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

Fault detection on bearings coupled to permanent magnet DC motors by using a generalized Takagi-Sugeno PI observer

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThis paper presents a fault detection system for rotative machinery. A permanent-magnet DC motor is used as case of study. The main idea is to estimate on-line the non-load torque (To) in order to monitor the bearing health condition. The fault detection system is based on the design of a generalized Takagi-Sugeno PI (proportional-integral) observer. The main advantage of this approach is that it can be easily implemented because the observer gains are obtained by solving a set of LMIs (linear matrix inequalities). Moreover, the method can be extended to more complicated nonlinear systems by using the Takagi-Sugeno approach. A simulation is performed to show that this fault detection scheme can be applied to detect abrupt faults on rotative machinery which can lead the system to undesirable performance caused by vibrations or breakdown.Accepted versio

Generalized H∞ observers design for systems with unknown inputs

Abstract-A generalized H ∞ observers design is proposed for linear systems with unknown inputs. It generalizes the existing results concerning the proportional observer (PO) design and the proportional integral observer (PIO) design. The approach is based on the solutions of the algebraic constraints obtained from the unbiasedness conditions of the estimation error. The observer design is obtained from the solutions of linear matrix inequalities (LMIs). A numerical example is given to illustrate our approach

Adaptive and Robust Braking-Traction Control Systems

The designs of commercial Anti-Lock Braking Systems often rely on assumptions of a torsionally rigid tire-wheel system and heavily rely on hub-mounted wheel speed sensors to manage tire-road slip conditions. However, advancements in high-bandwidth braking systems, in-wheel motors, variations in tire/wheel designs, and loss of inflation pressure, have produced scenarios where the tire\u27s torsional dynamics could be easily excited by the braking system actuator. In these scenarios, the slip conditions for the tire-belt/ring will be dynamically different from what can be inferred from the wheel speed sensors. This dissertation investigates the interaction of tire torsional dynamics with ABS & traction controllers and offers new control designs that incorporate schemes for identifying and accommodating these dynamics. To this end, suitable braking system and tire torsional dynamics simulation models as well as experimental test rigs were developed. It is found that, indeed, rigid-wheel based controllers give degraded performance when coupled with low torsional stiffness tires. A closed-loop observer/nonlinear controller structure is proposed that adapts to unknown tire sidewall and tread parameters during braking events. It also provides estimates of difficult to measure state variables such as belt/ring speed. The controller includes a novel virtual damper emulation that can be used to tune the system response. An adaptive sliding-mode controller is also introduced that combines robust stability characteristics with tire/tread parameter and state estimation. The sliding mode controller is shown to be very effective at tracking its estimated target, at the expense of reducing the tire parameter adaptation performance. Finally, a modular robust state observer is developed that allows for robust estimation of the system states in the presence of uncertainties and external disturbances without the need for sidewall parameter adaptation

Lie Group Observer Design for Robotic Systems: Extensions, Synthesis, and Higher-Order Filtering

The kinematics and dynamics of many robotic systems evolve on differential manifolds, rather than strictly in Euclidean space. Lie groups, a class of differential manifold with a group structure, arise naturally in the study of rigid-body kinematics. This dissertation studies the design of state observers for systems whose state evolves on a Lie group. State observers, or state estimators, are a crucial part of the guidance, navigation, and control algorithms necessary for autonomous operation of many ground, air, and marine vehicles. The design of state observers on Lie groups is therefore a highly practical exercise. One such nonlinear observer, the gradient-based observer, has generated significant interest in the literature due to its computational simplicity and stability guarantees. The first part of this dissertation explores several applications of the gradient-based observer, including both the attitude estimation problem and the simultaneous localization and mapping (SLAM) problem. By modifying the cost function associated with the observer, several novel attitude estimators are introduced that provide faster convergence when the initial attitude error is large. Further, a SLAM algorithm with guaranteed convergence is introduced and tested in both simulation and experiment. In the second part of this dissertation, the state of the art in Lie group observer design is extended by the development of a higher-order filter on a Lie group. By analogy to the classical linear complementary filter, the proposed method can be interpreted as a nonlinear complementary filter on a Lie group. A disturbance observer that accounts for constant and harmonic disturbances in the group velocity measurements is also considered. Local asymptotic stability about the desired equilibrium point is demonstrated. In addition, an H2-optimal filter synthesis method is derived and disturbance rejection via the internal model principle is considered. A numerical example that demonstrates the desirable properties of the higher-order nonlinear complementary filter, as well as the synthesis techniques, is presented in the context of rigid-body attitude estimation.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147655/1/dzlotnik_1.pd

