solve practical problems using data mining techniques. As the problem of electricity thefts via tampering with smart meters continues to increase, the abnormal behaviors of thefts become more diversified and more difficult to detect. Thus, a data analytics method for detecting various types of electricity thefts is required. However, the existing methods either require a labeled dataset or additional system information which is difficult to obtain in reality or have poor detection accuracy. In this paper, we combine two novel data mining techniques to solve the problem. One technique is the Maximum Information Coefficient (MIC), which can find the correlations between the non-technical loss (NTL) and a certain electricity behavior of the consumer. MIC can be used to precisely detect thefts that appear normal in shapes. The other technique is the clustering technique by fast search and find of density peaks (CFSFDP). CFSFDP finds the abnormal users among thousands of load profiles, making it quite suitable for detecting electricity thefts with arbitrary shapes. Next, a framework for combining the advantages of the two techniques is proposed. Numerical experiments on the Irish smart meter dataset are conducted to show the good performance of the combined method.

Passivity-based control is a cornerstone of control theory and an established design approach in robotics. Its strength is based on the passivity theorem, which provides a powerful interconnection framework for robotics. However, the design of passivity-based controllers and their optimal tuning remain challenging. We propose here an intuitive design approach for fully actuated robots, where the control action is determined by a `virtual-mechanism' as in classical virtual model control. The result is a robot whose controlled behavior can be understood in terms of physics. We achieve optimal tuning by applying algorithmic differentiation to ODE simulations of the rigid body dynamics. Overall, this leads to a flexible design and optimization approach: stability is proven by passivity of the virtual mechanism, while performance is obtained by optimization using algorithmic differentiation.

Traditional machine learning approaches assume that data comes from a single generating mechanism, which may not hold for most real life data. In these cases, the single mechanism assumption can result in suboptimal performance. We introduce a clustering framework that eliminates this assumption by grouping the data according to the relations between the features and the target values and we obtain multiple separate models to learn different parts of the data. We further extend our framework to applications having streaming data where we produce outcomes using an ensemble of models. For this, the ensemble weights are updated based on the incoming data batches. We demonstrate the performance of our approach over the widely-studied real life datasets, showing significant improvements over the traditional single-model approaches.

Large Language Models (LLMs) are increasingly adopted for complex scientific text generation tasks, yet they often suffer from limitations in accuracy, consistency, and hallucination control. This thesis introduces a Parameter-Efficient Fine-Tuning (PEFT) approach tailored for GPT-like models, aiming to mitigate hallucinations and enhance reproducibility, particularly in the computational domain of mass spectrometry. We implemented Low-Rank Adaptation (LoRA) adapters to refine GPT-2, termed MS-GPT, using a specialized corpus of mass spectrometry literature. Through novel evaluation methods applied to LLMs, including BLEU, ROUGE, and Perplexity scores, the fine-tuned MS-GPT model demonstrated superior text coherence and reproducibility compared to the baseline GPT-2, confirmed through statistical analysis with the Wilcoxon rank-sum test. Further, we propose a reproducibility metric based on cosine similarity of model outputs under controlled prompts, showcasing MS-GPT's enhanced stability. This research highlights PEFT's potential to optimize LLMs for scientific contexts, reducing computational costs while improving model reliability.

Optimizing the learning rate remains a critical challenge in machine learning, essential for achieving model stability and efficient convergence. The Vector Auxiliary Variable (VAV) algorithm introduces a novel energy-based self-adjustable learning rate optimization method designed for unconstrained optimization problems. It incorporates an auxiliary variable $r$ to facilitate efficient energy approximation without backtracking while adhering to the unconditional energy dissipation law. Notably, VAV demonstrates superior stability with larger learning rates and achieves faster convergence in the early stage of the training process. Comparative analyses demonstrate that VAV outperforms Stochastic Gradient Descent (SGD) across various tasks. This paper also provides rigorous proof of the energy dissipation law and establishes the convergence of the algorithm under reasonable assumptions. Additionally, $r$ acts as an empirical lower bound of the training loss in practice, offering a novel scheduling approach that further enhances algorithm performance.

