Made available in DSpace on 2016-08-17T14:53:22Z (GMT). No. of bitstreams: 1 Dissertacao Allan James.pdf: 3170694 bytes, checksum: 054a9e74e81a7c2099800246d0b6c530 (MD5) Previous issue date: 2012-09-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The union of methodologies for optimal control and dynamics programming has stimulated the development of algorithms for realization of discrete control systems of the type linear quadratic regulator (DLQR). The methodology is based on reinforcement learning methods based on temporal differences and approximate dynamic programming. The proposed method combines the approach of the value function by method RLS (recursive least squares) and approximate policy iteration schemes heuristic dynamic programming (HDP). The approach is directed to the assessment of convergence of the solution DLQR and the heuristic weighting matrices 􀜳 and 􀜴 of the utility function associated with DLQR. The investigation of convergence properties related to consistency, persistent excitation and polarization of the RLS estimator is performed. The methodology involved in a project achievements online DLQR controllers and is evaluated in a fourth order multivariable dynamic system. / A união das metodologias de controle ótimo e de programação dinâmica tem impulsionado o desenvolvimento de algoritmos para realizações de sistemas de controle discreto do tipo regulador linear quadrático (DLQR). A metodologia utilizada neste trabalho é fundamentada sobre métodos de aprendizagem por reforço baseados em diferenças temporais e programação dinâmica aproximada. O método proposto combina a aproximação da função valor através do método RLS (mínimos quadrados recursivos) e iteração de política aproximada em esquemas de programação dinâmica heurística (HDP). A abordagem é orientada para a avaliação da convergência da solução DLQR e para a sintonia heurística das matrizes de ponderação 􀜳 e 􀜴da função de utilidade associada ao DLQR. É realizada a investigação das propriedades de convergência relacionadas à consistência, excitação persistente e polarização do estimador RLS. A metodologia contempla realizações de projetos de forma online de controladores DLQR e é avaliada em um sistema dinâmico multivariável de quarta ordem.

La survie nette est un indicateur très utilisé en épidémiologie des cancers. Il s'agit de la survie que l'on observerait si la seule cause de mortalité était le cancer ; il est le seul indicateur épidémiologique utilisable à des fins de comparaisons de survie (entre périodes/pays) car il s'affranchit des éventuelles différences de mortalité dues aux autres causes que le cancer. Le premier objectif de notre travail était d'analyser les performances des différentes méthodes d'estimation de la survie nette sur données simulées ainsi que sur données réelles afin que les méthodes non biaisées soient reconnues scientifiquement et soient les seules à être utilisées par la suite. Nous avons ainsi démontré que deux approches étaient capables d'estimer sans biais la survie nette : l'approche non paramétrique de Pohar-Perme et l'approche reposant sur une modélisation multivariée du taux de mortalité en excès dû au cancer. Cette dernière approche impose une stratégie de construction difficile à mettre en place. Le deuxième objectif était de développer une boîte à outils composée de différents tests permettant de vérifier les différentes hypothèses faites lors de la construction d'un modèle de régression du taux de mortalité en excès. Ces hypothèses concernent habituellement la proportionnalité ou non de l'effet des covariables, leur forme fonctionnelle, ainsi que la fonction de lien utilisée. Le troisième objectif était une application épidémiologique qui visait à étudier l'impact des facteurs pronostiques, tel que le stade au diagnostic, sur la survie nette conditionnelle, en d'autres termes sur la dynamique du taux de mortalité en excès, après la survenue d'un cancer du côlon / Net survival is one of the most important indicators in cancer epidemiology. It is defined as the survival that would be observed if cancer were the only cause of death. This is the only one indicator allowing comparisons of cancer impact between countries or time periods because it is not influenced by death because of other causes. The first objective of this work was to compare the performance of several estimators of the net survival in a simulation study and then on real data in order to promote unbiased methods. Those methods are the non-parametric Pohar-Perme method and the parametric multivariable excess rate model. The latest one needs a model building strategy. The use of diagnostic procedures for model checking is an essential part of the modeling process. The second objective was to develop a tool box composed of diagnostic tools allowing to check hypothesis usually considered when constructing an excess mortality rate model, that is, the proportionality or not of the effect of covariates, their functional form and the link function. The third objective deals with the study of the impact of prognostic variables, such as stage at diagnosis, on conditional net survival, that is, on the dynamic of the excess hazard mortality after the diagnosis of colon cancer

This thesis presents the design and implementation of control strategies for building energy management systems (BEMS). The controllers considered include the multi PI-loop controllers, state-space designs, constrained input and output MIMO adaptive controllers, fuzzy logic solutions and genetic algorithm techniques. The control performances of the designs developed using the various methods based on aspects such as regulation errors squared, energy consumptions and the settling periods are investigated for different designs. The aim of the control strategy is to regulate the room temperature and the humidity to required comfort levels. In this study the building system under study is a 3 input/ 2 output system subject to external disturbances/effects. The three inputs are heating, cooling and humidification, and the 2 outputs are room air temperature and relative humidity. The external disturbances consist of climatic effects and other stochastic influences. The study is carried out within a simulation environment using the mathematical model of the test room at Loughborough University and the designed control solutions are verified through experimental trials using the full-scale BMS facility at the University of Bradford.

