The communication control delay between the inverters and the power plant controller can be caused by several factors related to the communication link between them. Under undesirable conditions, high delay values can produce oscillations in the wind power plant that can affect the rest of the power system. In this work, we present a new robust methodology for wind turbines to estimate the value of the communication control delay using PMU data. Several scenarios are considered where external faults are simulated and the performance of the algorithm is evaluated based on dynamic state estimation of the mathematical model of the wind turbine. In this paper, we have shown that the characterization of the delay can be performed offering the transmission system operator an online tool to identify the most suited communication delay for the plant controller models used in dynamic studies.
Accurate estimation of the whole-body center of mass (CoM) is essential for assessing human stability and postural control. However, selecting the most accurate estimation method is challenging due to the complexity of human movement, diverse nature of activities, and varying availability of equipment, such as marker-based systems and ground reaction force (GRF) sensors. This study compares three CoM estimation methods -- "Pelvis Markerset", "Whole-Body Markerset", and "Whole-Body Markerset & GRFs" -- across static activities, such as standing with eyes closed, and dynamic activities, such as picking up an object from the ground. Using the root mean square (RMS) of "external force residual" (the difference between measured ground reaction forces and estimated CoM accelerations multiplied by total body mass) as a performance metric, we found that while all methods performed similarly under static conditions, the "Pelvis Markerset" method showed 96% to 104% higher RMS external force residual values during dynamic activities compared to the two whole-body methods ($p<0.001$, Cohen's $d$:2.90-3.04). The accuracy of "Whole-Body Markerset & GRFs" (i.e., Kalman filter) was similar to "Whole-Body Markerset", suggesting that incorporating the GRFs through the presented Kalman filter does not improve the estimates from whole-body kinematics. Based on these findings, we recommend the "Whole-Body Markerset" as it performs well and does not require information from GRFs. The "Pelvis Markerset" method can be used in static activities or when markersets around the pelvis reflect whole-body kinematics. This method is not recommended for CoM state estimation in highly dynamic scenarios and when whole-body markersets are available.
This paper addresses the secure state estimation problem for continuous linear time-invariant systems with non-periodic and asynchronous sampled measurements, where the sensors need to transmit not only measurements but also sampling time-stamps to the fusion center. This measurement and communication setup is well-suited for operating large-scale control systems and, at the same time, introduces new vulnerabilities that can be exploited by adversaries through (i) manipulation of measurements, (ii) manipulation of time-stamps, (iii) elimination of measurements, (iv) generation of completely new false measurements, or a combination of these attacks. To mitigate these attacks, we propose a decentralized estimation algorithm in which each sensor maintains its local state estimate asynchronously based on its measurements. The local states are synchronized through time prediction and fused after time-stamp alignment. In the absence of attacks, state estimates are proven to recover the optimal Kalman estimates by solving a weighted least square problem. In the presence of attacks, solving this weighted least square problem with the aid of $\ell_1$ regularization provides secure state estimates with uniformly bounded error under an observability redundancy assumption. The effectiveness of the proposed algorithm is demonstrated using a benchmark example of the IEEE 14-bus system.
The reliability, lower computational complexity, and ease of implementation of control observers make them one of the most promising methods for the state estimation of Li-ion batteries (LIBs) in commercial applications. To pave their way, this study performs a comprehensive and systematic evaluation of four main categories of control observer-based methods in different practical scenarios considering estimation accuracy, computational time convergence speed, stability, and robustness against measurement uncertainties. Observers are designed using a second-order equivalent circuit model whose observability against different scenarios is rigorously investigated to verify the feasibility of the proposed analysis. Established techniques then are validated against driving datasets and their comparative usefulness is evaluated using an experimental setup. The analysis also evaluates the adaptability of different techniques to electric vehicle field data. The results indicate better accuracy, stability, robustness, and faster convergence for the PI and PID, while the estimations of the Luenberger observers find it hard to converge against highly dynamic loadfiles. Moreover, this study also discusses the sensitivity of observer-based techniques to battery ohmic polarization and voltage-related measurement uncertainties. The most remarkable contribution of the proposed study lies in providing guidance for researchers when choosing the control observers for online state estimation of LIBs.
