Fault-tolerant Stochastic Distributed Systems

The present doctoral thesis discusses the design of fault-tolerant distributed systems, placing emphasis in addressing the case where the actions of the nodes or their interactions are stochastic. The main objective is to detect and identify faults to improve the resilience of distributed systems to crash-type faults, as well as detecting the presence of malicious nodes in pursuit of exploiting the network. The proposed analysis considers malicious agents and computational solutions to detect faults. Crash-type faults, where the affected component ceases to perform its task, are tackled in this thesis by introducing stochastic decisions in deterministic distributed algorithms. Prime importance is placed on providing guarantees and rates of convergence for the steady-state solution. The scenarios of a social network (state-dependent example) and consensus (time- dependent example) are addressed, proving convergence. The proposed algorithms are capable of dealing with packet drops, delays, medium access competition, and, in particular, nodes failing and/or losing network connectivity. The concept of Set-Valued Observers (SVOs) is used as a tool to detect faults in a worst-case scenario, i.e., when a malicious agent can select the most unfavorable sequence of communi- cations and inject a signal of arbitrary magnitude. For other types of faults, it is introduced the concept of Stochastic Set-Valued Observers (SSVOs) which produce a confidence set where the state is known to belong with at least a pre-specified probability. It is shown how, for an algorithm of consensus, it is possible to exploit the structure of the problem to reduce the computational complexity of the solution. The main result allows discarding interactions in the model that do not contribute to the produced estimates. The main drawback of using classical SVOs for fault detection is their computational burden. By resorting to a left-coprime factorization for Linear Parameter-Varying (LPV) systems, it is shown how to reduce the computational complexity. By appropriately selecting the factorization, it is possible to consider detectable systems (i.e., unobservable systems where the unobservable component is stable). Such a result plays a key role in the domain of Cyber-Physical Systems (CPSs). These techniques are complemented with Event- and Self-triggered sampling strategies that enable fewer sensor updates. Moreover, the same triggering mechanisms can be used to make decisions of when to run the SVO routine or resort to over-approximations that temporarily compromise accuracy to gain in performance but maintaining the convergence characteristics of the set-valued estimates. A less stringent requirement for network resources that is vital to guarantee the applicability of SVO-based fault detection in the domain of Networked Control Systems (NCSs)

Integrated system identification/control design with frequency weightings.

