On designing H∞ filters with circular pole and error variance constraints

Copyright [2003] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we deal with the problem of designing a H∞ filter for discrete-time systems subject to error variance and circular pole constraints. Specifically, we aim to design a filter such that the H∞ norm of the filtering error-transfer function is not less than a given upper bound, while the poles of the filtering matrix are assigned within a prespecified circular region, and the steady-state error variance for each state is not more than the individual prespecified value. The filter design problem is formulated as an auxiliary matrix assignment problem. Both the existence condition and the explicit expression of the desired filters are then derived by using an algebraic matrix inequality approach. The proposed design algorithm is illustrated by a numerical example

Modelling techniques for biological systems

The objective of this investigation has been to develop and evaluate techniques which are appropriate to the modelling and simulation of biological reaction system behaviour. The model used as the basis for analysis of modelling and simulation techniques is a reduced version of the biological model proposed by the IAWPRC Task Group for mathematical modell ing in wastewater treatment design. This limited model has the advantage of being easily manageable in terms of analysis and presentation of the simulation techniQues whilst at the same time incorporating a range of features encountered with biological growth applications in general. Because a model may incorporate a number of different components and large number of biological conversion processes, a convenient method of presentation was found to be a matrix format. The matrix representation ensures clarity as to what compounds, processes and react ion terms are to be incorporated and allows easy comparison of different models. In addition, it facilitates transforming the model into a computer program. Simulation of the system response first involves specifying the reactor configuration and flow patterns. With this information fixed, mass balances for each compound in each reactor can be completed. These mass balances constitute a set of simultaneous non-linear differential and algebraic eQuations which, when solved, characterise the system behaviour

Identification of linear periodically time-varying (LPTV) systems

A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results. A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure the noise-contaminated output. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification. In the frequency domain, we show that the input and the output can be related by using the discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design

Efficient Multiband Algorithms for Blind Source Separation

The problem of blind separation refers to recovering original signals, called source signals, from the mixed signals, called observation signals, in a reverberant environment. The mixture is a function of a sequence of original speech signals mixed in a reverberant room. The objective is to separate mixed signals to obtain the original signals without degradation and without prior information of the features of the sources. The strategy used to achieve this objective is to use multiple bands that work at a lower rate, have less computational cost and a quicker convergence than the conventional scheme. Our motivation is the competitive results of unequal-passbands scheme applications, in terms of the convergence speed. The objective of this research is to improve unequal-passbands schemes by improving the speed of convergence and reducing the computational cost. The first proposed work is a novel maximally decimated unequal-passbands scheme.This scheme uses multiple bands that make it work at a reduced sampling rate, and low computational cost. An adaptation approach is derived with an adaptation step that improved the convergence speed. The performance of the proposed scheme was measured in different ways. First, the mean square errors of various bands are measured and the results are compared to a maximally decimated equal-passbands scheme, which is currently the best performing method. The results show that the proposed scheme has a faster convergence rate than the maximally decimated equal-passbands scheme. Second, when the scheme is tested for white and coloured inputs using a low number of bands, it does not yield good results; but when the number of bands is increased, the speed of convergence is enhanced. Third, the scheme is tested for quick changes. It is shown that the performance of the proposed scheme is similar to that of the equal-passbands scheme. Fourth, the scheme is also tested in a stationary state. The experimental results confirm the theoretical work. For more challenging scenarios, an unequal-passbands scheme with over-sampled decimation is proposed; the greater number of bands, the more efficient the separation. The results are compared to the currently best performing method. Second, an experimental comparison is made between the proposed multiband scheme and the conventional scheme. The results show that the convergence speed and the signal-to-interference ratio of the proposed scheme are higher than that of the conventional scheme, and the computation cost is lower than that of the conventional scheme

Aircraft adaptive learning control

The optimal control theory of stochastic linear systems is discussed in terms of the advantages of distributed-control systems, and the control of randomly-sampled systems. An optimal solution to longitudinal control is derived and applied to the F-8 DFBW aircraft. A randomly-sampled linear process model with additive process and noise is developed

Intelligent and High-Performance Behavior Design of Autonomous Systems via Learning, Optimization and Control

