Interconnected Observers for Robust Decentralized Estimation with Performance Guarantees and Optimized Connectivity Graph

Motivated by the need of observers that are both robust to disturbances and guarantee fast convergence to zero of the estimation error, we propose an observer for linear time-invariant systems with noisy output that consists of the combination of N coupled observers over a connectivity graph. At each node of the graph, the output of these interconnected observers is defined as the average of the estimates obtained using local information. The convergence rate and the robustness to measurement noise of the proposed observer's output are characterized in terms of $\mathcal{KL}$ bounds. Several optimization problems are formulated to design the proposed observer so as to satisfy a given rate of convergence specification while minimizing the $H_\infty$ gain from noise to estimates or the size of the connectivity graph. It is shown that that the interconnected observers relax the well-known tradeoff between rate of convergence and noise amplification, which is a property attributed to the proposed innovation term that, over the graph, couples the estimates between the individual observers. Sufficient conditions involving information of the plant only, assuring that the estimate obtained at each node of the graph outperforms the one obtained with a single, standard Luenberger observer are given. The results are illustrated in several examples throughout the paper.Comment: The technical report accompanying "Interconnected Observers for Robust Decentralized Estimation with Performance Guarantees and Optimized Connectivity Graph" to be published in IEEE Transactions on Control of Network Systems, 201

Automated Model Generation and Observer Design for Interconnected Systems : a Port-Hamiltonian Approach

Vernetzte Systeme stellen einen unverzichtbaren Teil moderner Gesellschaften dar. Mit dem Ausrollen neuer Kommunikationstechnologien und in Folge der fortgeschrittenen Nutzung von Synergiepotenzialen entstanden in den letzten Jahren vernetzte Systeme ungeahnten Ausmaßes. Aufgrund der Komplexität dieser Systeme, gelangen bestehende Modellierungs- und Beobachterentwurfsmethoden an ihre Grenzen. Modelle und Beobachter können deshalb häufig nur unter erheblichen Vereinfachungen entwickelt werden. Die vorliegende Dissertation schafft Abhilfe. Leitgedanke ist es, die Vorgänge der Modellerzeugung und des Beobachterentwurfs zu automatisieren. Hierzu werden in dieser Arbeit automatisierbare Modellierungs- und Beobachtermethoden auf Basis der Port-Hamiltonschen Systemtheorie entwickelt. Diese Methoden sind in einem Software-Prototyp namens AMOTO implementiert. In zwei Fallstudien wird AMOTO jeweils zur automatisierten Modellherleitung und zum automatisierten Beobachterentwurf eingesetzt. Computersimulationen weisen in beiden Fallstudien die Funktionstüchtigkeit der erzeugten Modelle und Beobachter nach und zeigen, dass diese genauere Ergebnisse liefern, als Modelle und Beobachter, die mit Methoden des bisherigen Stands der Technik entwickelt wurden. Dies unterstreicht die praktische Nutzbarkeit des vorgestellten Ansatzes. Es zeigt sich ferner, dass der Ansatz auf eine große Klasse vernetzter Systeme anwendbar ist. Somit leisten die Methoden, Algorithmen und Werkzeuge aus dieser Arbeit einen wichtigen Beitrag zur Bewältigung zukünftiger Herausforderungen in vernetzen Systemen

Mathematical control of complex systems

Copyright © 2013 ZidongWang 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

Automated Model Generation and Observer Design for Interconnected Systems : A Port-Hamiltonian Approach

This work addresses the automated generation of physical-based models and model-based observers. We develop port-Hamiltonian methods, which for the first time allow a complete and consistent automation of these two processes for a large class of interconnected systems

