Probabilistic robust control : theory and applications

In this work, the development of a probabilistic approach to robust control is motivated by structural control applications in civil engineering. Often in civil structural applications, a system's performance is specified in terms of its reliability. In addition, the model and input uncertainty for the system may be described most appropriately using probabilistic or "soft" bounds on the model and input sets. The probabilistic robust control methodology contrasts with existing H∞/μ robust control methodologies that do not use probability information for the model and input uncertainty sets, yielding only the guaranteed (i.e., "worst-case") system performance, and no information about the system's probable performance which would be of interest to civil engineers.

The design objective for the probabilistic robust controller is to maximize the reliability of the uncertain structure/controller system for a probabilistically-described uncertain excitation. The robust performance is computed for a set of possible models by weighting the conditional performance probability for a particular model by the probability of that model, then integrating over the set of possible models. This integration is accomplished efficiently using an asymptotic approximation. The probable performance can be optimized numerically over the class of allowable controllers to find the optimal controller. Also, if structural response data becomes available from a controlled structure, its probable performance can easily be updated using Bayes's Theorem to update the probability distribution over the set of possible models. An updated optimal controller can then be produced, if desired, by following the original procedure. Thus, the probabilistic framework integrates system identification and robust control in a natural manner.

The probabilistic robust control methodology is applied to two systems in this thesis. The first is a high-fidelity computer model of a benchmark structural control laboratory experiment. For this application, uncertainty in the input model only is considered. The probabilistic control design minimizes the failure probability of the benchmark system while remaining robust with respect to the input model uncertainty. The performance of an optimal low-order controller compares favorably with higher-order controllers for the same benchmark system which are based on other approaches. The second application is to the Caltech Flexible Structure, which is a light-weight aluminum truss structure actuated by three voice coil actuators. A controller is designed to minimize the failure probability for a nominal model of this system. Furthermore, the method for updating the model-based performance calculation given new response data from the system is illustrated.

Neural network design for switching network control

A neural network is a highly interconnected set of simple processors. The many connections allow information to travel rapidly through the network, and due to their simplicity, many processors in one network are feasible. Together these properties imply that we can build efficient massively parallel machines using neural networks. The primary problem is how do we specify the interconnections in a neural network. The various approaches developed so far such as outer product, learning algorithm, or energy function suffer from the following deficiencies: long training/ specification times; not guaranteed to work on all inputs; requires full connectivity.

Alternatively we discuss methods of using the topology and constraints of the problems themselves to design the topology and connections of the neural solution. We define several useful circuits-generalizations of the Winner-Take-All circuitthat allows us to incorporate constraints using feedback in a controlled manner. These circuits are proven to be stable, and to only converge on valid states. We use the Hopfield electronic model since this is close to an actual implementation. We also discuss methods for incorporating these circuits into larger systems, neural and nonneural. By exploiting regularities in our definition, we can construct efficient networks. To demonstrate the methods, we look to three problems from communications. We first discuss two applications to problems from circuit switching; finding routes in large multistage switches, and the call rearrangement problem. These show both, how we can use many neurons to build massively parallel machines, and how the Winner-Take-All circuits can simplify our designs.

Next we develop a solution to the contention arbitration problem of high-speed packet switches. We define a useful class of switching networks and then design a neural network to solve the contention arbitration problem for this class. Various aspects of the neural network/switch system are analyzed to measure the queueing performance of this method. Using the basic design, a feasible architecture for a large (1024-input) ATM packet switch is presented. Using the massive parallelism of neural networks, we can consider algorithms that were previously computationally unattainable. These now viable algorithms lead us to new perspectives on switch design.

Efficient methods for stochastic optimal control

The Hamilton Jacobi Bellman (HJB) equation is central to stochastic optimal control (SOC) theory, yielding the optimal solution to general problems specified by known dynamics and a specified cost functional. Given the assumption of quadratic cost on the control input, it is well known that the HJB reduces to a particular partial differential equation (PDE). While powerful, this reduction is not commonly used as the PDE is of second order, is nonlinear, and examples exist where the problem may not have a solution in a classical sense. Furthermore, each state of the system appears as another dimension of the PDE, giving rise to the curse of dimensionality. Since the number of degrees of freedom required to solve the optimal control problem grows exponentially with dimension, the problem becomes intractable for systems with all but modest dimension.