Nowadays, great societal demands have rapidly boosted the development of autonomous systems that densely interact with humans in many application domains, from manufacturing to transportation and from workplaces to daily lives. The shift from isolated working environments to human-dominated space requires autonomous systems to be empowered to handle not only environmental uncertainties such as external vibrations but also interaction uncertainties arising from human behavior which is in nature probabilistic, causal but not strictly rational, internally hierarchical and socially compliant.This dissertation is concerned with the design of intelligent and high-performance behavior of such autonomous systems, leveraging the strength from control, optimization, learning, and cognitive science. The work consists of two parts. In Part I, the problem of high-level hybrid human-machine behavior design is addressed. The goal is to achieve safe, efficient and human-like interaction with people. A framework based on the theory of mind, utility theories and imitation learning is proposed to efficiently represent and learn the complicated behavior of humans. Built upon that, machine behaviors at three different levels - the perceptual level, the reasoning level, and the action level - are designed via imitation learning, optimization, and online adaptation, allowing the system to interpret, reason and behave as human, particularly when a variety of uncertainties exist. Applications to autonomous driving are considered throughout Part I. Part II is concerned with the design of high-performance low-level individual machine behavior in the presence of model uncertainties and external disturbances. Advanced control laws based on adaptation, iterative learning and the internal structures of uncertainties/disturbances are developed to assure that the high-level interactive behaviors can be reliably executed. Applications on robot manipulators and high-precision motion systems are discussed in this part

A parallel implementation of a multisensor feature-based range-estimation method

There are many proposed vision based methods to perform obstacle detection and avoidance for autonomous or semi-autonomous vehicles. All methods, however, will require very high processing rates to achieve real time performance. A system capable of supporting autonomous helicopter navigation will need to extract obstacle information from imagery at rates varying from ten frames per second to thirty or more frames per second depending on the vehicle speed. Such a system will need to sustain billions of operations per second. To reach such high processing rates using current technology, a parallel implementation of the obstacle detection/ranging method is required. This paper describes an efficient and flexible parallel implementation of a multisensor feature-based range-estimation algorithm, targeted for helicopter flight, realized on both a distributed-memory and shared-memory parallel computer