Having a accurate model of a system is essential for many applications today, especially those related to advanced process control. When executing a project often a lot of time is spent performing experiments on the real system to estimate a model. By designing higher quality experiments the time needed to estimate and identify these models can be reduced saving both resources and engineering efforts. This masters thesis investigates optimal input design to minimize the time needed to identify a linear time-invariant multivariable system fulfilling certain requirements on the model accuracy. Previous input designs mostly focused on sequential excitation but here the effects of using combined simultaneous and sequential excitation is investigated. The design is performed in simulations and evaluated in closed loop using a model predictive controller to further guarantee that the output constraints are not violated. The results indicate that there are many cases where using combined simultaneous and sequential excitation outperforms the previous methods. The effects of the color of the noise on the input design is investigated and the ability of different designs to estimate system delay is also studied. In addition it is shown how an iterative scheme can be used to guarantee that the accuracy requirements on the estimated model are met. / Att ha en god modell av ett system är viktigt för många applikationer idag, särskilt de som är relaterade till avancerad processtyrning. När man genomför ett projekt läggs ofta mycket tid på att utföra experiment på det verkliga systemet för att identifiera en modell. Genom att utforma experiment av hög kvalitet kan den tid som behövs för att identifiera dessa modeller minskas, vilket minimerar både processpåverkan och ingenjörsinsatsen. Denna masteruppsats undersöker metoder för optimal experimentdesign för att minimera tiden som behövs för att identifiera ett multivariabelt system där det finns krav på modellens noggrannhet. Tidigare metoder fokuserade mest på sekventiella experiment, men här undersöks effekterna av att använda en kombination av samtidiga och sekventiella experiment. Här används simuleringar som utvärderas i sluten loop med hjälp av en modellprediktiv regulator för att undvika att utsignalbegränsningarna inte överskrids. Resultatet indikerar att det finns många fall där användning av kombinerade samtidiga och sekventiella experiment överträffar tidigare metoder. Effekterna av färgat brus på ingångsdesignen undersöks och olika metoders förmåga att uppskatta systemfördröjning studeras också. Dessutom visas hur ett iterativt schema kan användas för att garantera att noggrannhetskraven på den uppskattade modellen uppfylls.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-06-23T20:34:27Z No. of bitstreams: 1 ErnestoFerreira.pdf: 1744167 bytes, checksum: c125c90e5eb2aab2618350567f88cb31 (MD5) / Made available in DSpace on 2017-06-23T20:34:27Z (GMT). No. of bitstreams: 1 ErnestoFerreira.pdf: 1744167 bytes, checksum: c125c90e5eb2aab2618350567f88cb31 (MD5) Previous issue date: 2016-03-08 / The development and the numerical stability analysis of a new adaptive critic algorithm to approximate the state-value function for online discrete linear quadratic regulator (DLQR) optimal control system design based on heuristic dynamic programming (HDP) are presented in this work. The proposed algorithm makes use of unitary transformations and QR decomposition methods to improve the online learning e-ciency in the critic network through the recursive least-squares (RLS) approach. The developed learning strategy provides computational performance improvements in terms of numerical stability and computational cost which aim at making possible the implementations in real time of optimal control design methodology based upon actor-critic reinforcement learning paradigms. The convergence behavior and numerical stability of the proposed online algorithm, called RLSµ-QR-HDP-DLQR, are evaluated by computational simulations in three Multiple-Input and Multiple-Output (MIMO) models, that represent the automatic pilot of an F-16 aircraft of third order, a fourth order RLC circuit with two input voltages and two controllable voltage levels, and a doubly-fed induction generator with six inputs and six outputs for wind energy conversion systems. / Neste trabalho, apresenta-se o desenvolvimento e a análise da estabilidade numérica de um novo algoritmo crítico adaptativo para