by Ka-lun Tung.Thesis (M.Phil.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 168-[175]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Control with Uncertainties --- p.1Chapter 1.1.1 --- Adaptive Control --- p.2Chapter 1.1.2 --- H∞ Robust Control --- p.3Chapter 1.2 --- A Unified Framework: Adaptive Robust Control --- p.4Chapter 1.3 --- System Identification for Robust Control --- p.6Chapter 1.3.1 --- Choice of input signal --- p.7Chapter 1.4 --- Objectives and Contributions --- p.8Chapter 1.5 --- Thesis Outline --- p.9Chapter 2 --- Background on Robust Control --- p.11Chapter 2.1 --- Notation and Terminology --- p.12Chapter 2.1.1 --- Notation --- p.12Chapter 2.1.2 --- Linear System Terminology --- p.13Chapter 2.1.3 --- Norms --- p.15Chapter 2.1.4 --- More Terminology: A Standard Feedback Configuration --- p.17Chapter 2.2 --- Norms and Power for Signals and Systems --- p.18Chapter 2.3 --- Plant Uncertainty Model --- p.20Chapter 2.3.1 --- Multiplicative Unstructured Uncertainty --- p.21Chapter 2.3.2 --- Additive Unstructured Uncertainty --- p.22Chapter 2.3.3 --- Structured Uncertainty --- p.23Chapter 2.4 --- Motivation for H∞ Control Design --- p.23Chapter 2.4.1 --- Robust stabilization: Multiplicative Uncertainty and Weight- ing function W3 --- p.24Chapter 2.4.2 --- Robust stabilization: Additive Uncertainty and Weighting function W2 --- p.25Chapter 2.4.3 --- Tracking Problem --- p.26Chapter 2.4.4 --- Disturbance Rejection (or Sensitivity Minimization) --- p.27Chapter 2.5 --- The Robust Control Problem Statement --- p.28Chapter 2.5.1 --- The Mixed-Sensitivity Approach --- p.29Chapter 2.6 --- An Augmented Generalized Plant --- p.30Chapter 2.6.1 --- The Augmented Plant --- p.30Chapter 2.6.2 --- Adaptation of Augmented Plant to Sensitivity Minimiza- tion Problem --- p.32Chapter 2.6.3 --- Adaptation of Augmented Plant to Mixed-Sensitivity Prob- lem --- p.33Chapter 2.7 --- Using MATLAB Robust Control Toolbox --- p.34Chapter 3 --- Statistical Plant Set Estimation for Robust Control --- p.36Chapter 3.1 --- An Overview --- p.37Chapter 3.2 --- The Schroeder-phased Input Design --- p.39Chapter 3.3 --- The Statistical Additive Uncertainty Bounds --- p.40Chapter 3.4 --- Additive Uncertainty Characterization --- p.45Chapter 3.4.1 --- "Linear Programming Spectral Overbounding and Factor- ization Algorithm (LPSOF) [20,21]" --- p.45Chapter 4 --- Basic System Identification and Model Reduction Algorithms --- p.48Chapter 4.1 --- The Eigensystem Realization Algorithm --- p.49Chapter 4.1.1 --- Basic Algorithm --- p.49Chapter 4.1.2 --- Estimating Markov Parameters from Input/Output data: Observer/Kalman Filter Identification (OKID) --- p.51Chapter 4.2 --- The Frequency-Domain Identification via 2-norm Minimization --- p.54Chapter 4.3 --- Balanced Realization and Truncation --- p.55Chapter 4.4 --- Frequency Weighted Balanced Truncation --- p.56Chapter 5 --- Plant Model Reduction and Robust Control Design --- p.59Chapter 5.1 --- Problem Formulation --- p.59Chapter 5.2 --- Iterative Reweighting Scheme --- p.60Chapter 5.2.1 --- Rationale Behind the Scheme --- p.62Chapter 5.3 --- Integrated Model Reduction/ Robust Control Design with Iter- ated Reweighting --- p.63Chapter 5.4 --- A Design Example --- p.64Chapter 5.4.1 --- The Plant and Specification --- p.64Chapter 5.4.2 --- First Iteration --- p.65Chapter 5.4.3 --- Second Iteration --- p.67Chapter 5.5 --- Approximate Fractional Frequency Weighting --- p.69Chapter 5.5.1 --- Summary of Past Results --- p.69Chapter 5.5.2 --- Approximate Fractional Frequency Weighting Approach [40] --- p.70Chapter 5.5.3 --- Simulation Results --- p.71Chapter 5.6 --- Integrated System Identification/Control Design with Iterative Reweighting Scheme --- p.74Chapter 6 --- Controller Reduction and Robust Control Design --- p.82Chapter 6.1 --- Motivation for Controller Reduction --- p.83Chapter 6.2 --- Choice of Frequency Weightings for Controller Reduction --- p.84Chapter 6.2.1 --- Stability Margin Considerations --- p.84Chapter 6.2.2 --- Closed-Loop Transfer Function Considerations --- p.85Chapter 6.2.3 --- A New Way to Determine Frequency Weighting --- p.86Chapter 6.3 --- A Scheme for Iterative Frequency Weighted Controller Reduction (IFWCR) --- p.87Chapter 7 --- A Comparative Design Example --- p.90Chapter 7.1 --- Plant Model Reduction Approach --- p.90Chapter 7.2 --- Weighted Controller Reduction Approach --- p.94Chapter 7.2.1 --- A Full Order Controller --- p.94Chapter 7.2.2 --- Weighted Controller Reduction with Stability Considera- tions --- p.94Chapter 7.2.3 --- Iterative Weighted Controller Reduction --- p.96Chapter 7.3 --- Summary of Results --- p.101Chapter 7.4 --- Discussions of Results --- p.101Chapter 8 --- A Comparative Example on a Benchmark problem --- p.105Chapter 8.1 --- The Benchmark plant [54] --- p.106Chapter 8.1.1 --- Benchmark Format and Design Information --- p.106Chapter 8.1.2 --- Control Design Specifications --- p.107Chapter 8.2 --- Selection of Performance Weighting function --- p.108Chapter 8.2.1 --- Reciprocal Principle --- p.109Chapter 8.2.2 --- Selection of W1 --- p.110Chapter 8.2.3 --- Selection of W2 --- p.110Chapter 8.3 --- System Identification by ERA --- p.112Chapter 8.4 --- System Identification by Curve Fitting --- p.114Chapter 8.4.1 --- Spectral Estimate --- p.114Chapter 8.4.2 --- Curve Fitting Results --- p.114Chapter 8.5 --- Robust Control Design --- p.115Chapter 8.5.1 --- The selection of W1 weighting function --- p.115Chapter 8.5.2 --- Summary of Design Results --- p.116Chapter 8.6 --- Stress Level 1 --- p.117Chapter 8.6.1 --- System Identification Results --- p.117Chapter 8.6.2 --- Design Results --- p.119Chapter 8.6.3 --- Step Response --- p.121Chapter 8.7 --- Stress Level 2 --- p.124Chapter 8.7.1 --- System Identification Results --- p.124Chapter 8.7.2 --- Step Response --- p.125Chapter 8.8 --- Stress Level 3 --- p.128Chapter 8.8.1 --- System Identification Results --- p.128Chapter 8.8.2 --- Step Response --- p.129Chapter 8.9 --- Comparisons with Other Designs --- p.132Chapter 9 --- Conclusions and Recommendations for Further Research --- p.133Chapter 9.1 --- Conclusions --- p.133Chapter 9.2 --- Recommendations for Further Research --- p.135Chapter A --- Design Results of Stress Levels 2 and3 --- p.137Chapter A.1 --- Stress Level 2 --- p.137Chapter A.2 --- Stress Level 3 --- p.140Chapter B --- Step Responses with Reduced Order Controller --- p.142Chapter C --- Summary of Results of Other Groups on the Benchmark Prob- lem --- p.145Chapter C.1 --- Indirect and implicit adaptive predictive control [45] --- p.146Chapter C.2 --- H∞ Robust Control [51] --- p.150Chapter C.3 --- Robust Stability Degree Assignment [53] --- p.152Chapter C.4 --- Model Reference Adaptive Control [46] --- p.154Chapter C.5 --- Robust Pole Placement using ACSYDE (Automatic Control Sys- tem Design) [47] --- p.156Chapter C.6 --- Adaptive PI Control [48] --- p.157Chapter C.7 --- Adaptive Control with supervision [49] --- p.160Chapter C.8 --- Partial State Model Reference (PSRM) Control [50] --- p.162Chapter C.9 --- Contstrainted Receding Horizon Predictive Control (CRHPC) [52] --- p.165Bibliography --- p.16