MULTI-RATE VISUAL FEEDBACK ROBOT CONTROL

[EN] This thesis deals with two characteristic problems in visual feedback robot control: 1) sensor latency; 2) providing suitable trajectories for the robot and for the measurement in the image. All the approaches presented in this work are analyzed and implemented on a 6 DOF industrial robot manipulator or/and a wheeled robot. Focusing on the sensor latency problem, this thesis proposes the use of dual-rate high order holds within the control loop of robots. In this sense, the main contributions are: - Dual-rate high order holds based on primitive functions for robot control (Chapter 3): analysis of the system performance with and without the use of this multi-rate technique from non-conventional control. In addition, as consequence of the use of dual-rate holds, this work obtains and validates multi-rate controllers, especially dual-rate PIDs. - Asynchronous dual-rate high order holds based on primitive functions with time delay compensation (Chapter 3): generalization of asynchronous dual-rate high order holds incorporating an input signal time delay compensation component, improving thus the inter-sampling estimations computed by the hold. It is provided an analysis of the properties of such dual-rate holds with time delay compensation, comparing them with estimations obtained by the equivalent dual-rate holds without this compensation, as well as their implementation and validation within the control loop of a 6 DOF industrial robot manipulator. - Multi-rate nonlinear high order holds (Chapter 4): generalization of the concept of dual-rate high order holds with nonlinear estimation models, which include information about the plant to be controlled, the controller(s) and sensor(s) used, obtained from machine learning techniques. Thus, in order to obtain such a nonlinear hold, it is described a methodology non dependent of the machine technique used, although validated using artificial neural networks. Finally, an analysis of the properties of these new holds is carried out, comparing them with their equivalents based on primitive functions, as well as their implementation and validation within the control loop of an industrial robot manipulator and a wheeled robot. With respect to the problem of providing suitable trajectories for the robot and for the measurement in the image, this thesis presents the novel reference features filtering control strategy and its generalization from a multi-rate point of view. The main contributions in this regard are: - Reference features filtering control strategy (Chapter 5): a new control strategy is proposed to enlarge significantly the solution task reachability of robot visual feedback control. The main idea is to use optimal trajectories proposed by a non-linear EKF predictor-smoother (ERTS), based on Rauch-Tung-Striebel (RTS) algorithm, as new feature references for an underlying visual feedback controller. In this work it is provided both the description of the implementation algorithm and its implementation and validation utilizing an industrial robot manipulator. - Dual-rate Reference features filtering control strategy (Chapter 5): a generalization of the reference features filtering approach from a multi-rate point of view, and a dual Kalman-smoother step based on the relation of the sensor and controller frequencies of the reference filtering control strategy is provided, reducing the computational cost of the former algorithm, as well as addressing the problem of the sensor latency. The implementation algorithms, as well as its analysis, are described.[ES] La presente tesis propone soluciones para dos problemas característicos de los sistemas robóticos cuyo bucle de control se cierra únicamente empleando sensores de visión artificial: 1) la latencia del sensor; 2) la obtención de trayectorias factibles tanto para el robot así como para las medidas obtenidas en la imagen. Todos los métodos propuestos en este trabajo son analizados, validados e implementados utilizando brazo robot industrial de 6 grados de libertad y/o en un robot con ruedas. Atendiendo al problema de la latencia del sensor, esta tesis propone el uso de retenedores bi-frequencia de orden alto dentro de los lazos de control de robots. En este aspecto las principales contribuciones son: -Retenedores bi-frecuencia de orden alto basados en funciones primitivas dentro de lazos de control de robots (Capítulo 3): análisis del comportamiento del sistema con y sin el uso de esta técnica de control no convencional. Además, como consecuencia del empleo de los retenedores, obtención y validación de controladores multi-frequencia, concretamente de PIDs bi-frecuencia. -Retenedores bi-frecuencia asíncronos de orden alto basados en funciones primitivas con compensación de retardos (Capítulo 3): generalización de los retenedores bi-frecuencia asíncronos de orden alto incluyendo una componente de compensación del retardo en la señal de entrada, mejorando así las estimaciones inter-muestreo calculadas por el retenedor. Se proporciona un análisis de las propiedades de los retenedores con compensación del retardo, comparándolas con las obtenidas por sus predecesores sin compensación, así como su implementación y validación en un brazo robot de 6 grados de libertad. -Retenedores multi-frecuencia no lineales de orden alto (Capítulo 4): generalización del concepto de retenedor bi-frecuencia de orden alto con modelos de estimación no lineales, los cuales incluyen información tanto de la planta a controlar, como del controlador(es) y sensor(es) empleado(s), obtenida a partir de técnicas de aprendizaje. Así pues, para obtener dicho retenedor no lineal, se describe una metodología independiente de la herramienta de aprendizaje utilizada, aunque validada