A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Hybrid Descriptor System State Estimation through an IMM Approach

International audienceStochastic hybrid systems have been largely studied in the literature in the framework of Markov mode transitions and linear Gaussian state space mode models. In order to generalize such results to hybrid systems involving phenomena characterized by differential-algebraic equations, this paper studies the problem of state estimation for stochastic hybrid systems with modes described by descriptor equations. The proposed state estimation algorithm follows the interacting multiple model (IMM for short) approach, but the classical state space system Kalman filters are replaced by descriptor system Kalman filters. Because of the difficulty for computing the innovation of each descriptor system Kalman filter, a new method for likelihood evaluation is proposed, as one important step of the new IMM algorithm. Numerical examples are presented to illustrate the performance of the proposed algorithm

Modeling, Control and Estimation of Reconfigurable Cable Driven Parallel Robots

The motivation for this thesis was to develop a cable-driven parallel robot (CDPR) as part of a two-part robotic device for concrete 3D printing. This research addresses specific research questions in this domain, chiefly, to present advantages offered by the addition of kinematic redundancies to CDPRs. Due to the natural actuation redundancy present in a fully constrained CDPR, the addition of internal mobility offers complex challenges in modeling and control that are not often encountered in literature. This work presents a systematic analysis of modeling such kinematic redundancies through the application of reciprocal screw theory (RST) and Lie algebra while further introducing specific challenges and drawbacks presented by cable driven actuators. It further re-contextualizes well-known performance indices such as manipulability, wrench closure quality, and the available wrench set for application with reconfigurable CDPRs. The existence of both internal redundancy and static redundancy in the joint space offers a large subspace of valid solutions that can be condensed through the selection of appropriate objective priorities, constraints or cost functions. Traditional approaches to such redundancy resolution necessitate computationally expensive numerical optimization. The control of both kinematic and actuation redundancies requires cascaded control frameworks that cannot easily be applied towards real-time control. The selected cost functions for numerical optimization of rCDPRs can be globally (and sometimes locally) non-convex. In this work we present two applied examples of redundancy resolution control that are unique to rCDPRs. In the first example, we maximize the directional wrench ability at the end-effector while minimizing the joint torque requirement by utilizing the fitness of the available wrench set as a constraint over wrench feasibility. The second example focuses on directional stiffness maximization at the end-effector through a variable stiffness module (VSM) that partially decouples the tension and stiffness. The VSM introduces an additional degrees of freedom to the system in order to manipulate both reconfigurability and cable stiffness independently. The controllers in the above examples were designed with kinematic models, but most CDPRs are highly dynamic systems which can require challenging feedback control frameworks. An approach to real-time dynamic control was implemented in this thesis by incorporating a learning-based frameworks through deep reinforcement learning. Three approaches to rCDPR training were attempted utilizing model-free TD3 networks. Robustness and safety are critical features for robot development. One of the main causes of robot failure in CDPRs is due to cable breakage. This not only causes dangerous dynamic oscillations in the workspace, but also leads to total robot failure if the controllability (due to lack of cables) is lost. Fortunately, rCDPRs can be utilized towards failure tolerant control for task recovery. The kinematically redundant joints can be utilized to help recover the lost degrees of freedom due to cable failure. This work applies a Multi-Model Adaptive Estimation (MMAE) framework to enable online and automatic objective reprioritization and actuator retasking. The likelihood of cable failure(s) from the estimator informs the mixing of the control inputs from a bank of feedforward controllers. In traditional rigid body robots, safety procedures generally involve a standard emergency stop procedure such as actuator locking. Due to the flexibility of cable links, the dynamic oscillations of the end-effector due to cable failure must be actively dampened. This work incorporates a Linear Quadratic Regulator (LQR) based feedback stabilizer into the failure tolerant control framework that works to stabilize the non-linear system and dampen out these oscillations. This research contributes to a growing, but hitherto niche body of work in reconfigurable cable driven parallel manipulators. Some outcomes of the multiple engineering design, control and estimation challenges addressed in this research warrant further exploration and study that are beyond the scope of this thesis. This thesis concludes with a thorough discussion of the advantages and limitations of the presented work and avenues for further research that may be of interest to continuing scholars in the community

Sequential bayesian filtering for spatial arrival time estimation

Locating and tracking a source in an ocean environment as well as estimating environmental parameters of a sound propagation medium is of utmost importance in underwater acoustics. Matched field processing is often the method of choice for the estimation of such parameters. This approach, based on full field calculations, is computationally intensive and sensitive to assumptions on the structure of the environment. As an alternative, methods that use only select features of the acoustic field for source localization and environmental inversion have been proposed. The focus here is on inversion using arrival times of identified paths within recorded time-series. After a short study of a linearization techniques employing such features and numerical issues on their implementation, we turn our attention to the need for accurate extraction of arrival times for accurate estimation. We develop a particle filtering approach that treats arrival times as targets , dynamically modeling their location at arrays of spatially separated receivers. Using Monte Carlo simulations, we perform an evaluation of our method and compare it to conventional Maximum Likelihood (ML) estimation. The comparison demonstrates an advantage in using the proposed approach, which can be employed as a pre-inversion tool for minimization and quantification of uncertainty in arrival time estimation

Impact Assessment, Detection, And Mitigation Of False Data Attacks In Electrical Power Systems