Robust estimation of uncertain linear systems using a moving horizon approach

Abstract: Since the famous contributions of Kalman at the middle of the last century, the state estimation became a special issue related to the control theory. Countless modern control strategies, or statespace control approaches, assume the partial or overall knowledge of the system state. However, this is far to be found in practice, because the direct measurement of every state is not always possible. The state estimators solve the previous issue by using tools form the control theory. Roughly speaking, an state estimator uses both a system model and some measurements to build the dynamical behaviour of the system state. Regarding the type of dynamic system, there exist an important amount of state estimation designs. For instance, the well-known Kalman filter solves the optimal state estimation problem of a linear system with stochastic inputs modeled by white noises with known statistics. The optimization is with respect to the minimization of the estimation error variance. Robust filters in turn, solve a different problem. The most used assumptions are about the uncertainty of the disturbing noises and the parameters of the system. However, there is not enough evidence of contributions about robust filters using additional information in form of constraints. The present contribution is about a novel estimation scheme robust to unknown inputs and able to use a priori information of the system in form of constraints. The proposed scheme uses an alternative formulation of the MHE (moving horizon estimator) with the game-theoretical formulation of the Hinf filtering. On one hand, the MHE-based scheme gives a way to address constraints. On the other hand, a cost function in a form of a disturbance attenuation function offers a ‘worst-case’ framework. Following the classic MHE formulation, first the full information estimator based on the Hinf theory is proposed, namely, the Hinf-FIE. Then, an approximation is provided by means of the Hinf-MHE to avoid numerical feasibility problems. Different examples show the effectiveness of the proposed filter. The filter is also compared with respect the classic MHE and some robust schemes. A numerical approximation is used to provide a solution of the minimax optimization associated to the constrained Hinf-MHE.Resumen: Desde las contribuciones que hiciera Kalman a principios de los años 50’s del siglo pasado, la estimación de estados se ha convertido en un tópico fundamental de la teoría de control moderna. Innumerables estrategias de control moderno, o estrategias en el espacio de estados, suponen un conocimiento total o parcial del estado del sistema. Sin embargo, esto está lejos de ser posible en la práctica, dado que por diferentes razones la medición directa de los estados no es siempre posible. Los estimadores de estado resuelven el anterior inconveniente usando herramientas de la teoría de control. En términos generales, un estimador de estados usa conjuntamente un modelo matemático del sistema dinámico de interés y las mediciones de ciertas variables accesibles del sistema para reconstruir el comportamiento dinámico del estado. Dependiendo del tipo de sistema dinámico, existe una cantidad importante de alternativas para diseñar estimadores de estado (también conocidos como observadores de estado o simplemente filtros). Por ejemplo, el celebrado filtro de Kalman resuelve el problema de estimación óptima del estado de un sistema lineal sujeto a ruidos blancos con propiedades estadísticas conocidas. La optimización de este filtro se lleva a cabo minimizando la varianza del error de estimación. Los filtros robustos por su parte, resuelven un problema diferente al planteado por Kalman. Las suposiciones más comunes que se encuentran en el planteamiento de este problema se hacen acerca del desconocimiento de los ruidos (incertidumbre de modelado y ruido de medición) y de la incertidumbre sobre los parámetros del sistema dinámico. Sin embargo, existe una situación de la cual no se tiene suficiente evidencia en la literatura y está relacionada con la síntesis de filtros robustos que incorporen restricciones sobre las variables del sistema dinámico. El aporte de esta tesis está basado en la obtención de una estrategia de estimación de estados robusta ante entradas desconocidas que a la vez incluya información a priori del sistema dinámico en forma de restricciones. En esta investigación se obtiene una estrategia de estimación de estados basada en una formulación alternativa del MHE (moving horizon estimator), combinada con la aproximación por teoría de juegos al filtrado H¥. Por un lado, el MHE provee una estructura en la cual se hace un manejo directo de restricciones. Por otro lado, la formulación de una función de costo en la forma de una función de atenuación de perturbaciones, permite modificar la formulación clásica del MHE orientándolo hacia un esquema de ‘peor caso’. De manera dual al esquema MHE clásico, se propone primero un filtro de información completa, robusto ante entradas desconocidas, llamado H¥-FIE. Después se presenta la aproximación al filtro H¥-FIE mediante el H¥-MHE para evitar problemas de factibilidad numérica. Diferentes ejemplos muestran la efectividad de este último filtro con respecto al MHE clásico y a otras estrategias robustas. Se presenta una solución numérica al problema de H¥-MHE con restricciones mediante la solución aproximada de la optimización minimax que está asociada a la formulación del problema.Doctorad

Aplicación de técnicas robustas para detección y diagnóstico de fallos

La teoría de control es un área en constante desarrollo, donde muchas técnicas están basadas en el conocimiento del sistema en estudio. A nivel industrial, los sistemas son en su mayoría no lineales, y sus comportamientos ante la influencia del entorno pueden variar en poca o gran medida. Incorporar en el diseño del sistema de control un modulo de detección y diagnóstico de fallos mejora los procesos, la disponibilidad y mantenimiento del sistema, así como su desempeño y robustez. En esta investigación se aplican diferentes métodos de detección y diagnóstico de fallos (DDF) para lograr esquemas que presenten buen desempeño y robustez ante las incertidumbres, perturbaciones y el ruido. Un esquema de DDF que utiliza filtros basado en el modelo matemático del sistema es logrado con la aplicación de desigualdades matriciales lineales (\emph{Linear Matrix Inequalities}, LMIs). Esquemas de DDF que suministran información de las relaciones estadísticas de las señales son desarrollados con técnicas multivariantes de análisis de componentes principales (PCA) y de análisis de componentes independientes (ICA) en aplicaciones estáticas y dinámicas. El conocimiento de los comportamientos del sistema es estudiado mediante redes neuronales dinámicas, que utilizan filtros internos. En el caso en que se utiliza el modelo matemático de la planta se obtiene un esquema de planta generalizada donde se calcula un filtro para rechazar la incertidumbre de la planta, que es modelada por el estudio del comportamiento del sistema en diferentes puntos de operación, y un segundo filtro que es calculado para rechazar las perturbaciones y el ruido. Para los esquemas que utilizan las técnicas multivariantes se construye un banco de modelos que se corresponden con las relaciones estadísticas de las señales en cada uno de los comportamientos definidos del sistema. Cuando se utilizan las redes neuronales dinámicas se establecen patrones de aprendizaje para cada uno de los comportamientos definidos en el sistema, obteniéndose en este caso un banco de redes neuronales, cuyas respuestasDepartamento de Ingeniería de Sistemas y Automátic