con el uso de redes neuronales artificiales. Finalmente se realiza un análisis de las propiedades de estos nuevos retenedores, comparándolos con sus predecesores basados en funciones primitivas, así como su implementación y validación en un brazo robot de 6 grados de libertad y en un robot móvil con ruedas. Por lo que respecta al problema de generación de trayectorias factibles para el robot y para la medida en la imagen, esta tesis propone la nueva estrategia de control basada en el filtrado de la referencia y su generalización desde el punto de vista multi-frecuencial. -Estrategia de control basada en el filtrado de la referencia (Capítulo 5): una nueva estrategia de control se propone para ampliar significativamente el espacio de soluciones de los sistemas robóticos realimentados con sensores de visión artificial. La principal idea es utilizar las trayectorias óptimas obtenidas por una trayectoria predicha por un filtro de Kalman seguido de un suavizado basado en el algoritmo Rauch-Tung-Striebel (RTS) como nuevas referencias para un controlador dado. En este trabajo se proporciona tanto la descripción del algoritmo como su implementación y validación empleando un brazo robótico industrial. -Estrategia de control bi-frecuencia basada en el filtrado de la referencia (Capítulo 5): generalización de la estrategia de control basada en filtrado de la referencia desde un punto de vista multi-frecuencial, con un filtro de Kalman multi-frecuencia y un Kalman-smoother dual basado en la relación existente entre las frecuencias del sensor y del controlador, reduciendo así el coste computacional del algoritmo y, al mismo tiempo, dando solución al problema de la latencia del sensor. La validación se realiza utilizando un barzo robot industria asi[CA] La present tesis proposa solucions per a dos problemes característics dels sistemes robòtics el els que el bucle de control es tanca únicament utilitzant sensors de visió artificial: 1) la latència del sensor; 2) l'obtenció de trajectòries factibles tant per al robot com per les mesures en la imatge. Tots els mètodes proposats en aquest treball son analitzats, validats e implementats utilitzant un braç robot industrial de 6 graus de llibertat i/o un robot amb rodes. Atenent al problema de la latència del sensor, esta tesis proposa l'ús de retenidors bi-freqüència d'ordre alt a dins del llaços de control de robots. Al respecte, les principals contribucions son: - Retenidors bi-freqüència d'ordre alt basats en funcions primitives a dintre dels llaços de control de robots (Capítol 3): anàlisis del comportament del sistema amb i sense l'ús d'aquesta tècnica de control no convencional. A més a més, com a conseqüència de l'ús dels retenidors, obtenció i validació de controladors multi-freqüència, concretament de PIDs bi-freqüència. - Retenidors bi-freqüència asíncrons d'ordre alt basats en funcions primitives amb compensació de retards (Capítol 3): generalització dels retenidors bi-freqüència asíncrons d'ordre alt inclouen una component de compensació del retràs en la senyal d'entrada al retenidor, millorant així les estimacions inter-mostreig calculades per el retenidor. Es proporciona un anàlisis de les propietats dels retenidors amb compensació del retràs, comparant-les amb les obtingudes per el seus predecessors sense la compensació, així com la seua implementació i validació en un braç robot industrial de 6 graus de llibertat. - Retenidors multi-freqüència no-lineals d'ordre alt (Capítol 4): generalització del concepte de retenidor bi-freqüència d'ordre alt amb models d'estimació no lineals, incloent informació tant de la planta a controlar, com del controlador(s) i sensor(s) utilitzat(s), obtenint-la a partir de tècniques d'aprenentatge. Així doncs, per obtindre el retenidor no lineal, es descriu una metodologia independent de la ferramenta d'aprenentatge utilitzada, però validada amb l'ús de rets neuronals artificials. Finalment es realitza un anàlisis de les propietats d'aquestos nous retenidors, comparant-los amb els seus predecessors basats amb funcions primitives, així com la seua implementació i validació amb un braç robot de 6 graus de llibertat i amb un robot mòbil de rodes. Per el que respecta al problema de generació de trajectòries factibles per al robot i per la mesura en la imatge, aquesta tesis proposa la nova estratègia de control basada amb el filtrat de la referència i la seua generalització des de el punt de vista multi-freqüència. - Estratègia de control basada amb el filtrat de la referència (Capítol 5): una nova estratègia de control es proposada per ampliar significativament l'espai de solucions dels sistemes robòtics realimentats amb sensors de visió artificial. La principal idea es la d'utilitzar les trajectòries optimes obtingudes per una trajectòria predita per un filtre de Kalman seguit d'un suavitzat basat en l'algoritme Rauch-Tung-Striebel (RTS) com noves referències per a un control donat. En aquest treball es proporciona tant la descripció del algoritme així com la seua implementació i validació utilitzant un braç robòtic industrial de 6 graus de llibertat. - Estratègia de control bi-freqüència basada en el filtrat (Capítol 5): generalització de l'estratègia de control basada am filtrat de la referència des de un punt de vista multi freqüència, amb un filtre de Kalman multi freqüència i un Kalman-Smoother dual basat amb la relació existent entre les freqüències del sensor i del controlador, reduint així el cost computacional de l'algoritme i, al mateix temps, donant solució al problema de la latència del sensor. L'algoritme d'implementació d'aquesta tècnica, així com la seua validaciSolanes Galbis, JE. (2015). MULTI-RATE VISUAL FEEDBACK ROBOT CONTROL [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/57951TESI