The global energy market has seen a massive increase in investment and capital flow in the last few decades. This has completely transformed the way power grids operate - legacy systems are now being replaced by advanced smart grid infrastructures that attest to better connectivity and increased reliability. One popular example is the extensive deployment of phasor measurement units, which is referred to PMUs, that constantly provide time-synchronized phasor measurements at a high resolution compared to conventional meters. This enables system operators to monitor in real-time the vast electrical network spanning thousands of miles. However, a targeted cyber attack on PMUs can prompt operators to take wrong actions that can eventually jeopardize the power system reliability. Such threats originating from the cyber-space continue to increase as power grids become more dependent on PMU communication networks. Additionally, these threats are becoming increasingly efficient in remaining undetected for longer periods while gaining deep access into the power networks. An attack on the energy sector immediately impacts national defense, emergency services, and all aspects of human life. Cyber attacks against the electric grid may soon become a tactic of high-intensity warfare between nations in near future and lead to social disorder. Within this context, this dissertation investigates the cyber security of PMUs that affects critical decision-making for a reliable operation of the power grid. In particular, this dissertation focuses on false data attacks, a key vulnerability in the PMU architecture, that inject, alter, block, or delete data in devices or in communication network channels. This dissertation addresses three important cyber security aspects - (1) impact assessment, (2) detection, and (3) mitigation of false data attacks. A comprehensive background of false data attack models targeting various steady-state control blocks is first presented. By investigating inter-dependencies between the cyber and the physical layers, this dissertation then identifies possible points of ingress and categorizes risk at different levels of threats. In particular, the likelihood of cyber attacks against the steady-state power system control block causing the worst-case impacts such as cascading failures is investigated. The case study results indicate that false data attacks do not often lead to widespread blackouts, but do result in subsequent line overloads and load shedding. The impacts are magnified when attacks are coordinated with physical failures of generators, transformers, or heavily loaded lines. Further, this dissertation develops a data-driven false data attack detection method that is independent of existing in-built security mechanisms in the state estimator. It is observed that a convolutional neural network classifier can quickly detect and isolate false measurements compared to other deep learning and traditional classifiers. Finally, this dissertation develops a recovery plan that minimizes the consequence of threats when sophisticated attacks remain undetected and have already caused multiple failures. Two new controlled islanding methods are developed that minimize the impact of attacks under the lack of, or partial information on the threats. The results indicate that the system operators can successfully contain the negative impacts of cyber attacks while creating stable and observable islands. Overall, this dissertation presents a comprehensive plan for fast and effective detection and mitigation of false data attacks, improving cyber security preparedness, and enabling continuity of operations

Impact Assessment, Detection, and Mitigation of False Data Attacks in Electrical Power Systems

The global energy market has seen a massive increase in investment and capital flow in the last few decades. This has completely transformed the way power grids operate - legacy systems are now being replaced by advanced smart grid infrastructures that attest to better connectivity and increased reliability. One popular example is the extensive deployment of phasor measurement units, which is referred to PMUs, that constantly provide time-synchronized phasor measurements at a high resolution compared to conventional meters. This enables system operators to monitor in real-time the vast electrical network spanning thousands of miles. However, a targeted cyber attack on PMUs can prompt operators to take wrong actions that can eventually jeopardize the power system reliability. Such threats originating from the cyber-space continue to increase as power grids become more dependent on PMU communication networks. Additionally, these threats are becoming increasingly efficient in remaining undetected for longer periods while gaining deep access into the power networks. An attack on the energy sector immediately impacts national defense, emergency services, and all aspects of human life. Cyber attacks against the electric grid may soon become a tactic of high-intensity warfare between nations in near future and lead to social disorder. Within this context, this dissertation investigates the cyber security of PMUs that affects critical decision-making for a reliable operation of the power grid. In particular, this dissertation focuses on false data attacks, a key vulnerability in the PMU architecture, that inject, alter, block, or delete data in devices or in communication network channels. This dissertation addresses three important cyber security aspects - (1) impact assessment, (2) detection, and (3) mitigation of false data attacks. A comprehensive background of false data attack models targeting various steady-state control blocks is first presented. By investigating inter-dependencies between the cyber and the physical layers, this dissertation then identifies possible points of ingress and categorizes risk at different levels of threats. In particular, the likelihood of cyber attacks against the steady-state power system control block causing the worst-case impacts such as cascading failures is investigated. The case study results indicate that false data attacks do not often lead to widespread blackouts, but do result in subsequent line overloads and load shedding. The impacts are magnified when attacks are coordinated with physical failures of generators, transformers, or heavily loaded lines. Further, this dissertation develops a data-driven false data attack detection method that is independent of existing in-built security mechanisms in the state estimator. It is observed that a convolutional neural network classifier can quickly detect and isolate false measurements compared to other deep learning and traditional classifiers. Finally, this dissertation develops a recovery plan that minimizes the consequence of threats when sophisticated attacks remain undetected and have already caused multiple failures. Two new controlled islanding methods are developed that minimize the impact of attacks under the lack of, or partial information on the threats. The results indicate that the system operators can successfully contain the negative impacts of cyber attacks while creating stable and observable islands. Overall, this dissertation presents a comprehensive plan for fast and effective detection and mitigation of false data attacks, improving cyber security preparedness, and enabling continuity of operations