Model based fault diagnosis and prognosis of nonlinear systems

Rapid technological advances have led to more and more complex industrial systems with significantly higher risk of failures. Therefore, in this dissertation, a model-based fault diagnosis and prognosis framework has been developed for fast and reliable detection of faults and prediction of failures in nonlinear systems. In the first paper, a unified model-based fault diagnosis scheme capable of detecting both additive system faults and multiplicative actuator faults, as well as approximating the fault dynamics, performing fault type determination and time-to-failure determination, is designed. Stability of the observer and online approximator is guaranteed via an adaptive update law. Since outliers can degrade the performance of fault diagnostics, the second paper introduces an online neural network (NN) based outlier identification and removal scheme which is then combined with a fault detection scheme to enhance its performance. Outliers are detected based on the estimation error and a novel tuning law prevents the NN weights from being affected by outliers. In the third paper, in contrast to papers I and II, fault diagnosis of large-scale interconnected systems is investigated. A decentralized fault prognosis scheme is developed for such systems by using a network of local fault detectors (LFD) where each LFD only requires the local measurements. The online approximators in each LFD learn the unknown interconnection functions and the fault dynamics. Derivation of robust detection thresholds and detectability conditions are also included. The fourth paper extends the decentralized fault detection from paper III and develops an accommodation scheme for nonlinear continuous-time systems. By using both detection and accommodation online approximators, the control inputs are adjusted in order to minimize the fault effects. Finally in the fifth paper, the model-based fault diagnosis of distributed parameter systems (DPS) with parabolic PDE representation in continuous-time is discussed where a PDE-based observer is designed to perform fault detection as well as estimating the unavailable system states. An adaptive online approximator is incorporated in the observer to identify unknown fault parameters. Adaptive update law guarantees the convergence of estimations and allows determination of remaining useful life --Abstract, page iv

Decentralized Fault Diagnosis and Prognosis Scheme for Interconnected Nonlinear Discrete-Time Systems

This paper deals with the design of a decentralized fault diagnosis and prognosis scheme for interconnected nonlinear discrete-time systems which are modelled as the interconnection of several subsystems. For each subsystem, a local fault detector (LFD) is designed based on the dynamic model of the local subsystem and the local states. Each LFD consists of an observer with an online neural network (NN)-based approximator. The online NN approximators only use local measurements as their inputs, and are always turned on and continuously learn the interconnection as well as possible fault function. A fault is detected by comparing the output of each online NN approximator with a predefined threshold instead of using the residual. Derivation of robust detection thresholds and fault detectability conditions are also included. Due to interconnected nature of the overall system, the effect of faults propagate to other subsystems, thus a fault might be detected in more than one subsystem. Upon detection, faults local to the subsystem and from other subsystems are isolated by using a central fault isolation unit which receives detection time information from all LFDs. The proposed scheme also provides the time-to-failure or remaining useful life information by using local measurements. Simulation results provide the effectiveness of the proposed decentralized fault detection scheme

A Robust Nonlinear Observer-based Approach for Distributed Fault Detection of Input-Output Interconnected Systems

This paper develops a nonlinear observer-based approach for distributed fault detection of a class of interconnected input–output nonlinear systems, which is robust to modeling uncertainty and measurement noise. First, a nonlinear observer design is used to generate the residual signals required for fault detection. Then, a distributed fault detection scheme and the corresponding adaptive thresholds are designed based on the observer characteristics and, at the same time, filtering is used in order to attenuate the effect of measurement noise, which facilitates less conservative thresholds and enhanced robustness. Finally, a fault detectability condition characterizing quantitatively the class of detectable faults is derived

Robust and Decentralized Control of Web Winding Systems

This research addresses the velocity and tension regulation problems in web handling, including those found in the single element of an accumulator and those in the large-scale system settings. A continuous web winding system is a complex large-scale interconnected dynamics system with numerous tension zones to transport the web while processing it. A major challenge in controlling such systems is the unexpected disturbances that propagate through the system and affect both tension and velocity loops along the way. To solve this problem, a unique active disturbance rejection control (ADRC) strategy is proposed. Simulation results show remarkable disturbance rejection capability of the proposed control scheme in coping with large dynamic variations commonly seen in web winding systems. Another complication in web winding system stems from its large-scale and interconnected dynamics which makes control design difficult. This motivates the research in formulating a novel robust decentralized control strategy. The key idea in the proposed approach is that nonlinearities and interactions between adjunct subsystems are regarded as perturbations, to be estimated by an augmented state observer and rejected in the control loop, therefore making the local control design extremely simple. The proposed decentralized control strategy was implemented on a 3-tension-zone web winding processing line. Simulation results show that the proposed control method leads to much better tension and velocity regulation quality than the existing controller common in industry. Finally, this research tackles the challenging problem of stability analysis. Although ADRC has demonstrated the validity and advantage in many applications, the rigorous stability study has not been fully addressed previously. To this end, stability characterization of ADRC is carried out in this work. The closed-loop system is first reformulated, resulting in a form that allows the application of the well established singular perturbation method. Based on the decom