Hierarchical time series forecasting plays a crucial role in decision-making in various domains while presenting significant challenges for modelling as they involve multiple levels of aggregation, constraints, and availability of information. This study explores the influence of distinct information utilisation on the accuracy of hierarchical forecasts, proposing and evaluating locals and a range of Global Forecasting Models (GFMs). In contrast to local models, which forecast each series independently, we develop GFMs to exploit cross-series and cross-hierarchies information, improving both forecasting performance and computational efficiency. We employ reconciliation methods to ensure coherency in forecasts and use the Mean Absolute Scaled Error (MASE) and Multiple Comparisons with the Best (MCB) tests to assess statistical significance. The findings indicate that GFMs possess significant advantages for hierarchical forecasting, providing more accurate and computationally efficient solutions across different levels in a hierarchy. Two specific GFMs based on LightGBM are introduced, demonstrating superior accuracy and lower model complexity than their counterpart local models and conventional methods such as Exponential Smoothing (ES) and Autoregressive Integrated Moving Average (ARIMA).

Time series foundation models excel in zero-shot forecasting, handling diverse tasks without explicit training. However, the advancement of these models has been hindered by the lack of comprehensive benchmarks. To address this gap, we introduce the General TIme Series ForecasTing Model Evaluation, GIFT-Eval, a pioneering benchmark aimed at promoting evaluation across diverse datasets. GIFT-Eval encompasses 23 datasets over 144,000 time series and 177 million data points, spanning seven domains, 10 frequencies, multivariate inputs, and prediction lengths ranging from short to long-term forecasts. To facilitate the effective pretraining and evaluation of foundation models, we also provide a non-leaking pretraining dataset containing approximately 230 billion data points. Additionally, we provide a comprehensive analysis of 17 baselines, which includes statistical models, deep learning models, and foundation models. We discuss each model in the context of various benchmark characteristics and offer a qualitative analysis that spans both deep learning and foundation models. We believe the insights from this analysis, along with access to this new standard zero-shot time series forecasting benchmark, will guide future developments in time series foundation models. The success of foundation model pretraining in language and vision modalities has catalyzed similar progress in time series forecasting. By pretraining on extensive time series datasets, a universal forecasting model can be developed, equipped to address varied downstream forecasting tasks across multiple domains, frequencies, prediction lengths, and number of variates in a zero-shot manner (Woo et al., 2024; Rasul et al., 2023; Ansari et al., 2024). A critical aspect of foundation model research is creating a high-quality benchmark that includes large, diverse evaluation data, and preferably non-leaking pretraining data to fairly evaluate models and identify their weaknesses. Research in Natural Language Processing (NLP) has produced key benchmarks such as GLUE, MMLU, etc. (Wang et al., 2018; Hendrycks et al., 2020; Srivastava et al., 2022; Chen et al., 2021), which are crucial for developing high-quality models. Unlike NLP, time series foundation models lack a unified, diverse benchmark for fair comparison. For instance, Woo et al. (2024) introduces LOTSA, which remains the largest collection of time series forecasting pre-training data to date. However, the proposed architecture, Moirai, is evaluated on existing benchmarks that are tailored to specific forecasting tasks, such as the LSF (Zhou et al., 2020) dataset for long-term forecast, and the Monash (Godahewa et al., 2021) dataset for univariate forecasts.

This paper formalizes Hamiltonian-Informed Optimal Neural (Hion) controllers, a novel class of neural network-based controllers for dynamical systems and explicit non-linear model predictive control. Hion controllers estimate future states and compute optimal control inputs using Pontryagin's Maximum Principle. The proposed framework allows for customization of transient behavior, addressing limitations of existing methods. The Taylored Multi-Faceted Approach for Neural ODE and Optimal Control (T-mano) architecture facilitates training and ensures accurate state estimation. Optimal control strategies are demonstrated for both linear and non-linear dynamical systems.