Kalman Filters (KF) are fundamental to real-time state estimation applications, including radar-based tracking systems used in modern driver assistance and safety technologies. In a linear dynamical system with Gaussian noise distributions the KF is the optimal estimator. However, real-world systems often deviate from these assumptions. This deviation combined with the success of deep learning across many disciplines has prompted the exploration of data driven approaches that leverage deep learning for filtering applications. These learned state estimators are often reported to outperform traditional model based systems. In this work, one prevalent model, KalmanNet, was selected and evaluated on automotive radar data to assess its performance under real-world conditions and compare it to an interacting multiple models (IMM) filter. The evaluation is based on raw and normalized errors as well as the state uncertainty. The results demonstrate that KalmanNet is outperformed by the IMM filter and indicate that while data-driven methods such as KalmanNet show promise, their current lack of reliability and robustness makes them unsuited for safety-critical applications.
Deep learning has seen substantial achievements, with numerical and theoretical evidence suggesting that singularities of statistical models are considered a contributing factor to its performance. From this remarkable success of classical statistical models, it is naturally expected that quantum singular models will play a vital role in many quantum statistical tasks. However, while the theory of quantum statistical models in regular cases has been established, theoretical understanding of quantum singular models is still limited. To investigate the statistical properties of quantum singular models, we focus on two prominent tasks in quantum statistical inference: quantum state estimation and model selection. In particular, we base our study on classical singular learning theory and seek to extend it within the framework of Bayesian quantum state estimation. To this end, we define quantum generalization and training loss functions and give their asymptotic expansions through algebraic geometrical methods. The key idea of the proof is the introduction of a quantum analog of the likelihood function using classical shadows. Consequently, we construct an asymptotically unbiased estimator of the quantum generalization loss, the quantum widely applicable information criterion (QWAIC), as a computable model selection metric from given measurement outcomes.
In the last decade, the free energy principle (FEP) and active inference (AIF) have achieved many successes connecting conceptual models of learning and cognition to mathematical models of perception and action. This effort is driven by a multidisciplinary interest in understanding aspects of self-organizing complex adaptive systems, including elements of agency. Various reinforcement learning (RL) models performing active inference have been proposed and trained on standard RL tasks using deep neural networks. Recent work has focused on improving such agents' performance in complex environments by incorporating the latest machine learning techniques. In this paper, we take an alternative approach. Within the constraints imposed by the FEP and AIF, we attempt to model agents in an interpretable way without deep neural networks by introducing Free Energy Projective Simulation (FEPS). Using internal rewards only, FEPS agents build a representation of their partially observable environments with which they interact. Following AIF, the policy to achieve a given task is derived from this world model by minimizing the expected free energy. Leveraging the interpretability of the model, techniques are introduced to deal with long-term goals and reduce prediction errors caused by erroneous hidden state estimation. We test the FEPS model on two RL environments inspired from behavioral biology: a timed response task and a navigation task in a partially observable grid. Our results show that FEPS agents fully resolve the ambiguity of both environments by appropriately contextualizing their observations based on prediction accuracy only. In addition, they infer optimal policies flexibly for any target observation in the environment.
In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in existing approaches: susceptibility to measurement noise outliers and difficulties in incorporating constraints into state estimation. By formulating constrained state estimation as an optimization problem and employing the Majorization-Minimization (MM) approach, our framework provides a unified solution that enhances the robustness of the Kalman filter. Experimental results demonstrate high accuracy and computational efficiency achieved by our proposed approach, establishing it as a promising solution for robust and constrained state estimation in real-world applications.
