Background Mathematical modeling combined with prior knowledge of the pharmacokinetics of the liver specific contrast agent Gd-EOB-DTPA has the potential to extract more information from Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) data than previously possible. The ultimate goal of that work is to create a liver model that can describe DCE-MRI data well enough to be used as a diagnostic tool in liver function evaluation. Thus far this goal has not been fully reached and there is still some work to be done in this area. In this thesis, an already existing liver model will be implemented in the software Wolfram SystemModeler (WSM), the corresponding modeling framework will be further developed to better handle the temporally irregular sampling of DCE-MRI data and finally an attempt will be made to determine an optimal sampling design in terms of when and how often to collect images. In addition to these original goals, the work done during this project revealed two more issues that needed to be dealt with. Firstly, new standard deviation (SD) estimation methods regarding non-averaged DCE-MRI data were required in order to statistically evaluate the models. Secondly, the original model’s poor capability of describing the early dynamics of the system led to the creation of an additional liver model in attempt to model the bolus effect. Results The model was successfully implemented in WSM whereafter regional optimization was implemented as an attempt to handle clustered data. Tests on the available data did not result in any substantial difference in optimization outcome, but since the analyses were performed on only three patient data sets this is not enough to disregard the method. As a means of determining optimal sampling times, the determinant of the inverse Fisher Information Matrix was minimized, which revealed that frequent sampling is most important during the initial phase (~50-300 s post injection) and at the very end (~1500-1800 s). Three new means of estimating the SD were proposed. Of these three, a spatio-temporal SD was deemed most reasonable under the current circumstances. If a better initial fit is achieved, yet another method of estimating the variance as an optimization parameter might be implemented.    As a result of the new standard deviation the model failed to be statistically accepted during optimizations. The additional model that was created to include the bolus effect, and therefore be better able to fit the initial phase data, was also rejected. Conclusions The value of regional optimization is uncertain at this time and additional tests must be made on a large number of patient data sets in order to determine its value. The Fisher Information Matrix will be of great use in determining when and how often to sample once the model has achieved a more acceptable model fit in both the early and the late phase of the system. Even though the indications that it is important to sample densely in the early phase is rather intuitive due to a poor model fit in that region, the analyses also revealed that the final observations have a relatively high impact on the model prediction error. This was not previously known. Hence, an important measurement of how suitable the sampling design is in terms of the resulting model accuracy has been suggested. The original model was rejected due to its inability to fit the data during the early phase. This poor initial fit could not be improved enough by modelling the bolus effect and so the new implementation of the model was also rejected. Recommendations have been made in this thesis that might assist in the further development the liver model so that it can describe the true physiology and behaviour of the system in all phases. Such recommendations include, but are not limited to, the addition of an extra blood plasma compartment, a more thorough modelling of the spleen’s uptake of the contrast agent and a separation of certain differing signals that are now averaged.

Applications of the existing steady-state plant-wide optimization and the single-scale fast-rate dynamic optimization strategies to an integrated plant with material recycle have been impeded by several factors. While the steady-state optimization formulation is very simple, the very long transient dynamics of an integrated plant have limited the optimizers execution rate to be extremely low, yielding a suboptimal performance. In contrast, performing dynamic plant-wide optimization at the same rate as local controllers requires exorbitant on-line computational load and may increase the sensitivity to high-frequency dynamics that are irrelevant to the plant-level interactions, which are slow-scale in nature. This thesis proposes a novel multi-scale dynamic optimization and control strategy suitable for an integrated plant. The dynamic plant-wide optimizer in this framework executes at a slow rate to track the slow-scale plant-wide interactions and economics, while leaving the local controllers to handle fast changes related to the local units. Moreover, this slow execution rate demands less computational and modeling requirement than the fast-rate optimizer. An important issue of this method is obtaining a suitable dynamic model when first-principles are unavailable. The difficulties in the system identification process are designing proper input signal to excite this ill-conditioned system and handling the lack of slow-scale dynamic data when the plant experiment cannot be conducted for a long time compared to the settling time. This work presents a grey-box modeling method to incorporate steady-state information to improve the model prediction accuracy. A case study of an integrated plant example is presented to address limitations of the nonlinear model predictive control (NMPC) in terms of the on-line computation and its inability to handle stochastic uncertainties. Then, the approximate dynamic programming (ADP) framework is investigated. This method computes an optimal operating policy under uncertainties off-line. Then, the on-line multi-stage optimization can be transformed into a single-stage problem, thus reducing the real-time computational effort drastically. However, the existing ADP framework is not suitable for an integrated plant with high dimensional state and action space. In this study, we combine several techniques with ADP to apply nonlinear optimal control to the integrated plant example and show its efficacy over NMPC.