aproximar a função valor de estado para o projeto do sistema de controle ótimo online, utilizando o regulador linear quadrático discreto (DLQR), com base em programação dinâmica heurística (HDP). O algoritmo proposto faz uso de transformações unitárias e métodos de decomposição QR para melhorar a e-ciência da aprendizagem online na rede crítica por meio da abordagem dos mínimos quadrados recursivos (RLS). A estratégia de aprendizagem desenvolvida fornece melhorias no desempenho computacional em termos de estabilidade numérica e custo computacional, que visam tornar possíveis as implementações em tempo real da metodologia do projeto de controle ótimo com base em paradigmas de aprendizado por reforço ator-crítico. O comportamento de convergência e estabilidade numérica do algoritmo online proposto, denominado RLSµ-QR-HDP-DLQR, são avaliados por meio de simulações computacionais em três modelos Múltiplas-Entradas e Múltiplas-Saídas (MIMO), que representam o piloto automático de uma aeronave F-16 de terceira ordem, um circuito de quarta ordem RLC com duas tensões de entrada e dois níveis de tensão controláveis, e um gerador de indução duplamente alimentados com seis entradas e seis saídas para sistemas de conversão de energia eólica.

Submitted by Maria Aparecida (cidazen@gmail.com) on 2017-08-30T15:33:12Z No. of bitstreams: 1 Patricia Helena.pdf: 11110405 bytes, checksum: ca1f067231658f897d84b86181dbf1b9 (MD5) / Made available in DSpace on 2017-08-30T15:33:12Z (GMT). No. of bitstreams: 1 Patricia Helena.pdf: 11110405 bytes, checksum: ca1f067231658f897d84b86181dbf1b9 (MD5) Previous issue date: 2014-07-24 / In this thesis a proposal of an uni ed approach of dynamic programming, reinforcement learning and function approximation theories aiming at the development of methods and algorithms for design of optimal control systems is presented. This approach is presented in the approximate dynamic programming context that allows approximating the optimal feedback solution as to reduce the computational complexity associated to the conventional dynamic programming methods for optimal control of multivariable systems. Speci cally, in the state and action dependent heuristic dynamic programming framework, this proposal is oriented for the development of online approximated solutions, numerically stable, of the Riccati-type Hamilton-Jacobi-Bellman equation associated to the discrete linear quadratic regulator problem which is based on a formulation that combines value function estimates by means of a RLS (Recursive Least-Squares) structure, temporal di erences and policy improvements. The development of the proposed methodologies, in this work, is focused mainly on the UDU T factorization that is inserted in this framework to improve the RLS estimation process of optimal decision policies of the discrete linear quadratic regulator, by circumventing convergence and numerical stability problems related to the covariance matrix ill-conditioning of the RLS approach. / Apresenta-se nesta tese uma proposta de uma abordagem uni cada de teorias de programação dinâmica, aprendizagem por reforço e aproximação de função que tem por objetivo o desenvolvimento de métodos e algoritmos para projeto online de sistemas de controle ótimo. Esta abordagem é apresentada no contexto de programação dinâmica aproximada que permite aproximar a solução de realimentação ótima de modo a reduzir a complexidade computacional associada com métodos convencionais de programação dinâmica para controle ótimo de sistemas multivariáveis. Especi camente, no quadro de programação dinâmica heurística e programação dinâmica heurística dependente de ação, esta proposta é orientada para o desenvolvimento de soluções aproximadas online, numericamente estáveis, da equação de Hamilton-Jacobi-Bellman do tipo Riccati associada ao problema do regulador linear quadrático discreto que tem por base uma formulação que combina estimativas da função valor por meio de uma estrutura RLS (do inglês Recursive Least-Squares), diferenças temporais e melhorias de política. O desenvolvimento das metodologias propostas, neste trabalho, tem seu foco principal voltado para a fatoração UDU T que é inserida neste quadro para melhorar o processo de estimação RLS de políticas de decisão ótimas do regulador linear quadrá- tico discreto, contornando-se problemas de convergência e estabilidade numérica relacionados com o mal condicionamento da matriz de covariância da abordagem RLS.