The implementation of cyber-physical systems in real-world applications is challenged by safety requirements in the presence of sensor threats. Most cyber-physical systems, in particular the vulnerable multi-sensor systems, struggle to detect the attack in observation signals. In this paper, we tackle this issue by proposing a Gaussian-Bernoulli Secure (GBS) estimator, which effectively transforms the assessment of sensor status into an optimal estimation problem concerning the system state and observation indicators. It encompasses two theoretical sub-problems: sequential state estimation with partial observations and estimation updates with disordered new observations. Within the framework of Kalman filter, we derive closed-form solutions for these two issues. However, due to their computational inefficiency, we propose the iterative approach employing proximal gradient descent to accelerate the estimation update. We conduct comprehensive experiments from three perspectives: computational efficiency, detection and estimation performance, and characterization of observation error. Our GBS estimator shows the improvements compared to other methods.
The goal of multi-object tracking (MOT) is to detect and track all objects in a scene across frames, while maintaining a unique identity for each object. Most existing methods rely on the spatial-temporal motion features and appearance embedding features of the detected objects in consecutive frames. Effectively and robustly representing the spatial and appearance features of long trajectories has become a critical factor affecting the performance of MOT. We propose a novel approach for appearance and spatial-temporal motion feature representation, improving upon the hierarchical clustering association method MOT FCG. For spatialtemporal motion features, we first propose Diagonal Modulated GIoU, which more accurately represents the relationship between the position and shape of the objects. Second, Mean Constant Velocity Modeling is proposed to reduce the effect of observation noise on target motion state estimation. For appearance features, we utilize a dynamic appearance representation that incorporates confidence information, enabling the trajectory appearance features to be more robust and global. Based on the baseline model MOT FCG, we have realized further improvements in the performance of all. we achieved 63.1 HOTA, 76.9 MOTA and 78.2 IDF1 on the MOT17 test set, and also achieved competitive performance on the MOT20 and DanceTrack sets.
We propose a machine learning-based estimator of the hand state for rehabilitation purposes, using light exoskeletons. These devices are easy to use and useful for delivering domestic and frequent therapies. We build a supervised approach using information from the muscular activity of the forearm and the motion of the exoskeleton to reconstruct the hand's opening degree and compliance level. Such information can be used to evaluate the therapy progress and develop adaptive control behaviors. Our approach is validated with a real light exoskeleton. The experiments demonstrate good predictive performance of our approach when trained on data coming from a single user and tested on the same user, even across different sessions. This generalization capability makes our system promising for practical use in real rehabilitation.
Data assimilation (DA) combines partial observations with a dynamical model to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past and future observations. It aims to fill in missing data, provide more accurate estimations, and develop high-quality datasets. However, the standard smoothing procedure requires using all historical state estimations, which is storage-demanding, especially for high-dimensional systems. This paper develops an adaptive-lag online smoother for a large class of complex dynamical systems with strong nonlinear and non-Gaussian features, which has important applications to many real-world problems. The adaptive lag allows the DA to utilize only observations within a nearby window, significantly reducing computational storage. Online lag adjustment is essential for tackling turbulent systems, where temporal autocorrelation varies significantly over time due to intermittency, extreme events, and nonlinearity. Based on the uncertainty reduction in the estimated state, an information criterion is developed to systematically determine the adaptive lag. Notably, the mathematical structure of these systems facilitates the use of closed analytic formulae to calculate the online smoother and the adaptive lag, avoiding empirical tunings as in ensemble-based DA methods. The adaptive online smoother is applied to studying three important scientific problems. First, it helps detect online causal relationships between state variables. Second, its advantage of computational storage is illustrated via Lagrangian DA, a high-dimensional nonlinear problem. Finally, the adaptive smoother advances online parameter estimation with partial observations, emphasizing the role of the observed extreme events in accelerating convergence.