In the last decade researchers have found that under certain, fairly non-restrictive structural assumptions, the HJB may be transformed into a linear PDE, with an interesting analogue in the discretized domain of Markov Decision Processes (MDP). The work presented in this thesis uses the linearity of this particular form of the HJB PDE to push the computational boundaries of stochastic optimal control.

This is done by crafting together previously disjoint lines of research in computation. The first of these is the use of Sum of Squares (SOS) techniques for synthesis of control policies. A candidate polynomial with variable coefficients is proposed as the solution to the stochastic optimal control problem. An SOS relaxation is then taken to the partial differential constraints, leading to a hierarchy of semidefinite relaxations with improving sub-optimality gap. The resulting approximate solutions are shown to be guaranteed over- and under-approximations for the optimal value function. It is shown that these results extend to arbitrary parabolic and elliptic PDEs, yielding a novel method for Uncertainty Quantification (UQ) of systems governed by partial differential constraints. Domain decomposition techniques are also made available, allowing for such problems to be solved via parallelization and low-order polynomials.

The optimization-based SOS technique is then contrasted with the Separated Representation (SR) approach from the applied mathematics community. The technique allows for systems of equations to be solved through a low-rank decomposition that results in algorithms that scale linearly with dimensionality. Its application in stochastic optimal control allows for previously uncomputable problems to be solved quickly, scaling to such complex systems as the Quadcopter and VTOL aircraft. This technique may be combined with the SOS approach, yielding not only a numerical technique, but also an analytical one that allows for entirely new classes of systems to be studied and for stability properties to be guaranteed.

The analysis of the linear HJB is completed by the study of its implications in application. It is shown that the HJB and a popular technique in robotics, the use of navigation functions, sit on opposite ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. Analytical solutions to the HJB in these settings are available in simplified domains, yielding guidance towards optimality for approximation schemes. Finally, the use of HJB equations in temporal multi-task planning problems is investigated. It is demonstrated that such problems are reducible to a sequence of SOC problems linked via boundary conditions. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification.

Diseño, fabricación y control de un sistema neumático de agarre de 1 grado de libertad

[ES]El presente Trabajo de Fin de Grado tiene la finalidad de contribuir al desarrollo de una línea de investigación mediante la implementación de un sistema neumático de agarre al mecanismo de cinemática paralela 5R. Dicho proyecto se integra dentro de una línea de investigación basada en el desarrollo y estudio de mecanismos de este tipo. Así, este Trabajo supone una pequeña parte de un proyecto de mayor envergadura, para cuyo éxito será necesaria la colaboración con otros investigadores y la integración de este trabajo al realizado por ellos. Consiste en diseñar, fabricar y controlar un sistema neumático de agarre al mecanismo 5R. El diseño se realizará sopesándose las distintas alternativas que existen, teniéndose en cuenta las limitaciones impuestas por el 5R. En el diseño se escogen los componentes correctos para conseguir que el sistema realice sus dos funciones:  Agarrar piezas.  Movimiento en el eje z que le permita desplazar el objeto. Antes del ensamblaje de los componentes neumáticos, y teniendo en cuenta el diseño realizado, se fabricarán las piezas necesarias para poder integrarlo al 5R y para, a su vez, juntar los componentes entre sí. A continuación, se desarrollará un programa informático para poder controlar el sistema. Finalmente, para verificar su correcto funcionamiento, se realizarán las pruebas pertinentes.

Convex model predictive control for vehicular systems

In this work, the author presents a method called Convex Model Predictive Control (CMPC) to control systems whose states are elements of the rotation matrices SO(n) for n = 2, 3. This is done without charts or any local linearization, and instead is performed by operating over the orbitope of rotation matrices. This results in a novel model predictive control (MPC) scheme without the drawbacks associated with conventional linearization techniques such as slow computation time and local minima. Of particular emphasis is the application to aeronautical and vehicular systems, wherein the method removes many of the trigonometric terms associated with these systems’ state space equations. Furthermore, the method is shown to be compatible with many existing variants of MPC, including obstacle avoidance via Mixed Integer Linear Programming (MILP).