In advanced process control, the Model Predictive Control (MPC) may be considered the most important innovation in recent years and the standard tool for industrial applications due to the fact that it keeps the plant operating in the constraints more profitable. However, like every control algorithm, the MPC after some time in operation rarely works as originally designed. Thus, to preserve the benefits of MPC systems for a long period of time, their performance needs to be monitored and evaluated during the operation. This task require the presence of reliable and effective tools to detect when the controller performance is below of the desirable, to define the need, or not, of recommissioning the system. Thus, the objective of this work is development of techniques for monitoring and evaluating the performance of multivariable predictive controllers, being developed two new tools: LQG benchmark Modified and IHMC benchmark. The results obtained from numerical simulations were satisfactory and consistent with the technical literature applied in the developments of the evaluators, which were used in the monitoring of the control system MPC of the oil-water-gas three-phase separation process, offering an appropriate solution and providing subsidies for implementations in real industrial systems. / Em controle avançado de processos, o controlador preditivo ou MPC (Model Predictive Control) pode ser considerado como a mais importante inovação dos últimos anos e a ferramenta padrão para aplicações industriais, devido ao fato do MPC manter a planta operando dentro das suas restrições de forma mais lucrativa. Entretanto, como todo algoritmo de controle, o MPC depois de algum tempo em operação dificilmente funciona como quando fora inicialmente projetado. Desta forma, com o objetivo de manter os benefícios dos sistemas MPC por um longo período de tempo, seu desempenho precisa ser monitorado e avaliado durante a operação. Esta tarefa requer a presença de ferramentas efetivas e confiáveis para detectar quando o desempenho do controlador estiver abaixo do desejável, para definir a necessidade, ou não, de um recomissionamento do sistema. Destarte, aborda-se neste trabalho o desenvolvimento de técnicas para monitoramento e avaliação de desempenho de controladores preditivos multivariáveis, sendo desenvolvidas duas novas ferramentas: LQG benchmark Modificado e IHMC benchmark. Os resultados obtidos a partir de simulações numéricas foram satisfatórios e coerentes com a literatura técnica aplicada no desenvolvimento dos avaliadores, os quais foram utilizados no monitoramento do sistema de controle MPC do processo de separação trifásica água-óleo-gás, oferecendo assim uma solução apropriada e fornecendo subsídios para implementações em sistemas industrias reais.

Les systèmes réels sont généralement de nature non-linéaire, et leurs modélisations etsurveillance restent une tâche difficile à accomplir. Néanmoins, avec les progrès technologiqueson dispose maintenant d'un atout de taille sur ces systèmes qui est les données.Ce travail présente une technique de diagnostic de défaut et de modélisation basée en grandepartie sur la méthode d'apprentissage automatique « Les Machines à Vecteurs de Support,SVM » qui est basée sur les données. La méthodologie proposée est appliquée à différentessystèmes multivariables et non linéaires, à savoir : un procédé de traitement des eaux usées, unsystème éolien et un réacteur chimique parfaitement agité.L'objectif de cette thèse de doctorat est d'examiner la possibilité d'extraire le maximumd'information à partir de données afin de surveiller efficacement le comportement de systèmesréels et de détecter rapidement tout défaut qui peut compromettre leur bon fonctionnement. Lamême méthode est utilisée pour la modélisation des différents systèmes. Plusieurs défis ont étérelevés tels que la complexité du comportement des systèmes, le grand nombre de mesuresvariant à différentes échelles de temps, la présence de bruit et les perturbations. Une méthodegénérique de diagnostic de défauts est proposée par la génération des caractéristiques de chaquedéfaut suivie d’une étape d'évaluation de ces caractéristiques avec une amélioration du transfertde connaissances en modélisation.Dans cette thèse ont a démontré l'utilité de l'outil Machines à Vecteurs de Support, enclassification par la construction de modèles de décision SVM dédiés à l'évaluation descaractéristiques de défaut, et aussi en tant qu'estimateur non linéaire/ou pour la modélisation parl'utilisation des machines à vecteurs de support dédiés pour la régression (SVR).La combinaison de SVM et d’une méthode basée sur le modèle "observateur" a été aussi étudiéeet a été nécessaire dans certains cas pour garantir un bon diagnostic de défauts. / Real systems are usually nonlinear and their modeling and monitoring remains adifficult task. However, with advances in technology and the availability of big amounts of data,we have a facility to operate these systems.This work presents a methodology for fault diagnosis and modeling which is in large part basedon the method of Support Vector Machines (SVM) which data-based. The proposedmethodology is applied to various nonlinear multivariable systems including: wastewatertreatment processes, wind turbines and stirred tank reactors.The objective of this PhD is to examine the possibility of extracting the maximum of informationfrom data to effectively monitor the behavior of real systems and rapidly detect any faults whichmay impair their proper functioning. The same method is used for modeling the differentsystems. Several challenges were identified and surmounted such as the complexity of thesystem behavior, large amount of data varying at different time scales, the presence of noise anddisturbances. A generic method of fault diagnosis is proposed for the generation of the faultcharacteristics followed by an evaluation of these characteristics as well as an improved transferof knowledge in modeling.In this thesis the usefulness of the tool Support Vector Machines in Classification has beendemonstrated by the construction of decision models dedicated to evaluating the characteristicsof faults, and also its usefulness for modeling/ or as estimator for the nonlinear systems usingsupport vector machines dedicated for regression (SVR).The combination of SVM and a method based on models “observer” was also considered andwas found to be interesting in some cases to ensure proper fault diagnosis.

We consider the problem of Adaptive Control of finite-dimensional, stable, Linear Time Invariant (LTI) plants. Amongst such plants, the subclass regarding which an upper bound on the order is not known or which are known to be nonminimum phase (zeros in the unstable region) pose formidable problems in their own right. On one hand, if an upper bound on the order of the plant is not known, adaptive control usually involves some form of order estimation. On the other hand, when the plant is allowed to be either minimum phase or nonminimum phase, the adaptive control problem, as is well-known, becomes considerably-less tractable. In this study, the class of unknown plants considered is such that no information is available on the upper bound of the plant order and, further, the plant may be either minimum phase or nonminimum phase. Albeit known to be stable, such plants throw myriads of challenges in the context of adaptive control. Adaptive control involving such plants has been addressed [79] in a Model Reference Adaptive Control (MRAC) framework. There, the inputs and outputs of the unknown plant are the only quantities available by measurement in terms of which any form of modeling of the unknown plant may be made. Inputs to the reference model have been taken from certain restricted classes of bounded signals. In particular, the three classes of inputs considered are piecewise continuous bounded functions which asymptotically approach • a nonzero constant, • a sinusoid, and • a sinusoid with a nonzero shift. Moreover, the control law is such that adaptation is carried out at specific instants separated by progressively larger intervals of time. The schemes there have been proved to be e-optimal in the sense of a suitably formulated optimality criterion. If, however, the reference model inputs be extended to the class of piecewise continuous bounded functions, that would compound the complexity of the adaptive control problem. Only one attempt [78] in adaptive control in such a setting has come to our notice. The problem there has been tackled by an application of the theory of Pade Approximations to time moments of an LTI system. Based on a time moments estimation procedure, a simple adaptive scheme for Single-Input Single-Output (SISO) systems with only a cascade compensator has been reported. The first chapter is essentially meant to ensure that the problem we seek to address in the field of adaptive control indeed has scope for research. Having defined Adaptive Control, we selectively scan through the literature on LTI systems, with focus on MRAC. We look out in particular for studies involving plants of which not much is known regarding their order and systems which are possibly nonminimum phase. We found no evidence to assert that the problem of adaptive control of stable LTI systems, not necessarily minimum phase and of unknown upper bound on the order, was explored enough, save two attempts involving SISO systems. Taking absence of evidence (of in-depth study) for evidence of absence, we make a case for the problem and formally state it. We preview the thesis. We set two targets before us in Chapter 2. The first is to review one of the existing procedures attacking the problem we intend to address. Since the approach is based on the notion of time moments of an LTI system, and as we are to employ Pade Approximations as a tool, we uncover these concepts to the limited extent of our requirement. The adaptive procedure, Plant Command Modifier Scheme (PCMS) [78], for SISO plants is reported in some detail. It stands supported on an algorithm specially designed to estimate the time moments of an LTI system given no more than its input and output. Model following there has been sought to be achieved by