Accurately estimating spatiotemporal traffic states on freeways is a significant challenge due to limited sensor deployment and potential data corruption. In this study, we propose an efficient and robust low-rank model for precise spatiotemporal traffic speed state estimation (TSE) using lowpenetration vehicle trajectory data. Leveraging traffic wave priors, an oblique grid-based matrix is first designed to transform the inherent dependencies of spatiotemporal traffic states into the algebraic low-rankness of a matrix. Then, with the enhanced traffic state low-rankness in the oblique matrix, a low-rank matrix completion method is tailored to explicitly capture spatiotemporal traffic propagation characteristics and precisely reconstruct traffic states. In addition, an anomaly-tolerant module based on a sparse matrix is developed to accommodate corrupted data input and thereby improve the TSE model robustness. Notably, driven by the understanding of traffic waves, the computational complexity of the proposed efficient method is only correlated with the problem size itself, not with dataset size and hyperparameter selection prevalent in existing studies. Extensive experiments demonstrate the effectiveness, robustness, and efficiency of the proposed model. The performance of the proposed method achieves up to a 12% improvement in Root Mean Squared Error (RMSE) in the TSE scenarios and an 18% improvement in RMSE in the robust TSE scenarios, and it runs more than 20 times faster than the state-of-the-art (SOTA) methods.
Proprioceptive sensors on planetary rovers serve for state estimation and for understanding terrain and locomotion performance. While inertial measurement units (IMUs) are widely used to this effect, force-torque sensors are less explored for planetary navigation despite their potential to directly measure interaction forces and provide insights into traction performance. This paper presents an evaluation of the performance and use cases of force-torque sensors based on data collected from a six-wheeled rover during tests over varying terrains, speeds, and slopes. We discuss challenges, such as sensor signal reliability and terrain response accuracy, and identify opportunities regarding the use of these sensors. The data is openly accessible and includes force-torque measurements from each of the six-wheel assemblies as well as IMU data from within the rover chassis. This paper aims to inform the design of future studies and rover upgrades, particularly in sensor integration and control algorithms, to improve navigation capabilities.
Designing the terminal ingredients of direct data-driven predictive control presents challenges due to its reliance on an implicit, non-minimal input-output data-driven representation. By considering the class of constrained LTI systems with unknown time delays, we propose a set-theoretic direct data-driven predictive controller that does not require a terminal cost to provide closed-loop guarantees. In particular, first, starting from input/output data series, we propose a sample-based method to build N-step input output backward reachable sets. Then, we leverage the constructed family of backward reachable sets to derive a data-driven control law. The proposed method guarantees finite-time convergence and recursive feasibility, independent of objective function tuning. It requires neither explicit state estimation nor an explicit prediction model, relying solely on input-output measurements; therefore, unmodeled dynamics can be avoided. Finally, a numerical example highlights the effectiveness of the proposed method in stabilizing the system, whereas direct data-driven predictive control without terminal ingredients fails under the same conditions.
The growing demand for robust scene understanding in mobile robotics and autonomous driving has highlighted the importance of integrating multiple sensing modalities. By combining data from diverse sensors like cameras and LIDARs, fusion techniques can overcome the limitations of individual sensors, enabling a more complete and accurate perception of the environment. We introduce a novel approach to multi-modal sensor fusion, focusing on developing a graph-based state representation that supports critical decision-making processes in autonomous driving. We present a Sensor-Agnostic Graph-Aware Kalman Filter [3], the first online state estimation technique designed to fuse multi-modal graphs derived from noisy multi-sensor data. The estimated graph-based state representations serve as a foundation for advanced applications like Multi-Object Tracking (MOT), offering a comprehensive framework for enhancing the situational awareness and safety of autonomous systems. We validate the effectiveness of our proposed framework through extensive experiments conducted on both synthetic and real-world driving datasets (nuScenes). Our results showcase an improvement in MOTA and a reduction in estimated position errors (MOTP) and identity switches (IDS) for tracked objects using the SAGA-KF. Furthermore, we highlight the capability of such a framework to develop methods that can leverage heterogeneous information (like semantic objects and geometric structures) from various sensing modalities, enabling a more holistic approach to scene understanding and enhancing the safety and effectiveness of autonomous systems.