Contributions to nonlinear system modelling and controller synthesis via convex structures

Esta tesis discute diferentes metodologías de modelado para extraer mejores prestaciones o resultados de estabilidad que aquéllas que el modelado convencional basado en sector no-lineal de sistemas Takagi-Sugeno (también denominados cuasi-LPV) es capaz de producir. En efecto, incluso si las LMIs pueden probar distintas cotas de prestaciones o márgenes de estabilidad (tasa de decaimiento, $\mathcal H_\infty$, etc.) para sistemas politópicos, es bien conocido que las prestaciones probadas dependen del modelo elegido y, dado un sistema no-lineal, dicho modelo politópico no es único. Por tanto, se presentan exploraciones hacia cómo obtener el modelo que es menos perjudicial para la medida de prestaciones elegida. Como una última contribución, mejores resultados son obtenidos mediante la extensión del modelado politópico Takagi-Sugeno a un marco de inclusiones en diferencias cuasi-convexas con planificación de ganancia. En efecto, una versión sin planificación de ganancia fue propuesta por un equipo de investigadores de la Universidad de Sevilla (Fiaccini, Álamo, Camacho) para generalizar el modelado politópico, y esta tesis propone una version aún más general de algunos de dichos resultados que incorpora planificación de ganancia.This thesis discusses different modelling methodologies to eke out best performance/stability results than conventional sector-nonlinearity Takagi-Sugeno (also known as quasi-LPV) systems modelling techniques are able to yield. Indeed, even if LMIs can prove various performance and stability bounds (decay rate, $\mathcal H_\infty$, etc.) for polytopic systems, it is well known that the proven performance depends on the chosen model and, given a nonlinear dynamic systems, the polytopic embeddings available for it are not unique. Thus, explorations on how to obtain the model which is less deletereous for performance are presented. As a last contribution, extending the polytopic Takagi-Sugeno setup to a gain-scheduled quasi-convex difference inclusion framework allows to improve the results over the polytopic models. Indeed, the non-scheduled convex difference inclusion framework was proposed by a research team in University of Seville (Fiacchini, Alamo, Camacho) as a generalised modelling methodology which included the polytopic one; this thesis poses a further generalised gain-scheduled version of some of these results.Aquesta tesi discuteix diferents metodologies de modelatge per extreure millors prestacions o resultats d'estabilitat que aquelles que el modelatge convencional basat en sector no-lineal de sistemes Takagi-Sugeno (també anomenats quasi-LPV) és capaç de produir. En efecte, fins i tot si les LMIs poden provar diferents cotes de prestacions o marges d'estabilitat (taxa de decaïment, $\mathcal H_\infty$, etc.) per a sistemes politòpics, és ben conegut que les prestacions provades depenen del model triat i, donat un sistema no-lineal, el dit model politòpic no és únic. Per tant, es presenten exploracions cap a com obtenir el model que és menys perjudicial per a la mesura de prestacions triada. Com una darrera contribució, millors resultats són obtinguts mitjançant l'extensió del modelatge politòpic Takagi-Sugeno a un marc d'inclusions en diferències quasi-convexes amb planificació de guany. En efecte, una versió sense planificació de guany va ser proposada per un equip d'investigadors de la Universitat de Sevilla (Fiaccini, Álamo, Camacho) per a generalitzar el modelatge politòpic, i aquesta tesi proposa una versió més general d'alguns d'aquests resultats que incorpora planificació de guany.Robles Ruiz, R. (2018). Contributions to nonlinear system modelling and controller synthesis via convex structures [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/100848TESI