matching the first few time moments of the reference model by the corresponding ones of the overall compensated plant. The plant time moment estimates have been taken to represent the unknown plant. The second of the goals is to analyze PCMS critically so that it may serve as a forerunner to our work. We conclude the chapter after accomplishing these goals. In Chapter 3, we devise a time moment estimator for SISO systems from a perspective which is conceptually equivalent to, yet functionally different from, that appropriated in [78]. It is a recipe to obtain estimates of time moments of a system by computing time moment estimates of system input and output signals measured up to current time. Pade approximations come by handy for this purpose. The lacunae exposed by a critical examination of PCMS in Chapter 2 guide us to progressively refine the estimator. Infirmities in the control part of PCMS too have come to light on our probing into it. A few of these will be fixed by way of fabricating two exclusively cascade compensators. We encounter some more issues, traceable to the estimator, which need redressal. Instead of directly fine-tuning the estimator itself, as is the norm, we propose the idea of 'estimating' the lopsidedness of the estimator by using it on the fully known reference model. This will enable us to effect corrections and obtain admissible estimates. Next, we explore the possibility of incorporating feedback compensation in addition to the existing cascade compensation. With output error minimization in mind, we come up with three schemes in this category. In the process, we anticipate the risk of instability due to feedback and handle it by means of an instability preventer with an inbuilt instability detector. Extensive simulations with minimum and rionminimum phase unknown plants employing the various schemes proposed are presented. A systematic study of simulation results reveals a dyad of hierarchies of progressively enhanced overall performance. One is in the sequence of the proposed schemes and the other in going for matching more and more moments. Based on our experiments we pick one of the feedback schemes as the best. Chapter 4 is conceived of as a bridge between SISO and multivariable systems. A transition from SISO to Multi-Input Multi-Output (MIMO) adaptive control is not a proposition confined to the mathematics of dimension-enhancement. A descent from the MIMO to the SISO case is expected to be relatively simple, though. So to transit as smoothly and gracefully as possible, some issues have to be placed in perspective before exploring multivariable systems. We succinctly debate on the efforts in pursuit of the exact vis-a-vis the accurate, and their implications. We then set some notations and formulate certain results which serve to unify and simplify the development in the subsequent three chapters. We list a few standard results from matrix theory which are to be of frequent use in handling multivariable systems. We derive control laws for Single-Input Multi-Output (SIMO) systems in Chapter 5. Expectedly, SIMO systems display traits of observability and uncontrollability. Results of illustrative simulations are furnished. In Chapter 6, we formulate control laws for Multi-Input Single-Output (MISO) systems. Characteristics of unobservability and controllability stand out there. We present case studies. Before actually setting foot onto MIMO systems, we venture to conjecture on what to expect there. We work out all the cascade and feedback adaptive schemes for square and nonsquare MIMO systems in Chapter 7. We show that MIMO laws when projected to MISO, SIMO and SISO cases agree with the corresponding laws in the respective cases. Thus the generality of our treatment of MIMO systems over other multivariable and scalar systems is established. We report simulations of instances depicting satisfactory performance and highlight the limitations of the schemes in tackling the family of plants of unknown upper bound on the order and possibly nonminimum phase. This forms the culmination of our exercise which took off from the reported work involving SISO systems [78]. Up to the end of the 7th chapter, we are in pursuit of solutions for the problem as general as in §1.4. For SISO systems, with input restrictions, the problem has been addressed in [79]. The laws proposed there carry out adaptation only at certain discrete instants; with respect to a suitably chosen cost, the final laws are proved to be e>optimal. In Chapter 8, aided by initial suboptimal control laws, we finally devise two algorithms with continuous-time adaptation and prove their optimality. Simulations with minimum and nonminimum phase plants reveal the effectiveness of the various laws, besides throwing light on the bootstrapping and auto-rectifying features of the algorithms. In the tail-piece, we summarize the work and wind up matters reserved for later deliberation. As we critically review the present work, we decant the take-home message. A short note on applications followed by some loud thinking as a spin-off of this report will take us to finis.