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.
This paper discusses the theory and algorithms for interacting large language model agents (LLMAs) using methods from statistical signal processing and microeconomics. While both fields are mature, their application to decision-making involving interacting LLMAs remains unexplored. Motivated by Bayesian sentiment analysis on online platforms, we construct interpretable models and algorithms that enable LLMAs to interact and perform Bayesian inference. Because interacting LLMAs learn from both prior decisions and external inputs, they can exhibit bias and herding behavior. Thus, developing interpretable models and stochastic control algorithms is essential to understand and mitigate these behaviors. This paper has three main results. First, we show using Bayesian revealed preferences from microeconomics that an individual LLMA satisfies the necessary and sufficient conditions for rationally inattentive (bounded rationality) Bayesian utility maximization and, given an observation, the LLMA chooses an action that maximizes a regularized utility. Second, we utilize Bayesian social learning to construct interpretable models for LLMAs that interact sequentially with each other and the environment while performing Bayesian inference. Our proposed models capture the herding behavior exhibited by interacting LLMAs. Third, we propose a stochastic control framework to delay herding and improve state estimation accuracy under 2 settings: (a) centrally controlled LLMAs (b) autonomous LLMAs with incentives. We demonstrate the effectiveness of our methods on real datasets for hate speech classification and product quality assessment, using open-source models like LLaMA and closed-source models like ChatGPT. The main takeaway of this paper, based on empirical analysis and mathematical formalism, is that LLMAs act as rationally bounded Bayesian agents that exhibit social learning when interacting.
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables. We concentrate on linear time-invariant systems, in which the observation matrix serves as the algebraic representation of a graph object. This graph object encapsulates the availability of relative measurements. Utilizing algebraic graph theory and abstract linear algebra (geometric) tools, we establish a link between the structure of the graph of relative measurements and the system-theoretic observability subspace of linear systems. Special emphasis is given to multi-agent networked systems whose dynamics are governed by the linear consensus protocol. We demonstrate the importance of absolute information and its placement to the system's dynamics in achieving full-state estimation. Finally, the analysis shifts to the synthesis of a distributed observer with relative measurements for single integrator dynamics, exemplifying the relevance of the preceding analytical findings. We support our theoretical analysis with numerical simulations.
Deep learning is widely used to predict complex dynamical systems in many scientific and engineering areas. However, the black-box nature of these deep learning models presents significant challenges for carrying out simultaneous data assimilation (DA), which is a crucial technique for state estimation, model identification, and reconstructing missing data. Integrating ensemble-based DA methods with nonlinear deep learning models is computationally expensive and may suffer from large sampling errors. To address these challenges, we introduce a deep learning framework designed to simultaneously provide accurate forecasts and efficient DA. It is named Conditional Gaussian Koopman Network (CGKN), which transforms general nonlinear systems into nonlinear neural differential equations with conditional Gaussian structures. CGKN aims to retain essential nonlinear components while applying systematic and minimal simplifications to facilitate the development of analytic formulae for nonlinear DA. This allows for seamless integration of DA performance into the deep learning training process, eliminating the need for empirical tuning as required in ensemble methods. CGKN compensates for structural simplifications by lifting the dimension of the system, which is motivated by Koopman theory. Nevertheless, CGKN exploits special nonlinear dynamics within the lifted space. This enables the model to capture extreme events and strong non-Gaussian features in joint and marginal distributions with appropriate uncertainty quantification. We demonstrate the effectiveness of CGKN for both prediction and DA on three strongly nonlinear and non-Gaussian turbulent systems: the projected stochastic Burgers-Sivashinsky equation, the Lorenz 96 system, and the El Ni\~no-Southern Oscillation. The results justify the robustness and computational efficiency of CGKN.