Sistema de control reconfigurable en célula de manipulación

[ES]Este trabajo trata sobre los sistemas de control reconfigurables. El objetivo es conseguir que el sistema de control siga controlando el proceso antes situaciones de cambio solicitadas por el usuario o ante situaciones de fallo en los controladores. Se aplicará sobre la primera estación de la célula de manipulación didáctica FMS 200 del laboratorio del Departamento de Ingeniería de Sistemas y Automática (DISA) de la ETSI de Bilbao.

Control computerizado mediante Kinect

[ES]En el presente trabajo se tratará de exponer el método de trabajo, el desarrollo y los posibles usos de este dispositivo como un método de control en un marco de uso industrial orientado a la economía

Part I. Electric birefringence studies of deoxyribonucleic acids. Part II. Selective dissociation of nucleohistone complexes

Part I

The electric birefringence of dilute DNA solutions has been studied in considerable detail and on a large number of samples, but no new and reliable information was discovered concerning the tertiary structure of DNA. The large number of variables which effect the birefringence results is discussed and suggestions are made for further work on the subject.

The DNA molecules have been aligned in a rapidly alternating (10 to 20 kc/sec) square wave field confirming that the orientation mechanism is that of counterion polarization. A simple empirical relation between the steady state birefringence, Δn_st, and the square of the electric field, E, has been found: Δn_st = E²/(a E² + b), where a = 1/Δn_s and b = (E²/Δn_st)_E→o. Δn_s is the birefringence extrapolated to infinite field strength.

The molecules show a distribution of relaxation times from 10^-4 to 0.2 sec, which is consistent with expectations for flexible coil molecules. The birefringence and the relaxation times decrease with increasing salt concentrations. They also depend on the field strength and pulse duration in a rather non-reproducible manner, which may be due in part to changes in the composition of the solution or in the molecular structure of the DNA (other than denaturation). Further progress depends on the development of some control over these effects.

Part II

The specificity of the dissociation of reconstituted and native deoxyribonucleohistones (DNH) by monovalent salt solutions has been investigated. A novel zone ultracentrifugation method is used in which the DNH is sedimented as a zone through a preformed salt gradient, superimposed on a stabilizing D₂O (sucrose) density gradient. The results, obtained by scanning the quartz sedimentation tubes in a spectrophotometer, were verified by the conventional, preparative sedimentation technique. Procedures are discussed for the detection of microgram quantities of histones, since low concentrations must be used to prevent excessive aggregation of the DNH.

The data show that major histone fractions are selectively dissociated from DNH by increasing salt concentrations: Lysine rich histone (H I) dissociates gradually between 0.1 and 0.3 F, slightly lysine rich histone (H II) dissociates as a narrow band between 0.35 and 0.5 F, and arginine rich histone (H III, H IV) dissociates gradually above 0.5 F NaClO₄.

The activity of the partially dissociated, native DNH in sustaining RNA synthesis, their mobility and their unusual heat denaturation and renaturation behavior are described. The two-step melting behavior of the material indicates that the histones are non-randomly distributed along the DNA, but the implications are that the uncovered regions are not of gene-size length.

Optimization and Control of Power Flow in Distribution Networks

Climate change is arguably the most critical issue facing our generation and the next. As we move towards a sustainable future, the grid is rapidly evolving with the integration of more and more renewable energy resources and the emergence of electric vehicles. In particular, large scale adoption of residential and commercial solar photovoltaics (PV) plants is completely changing the traditional slowly-varying unidirectional power flow nature of distribution systems. High share of intermittent renewables pose several technical challenges, including voltage and frequency control. But along with these challenges, renewable generators also bring with them millions of new DC-AC inverter controllers each year. These fast power electronic devices can provide an unprecedented opportunity to increase energy efficiency and improve power quality, if combined with well-designed inverter control algorithms. The main goal of this dissertation is to develop scalable power flow optimization and control methods that achieve system-wide efficiency, reliability, and robustness for power distribution networks of future with high penetration of distributed inverter-based renewable generators.

Proposed solutions to power flow control problems in the literature range from fully centralized to fully local ones. In this thesis, we will focus on the two ends of this spectrum. In the first half of this thesis (chapters 2 and 3), we seek optimal solutions to voltage control problems provided a centralized architecture with complete information. These solutions are particularly important for better understanding the overall system behavior and can serve as a benchmark to compare the performance of other control methods against. To this end, we first propose a branch flow model (BFM) for the analysis and optimization of radial and meshed networks. This model leads to a new approach to solve optimal power flow (OPF) problems using a two step relaxation procedure, which has proven to be both reliable and computationally efficient in dealing with the non-convexity of power flow equations in radial and weakly-meshed distribution networks. We will then apply the results to fast time- scale inverter var control problem and evaluate the performance on real-world circuits in Southern California Edison’s service territory.

