The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or physically impossible to have enough sensor nodes to make the system fully observable. Even if the system is in principle observable, high-dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, we instead require the system to be functionally observable, meaning that a targeted subset of state variables can be reconstructed from the available measurements. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to i) determine the minimal set of required sensors and ii) design the corresponding state observer of minimum order. Compared to the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and computational resources, making it suitable for large-scale networks. We apply the proposed methods to the detection of cyber-attacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.
Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time-ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are often low dimensional or even univariate, thus requiring embedding methods to reconstruct the original system's state space. The observability of a system establishes fundamental conditions under which such reconstruction is possible. However, complete observability is too restrictive in applications where reconstructing the entire state space is not necessary…
In this paper, we introduce the concept of observability of targeted state variables for systems that may not be fully observable. For their estimation, we introduce and exemplify a deep filter, which is a neural network specifically designed for the estimation of targeted state variables without computing the trajectory of the entire system. The observability definition is quantitative rather than a yes or no answer so that one can compare the level of observability between different sensor locations.
This paper is concerned with the design of an augmented state feedback controller for finite-dimensional linear systems with nonlinear observation dynamics. Most of the theoretical results in the area of (optimal) feedback design are based on the assumption that the state is available for measurement. In this paper, we focus on finding a feedback control that avoids state trajectories with undesirable observability properties. In particular, we introduce an optimal control problem that specifically considers an index of observability in the control synthesis. The resulting cost functional is a…
This paper addresses the observability analysis and the optimal design of observation parameters in the presence of noisy measurements and parametric uncertainties. The main underlying frameworks are the nonlinear constrained moving horizon estimator design and the probabilistic certification via randomized optimization. As the perfect observability concept is not relevant under the considered uncertain and noisy context, the notion of almost $ε$-observability is introduced and a systematic procedure to assess its satisfaction for a given system with a priori known measurement noise statistics…
Multi-Robot Relative Pose Estimation in SE(2) with Observability Analysis: A Comparison of Extended Kalman Filtering and Robust Pose Graph Optimization
Graph-Theoretic Framework for Unified Analysis of Observability and Data Injection Attacks in the Smart Grid
Virginia Tech（弗吉尼亚理工大学）；Flemish Institute for Technological Research, VITO/EnergyVille（佛兰德技术研究所，VITO/能源村）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Aalto University（阿尔托大学）；Semnan University（塞姆南大学）；University of Cyprus（塞浦路斯大学）
We propose a linear time-difference-of-arrival (TDOA) measurement model to improve \textit{distributed} estimation performance for localized target tracking. We design distributed filters over sparse (possibly large-scale) communication networks using consensus-based data-fusion techniques. The proposed distributed and localized tracking protocols considerably reduce the sensor network's required connectivity and communication rate. We, further, consider $κ$-redundant observability and fault-tolerant design in case of losing communication links or sensor nodes. We present the minimal condition…
Functional target controllability of networks: structural properties and efficient algorithms
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；GIPSA-lab（GIPSA实验室）；DIAM, EWI, Delft University of Technology（代尔夫特理工大学电子、数学与计算机工程院计算系统研究所）；Inria（法国国家信息与自动化研究所）
Cooperative Integrated Estimation-Guidance for Simultaneous Interception of Moving Targets
Intelligent Systems & Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay（智能系统与控制实验室，航空航天工程系，印度理工学院班加罗尔）；Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati（智能系统引导、自主、学习与控制实验室，航空航天工程与工程力学系，辛辛那提大学）
Massachusetts Institute of Technology（麻省理工学院）；University of Arizona（亚利桑那大学）
We use Reinforcement Meta-Learning to optimize an adaptive integrated guidance, navigation, and control system suitable for exoatmospheric interception of a maneuvering target. The system maps observations consisting of strapdown seeker angles and rate gyro measurements directly to thruster on-off commands. Using a high fidelity six degree-of-freedom simulator, we demonstrate that the optimized policy can adapt to parasitic effects including seeker angle measurement lag, thruster control lag, the parasitic attitude loop resulting from scale factor errors and Gaussian noise on angle and rotatio…