A Bayesian approach to robust identification: application to fault detection

In the Control Engineering field, the so-called Robust Identification techniques deal with the problem of obtaining not only a nominal model of the plant, but also an estimate of the uncertainty associated to the nominal model. Such model of uncertainty is typically characterized as a region in the parameter space or as an uncertainty band around the frequency response of the nominal model. Uncertainty models have been widely used in the design of robust controllers and, recently, their use in model-based fault detection procedures is increasing. In this later case, consistency between new measurements and the uncertainty region is checked. When an inconsistency is found, the existence of a fault is decided. There exist two main approaches to the modeling of model uncertainty: the deterministic/worst case methods and the stochastic/probabilistic methods. At present, there are a number of different methods, e.g., model error modeling, set-membership identification and non-stationary stochastic embedding. In this dissertation we summarize the main procedures and illustrate their results by means of several examples of the literature. As contribution we propose a Bayesian methodology to solve the robust identification problem. The approach is highly unifying since many robust identification techniques can be interpreted as particular cases of the Bayesian framework. Also, the methodology can deal with non-linear structures such as the ones derived from the use of observers. The obtained Bayesian uncertainty models are used to detect faults in a quadruple-tank process and in a three-bladed wind turbine

Systems Structure and Control

The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc

Polynomial Chaos Approximation of the Quadratic Performance of Uncertain Time-Varying Linear Systems

This paper presents a novel approach to robustness analysis based on quadratic performance metrics of uncertain time-varying systems. The considered time-varying systems are assumed to be linear and defined over a finite time horizon. The uncertainties are described in the form of real-valued random variables with a known probability distribution. The quadratic performance problem for this class of systems can be posed as a parametric Riccati differential equation (RDE). A new approach based on polynomial chaos expansion is proposed that can approximately solve the resulting parametric RDE and, thus, provide an approximation of the quadratic performance. Moreover, it is shown that for a zeroth order expansion this approximation is in fact a lower bound to the actual quadratic performance. The effectiveness of the approach is demonstrated on the example of a worst-case performance analysis of a space launcher during its atmospheric ascent

Control and Optimization for Aerospace Systems with Stochastic Disturbances, Uncertainties, and Constraints

The topic of this dissertation is the control and optimization of aerospace systems under the influence of stochastic disturbances, uncertainties, and subject to chance constraints. This problem is motivated by the uncertain operating environments of many aerospace systems, and the ever-present push to extract greater performance from these systems while maintaining safety. Explicitly accounting for the stochastic disturbances and uncertainties in the constrained control design confers the ability to assign the probability of constraint satisfaction depending on the level of risk that is deemed acceptable and allows for the possibility of theoretical constraint satisfaction guarantees. Along these lines, this dissertation presents novel contributions addressing four different problems: 1) chance-constrained path planning for small unmanned aerial vehicles in urban environments, 2) chance-constrained spacecraft relative motion planning in low-Earth orbit, 3) stochastic optimization of suborbital launch operations, and 4) nonlinear model predictive control for tracking near rectilinear halo orbits and a proposed stochastic extension. For the first problem, existing dynamic and informed rapidly-expanding random trees algorithms are combined with a novel quadratic programming-based collision detection algorithm to enable computationally efficient, chance-constrained path planning. For the second problem, a previously proposed constrained relative motion approach based on chained positively invariant sets is extended in this dissertation to the case where the spacecraft dynamics are controlled using output feedback on noisy measurements and are subject to stochastic disturbances. Connectivity between nodes is determined through the use of chance-constrained admissible sets, guaranteeing that constraints are met with a specified probability. For the third problem, a novel approach to suborbital launch operations is presented. It utilizes linear covariance propagation and stochastic clustering optimization to create an effective software-only method for decreasing the probability of a dangerous landing with no physical changes to the vehicle and only minimal changes to its flight controls software. For the fourth problem, the use of suboptimal nonlinear model predictive control (NMPC) coupled with low-thrust actuators is considered for station-keeping on near rectilinear halo orbits. The nonlinear optimization problems in NMPC are solved with time-distributed sequential quadratic programming techniques utilizing the FBstab algorithm. A stochastic extension for this problem is also proposed. The results are illustrated using detailed numerical simulations.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162992/1/awbe_1.pd