The second half (chapters 4 and 5), however, is dedicated to study local control approaches, as they are the only options available for immediate implementation on today’s distribution networks that lack sufficient monitoring and communication infrastructure. In particular, we will follow a reverse and forward engineering approach to study the recently proposed piecewise linear volt/var control curves. It is the aim of this dissertation to tackle some key problems in these two areas and contribute by providing rigorous theoretical basis for future work.

A control of gas-vacuolate cyanobacteria

The cyanobacteria that cause problems in water supply are principally the colonial forms that are buoyed up by gas vesicles. The success of these organisms is due, in part, to their gas vesicles, which enable them to perform vertical migrations or to maintain themselves in the euphotic zone. The gas vesicles are also the root cause of the problems. In calm periods they cause the cyanobacteria to float to the water surface forming noxious scums, and they may prevent the colonies from sedimenting in water treatment plants. Gas vesicles are hollow, gas-filled structures; they are rigid but can be collapsed by the application of pressure. Their critical collapse pressure is influenced by their dimensions, which vary in different organisms. Gas vesicles are formed by the assembly of two types of protein, which determine their mechanical and physical properties. Methods for collapsing gas vesicles in natural populations of cyanobacteria will be considered. They may have application to the control of cyanobacteria in water supply.

A Real-Time Sliding Mode Control for a Wind Energy System Based on a Doubly Fed Induction Generator

In this paper, a real time sliding mode control scheme for a variable speed wind turbine that incorporates a doubly feed induction generator is described. In this design, the so-called vector control theory is applied, in order to simplify the system electrical equations. The proposed control scheme involves a low computational cost and therefore can be implemented in real-time applications using a low cost Digital Signal Processor (DSP). The stability analysis of the proposed sliding mode controller under disturbances and parameter uncertainties is provided using the Lyapunov stability theory. A new experimental platform has been designed and constructed in order to analyze the real-time performance of the proposed controller in a real system. Finally, the experimental validation carried out in the experimental platform shows; on the one hand that the proposed controller provides high-performance dynamic characteristics, and on the other hand that this scheme is robust with respect to the uncertainties that usually appear in the real systems.

Nonperturbative dynamical decoupling with random control

Parametric fluctuations or stochastic signals are introduced into the rectangular pulse sequence to investigate the feasibility of random dynamical decoupling. In a large parameter region, we find that the out-of-order control pulses work as well as the regular pulses for dynamical decoupling and dissipation suppression. Calculations and analysis are enabled by and based on a nonperturbative dynamical decoupling approach allowed by an exact quantum-state-diffusion equation. When the average frequency and duration of the pulse sequence take proper values, the random control sequence is robust, fault-tolerant, and insensitive to pulse strength deviations and interpulse temporal separation in the quasi-periodic sequence. This relaxes the operational requirements placed on quantum control devices to a great deal.

A Data Dropout Compensation Algorithm Based on the Iterative Learning Control Methodology for Discrete-Time Systems

This paper deals with the convergence of a remote iterative learning control system subject to data dropouts. The system is composed by a set of discrete-time multiple input-multiple output linear models, each one with its corresponding actuator device and its sensor. Each actuator applies the input signals vector to its corresponding model at the sampling instants and the sensor measures the output signals vector. The iterative learning law is processed in a controller located far away of the models so the control signals vector has to be transmitted from the controller to the actuators through transmission channels. Such a law uses the measurements of each model to generate the input vector to be applied to its subsequent model so the measurements of the models have to be transmitted from the sensors to the controller. All transmissions are subject to failures which are described as a binary sequence taking value 1 or 0. A compensation dropout technique is used to replace the lost data in the transmission processes. The convergence to zero of the errors between the output signals vector and a reference one is achieved as the number of models tends to infinity.

Propiedades básicas de materiales soporte y parámetros de control en biofiltración.

[ES]En la problemática medioambiental generada por la contaminación atmosférica hay tres aspectos que marcan las directrices de actuación institucional: la presión social, la legislación vigente y la tecnología disponible. En cuanto a este último aspecto, la biofiltración es una tecnología eficaz, asequible y sostenible basada en la actividad biodegradadora de microorganismos específicos adheridos a la superficie de un material soporte que constituye el lecho del biofiltro. La elección de un material soporte adecuado es de especial importancia para asegurar el correcto funcionamiento de los biofiltros. Esta decisión está basada en las propiedades intrínsecas del material que deben ser analizadas previamente a su uso. En este proyecto se ha seleccionado cuales son estas propiedades básicas a partir de una revisión bibliográfica, destacando la capacidad de retención de humedad, superficie específica, porosidad, y estabilidad física y química del material. En este trabajo, también se han fijado los parámetros de control que deben ser medidos de forma rutinaria en un biofiltro para asegurar la eficacia del tratamiento de descontaminación. En base a la información bibliográfica recopilada, se ha concluido que los parámetros básicos son pH, temperatura, contenido de humedad del lecho y pérdidas de carga. A nivel experimental, se han medido las pérdidas de carga generadas en biofiltros empacados con tres materiales soportes que son de especial interés para una investigación posterior a desarrollar por el grupo Biofiltración de la Universidad del País Vasco (UPV/EHU). Durante el período de arranque inicial de los tres biofiltros, las pérdidas de carga medidas fueron muy bajas en los tres casos, aunque algo superiores cuando la alimentación era en sentido ascendente frente al flujo descendente. Sin embargo, cuando se midieron las pérdidas de carga bajo condiciones de encharcamiento del lecho, que es una de las situaciones más problemáticas en un biofiltro, todos los soportes presentaron un aumento puntual de la pérdida de carga aunque la tendencia en los días posteriores fue claramente descendente, recuperando valores de operación habituales. La comparativa del comportamiento frente a las pérdidas de carga permitió seleccionar el soporte más idóneo de los tres analizados, aunque los otros dos podrían ser alternativas viables en caso de sustitución.

Alveolar nitric oxide and its role in pediatric asthma control assessment

Resumen Background: Nitric oxide can be measured at multiple flow rates to determine proximal (maximum airway nitric oxide flux; Jaw(NO)) and distal inflammation (alveolar nitric oxide concentration; CA(NO)). The main aim was to study the association among symptoms, lung function, proximal (maximum airway nitric oxide flux) and distal (alveolar nitric oxide concentration) airway inflammation in asthmatic children treated and not treated with inhaled glucocorticoids. Methods: A cross-sectional study with prospective data collection was carried out in a consecutive sample of girls and boys aged between 6 and 16 years with a medical diagnosis of asthma. Maximum airway nitric oxide flux and alveolar nitric oxide concentration were calculated according to the two-compartment model. In asthmatic patients, the asthma control questionnaire (CAN) was completed and forced spirometry was performed. In controls, differences between the sexes in alveolar nitric oxide concentration and maximum airway nitric oxide flux and their correlation with height were studied. The correlation among the fraction of exhaled NO at 50 ml/s (FENO50), CA(NO), Jaw(NO), forced expiratory volume in 1 second (FEV1) and the CAN questionnaire was measured and the degree of agreement regarding asthma control assessment was studied using Cohen's kappa. Results: We studied 162 children; 49 healthy (group 1), 23 asthmatic participants without treatment (group 2) and 80 asthmatic patients treated with inhaled corticosteroids (group 3). CA(NO) (ppb) was 2.2 (0.1-4.5), 3 (0.2-9.2) and 2.45 (0.1-24), respectively. Jaw(NO) (pl/s) was 516 (98.3-1470), 2356.67 (120-6110) and 1426 (156-11805), respectively. There was a strong association (r = 0.97) between FENO50 and Jaw(NO) and the degree of agreement was very good in group 2 and was good in group 3. There was no agreement or only slight agreement between the measures used to monitor asthma control (FEV1, CAN questionnaire, CA(NO) and Jaw(NO)). Conclusions: The results for CA(NO) and Jaw(NO) in controls were similar to those found in other reports. There was no agreement or only slight agreement among the three measure instruments analyzed to assess asthma control. In our sample, no additional information was provided by CA(NO) and Jaw(NO).