This thesis presents an integrated framework for online obstacle avoidance of rotary-wing unmanned aerial vehicles (UAVs), which can provide UAVs an obstacle field navigation capability in a partially or completely unknown obstacle-rich environment. The framework is composed of a LIDAR interface, a local obstacle grid generation, a receding horizon (RH) trajectory optimizer, a global shortest path search algorithm, and a climb rate limit detection logic. The key feature of the framework is the use of an optimization-based trajectory generation in which the obstacle avoidance problem is formulated as a nonlinear trajectory optimization problem with state and input constraints over the finite range of the sensor. This local trajectory optimization is combined with a global path search algorithm which provides a useful initial guess to the nonlinear optimization solver. Optimization is the natural process of finding the best trajectory that is dynamically feasible, safe within the vehicle's flight envelope, and collision-free at the same time. The optimal trajectory is continuously updated in real time by the numerical optimization solver, Nonlinear Trajectory Generation (NTG), which is a direct solver based on the spline approximation of trajectory for dynamically flat systems. In fact, the overall approach of this thesis to finding the optimal trajectory is similar to the model predictive control (MPC) or the receding horizon control (RHC), except that this thesis followed a two-layer design; thus, the optimal solution works as a guidance command to be followed by the controller of the vehicle. The framework is implemented in a real-time simulation environment, the Georgia Tech UAV Simulation Tool (GUST), and integrated in the onboard software of the rotary-wing UAV test-bed at Georgia Tech. Initially, the 2D vertical avoidance capability of real obstacles was tested in flight. Then the flight test evaluations were extended to the benchmark tests for 3D avoidance capability over the virtual obstacles, and finally it was demonstrated on real obstacles located at the McKenna MOUT site in Fort Benning, Georgia. Simulations and flight test evaluations demonstrate the feasibility of the developed framework for UAV applications involving low-altitude flight in an urban area.

Real-Time Optimization (RTO) is a family of techniques that pursue to improve the performance of chemical processes. As general scheme, the method reevaluates the process conditions in a frequent basis and tries to adjust some selected variables, taking into account the plant state, actual operational constraints and optimization objectives. Several RTO approaches have born from the academy research and industrial practices, at the same time that more applications have been implemented in real facilities. Between the main motivations to apply RTO are the dynamic of markets, the seek for quality in the process results and environmental sustainability. That is why the interest on deeply understand the phases and steps involved in an RTO application has increased in recent years. Nevertheless, the fact that most of the existing RTO systems have been developed by commercial organizations makes it difficult to meet that understanding. This work studies the nature of RTO systems from a software point of view. Software requirements for a generic system are identied. Based on that, a software architecture is proposed that could be adapted for specfic cases. Benefits of the designed architecture are listed. At the same time, the work proposes a new approach to implement that architecture as a Multi-Agent System (MAS). Two RTO system prototypes were developed then, one for a well-know academic case study and the other oriented to be used in a real unit. The benefits of the MAS approach and the architecture, for researching on the RTO field and implementation on real plants, are analyzed in the text. A sub-product of the development, a software framework covering main concepts from the RTO ontology, is proposed as well. As the framework was designed to be generic, it can be used in new applications development and extended to very specific scenarios. / Otimização em Tempo Real (OTR) é uma família de técnicas que buscam melhorar o desempenho dos processos químicos. Como esquema geral, o método reavalia frequentemente as condições do processo e tenta ajustar algumas variáveis selecionadas, levando em considera ção o estado da planta, restrições operacionais e os objetivos da otimização. Várias abordagens para OTR t^em surgido da pesquisa acadêmica e das práticas industriais, ao mesmo tempo em que mais aplicações têm sido implementadas em plantas reais. As principais motivações para aplicar OTR são: a dinâmica dos mercados, a busca de qualidade nos resultados dos processos e a sustentabilidade ambiental. É por isso que o interesse em entender as fases e etapas envolvidas em uma aplicação OTR cresceu nos últimos anos. No entanto, o fato de que a maioria dos sistemas OTR em operação foram desenvolvidos por organizações comerciais dificulta o caminho para chegar nesse entendimento. Este trabalho analisa a natureza dos sistemas OTR desde o ponto de vista do software. Os requerimentos para um sistema genérico são levantados. Baseado nisso, é proposta uma arquitetura de software que pode ser adaptada para casos específicos. Os benefícios da arquitetura projetada foram listados. Ao mesmo tempo, o trabalho propõe uma nova abordagem para implementar essa arquitetura: Sistema Multi-Agentes (SMA). Dois protótipos de sistema OTR foram desenvolvidos. O primeiro aplicado num estudo de caso bem conhecido na literatura acadêmica. O segundo voltado para ser usado em uma unidade industrial. Os benefícios da abordagem SMA e da arquitetura, tanto na pesquisa relacionada com OTR, quanto na implementação em plantas reais, são analisados no texto. Um arcabouço de software que abrange os principais conceitos da ontologia OTR é proposto como resultado derivado do desenvolvimento. O arcabouço foi projetado para ser genérico, possibilitando seu uso no desenvolvimento de novas aplicações OTR e sua extensão a cenários muito específicos.

The increasing economic competition drives the industry to implement tools that improve their processes efficiencies. The process automation is one of these tools, and the Real Time Optimization (RTO) is an automation methodology that considers economic aspects to update the process control in accordance with market prices and disturbances. Basically, RTO uses a steady-state phenomenological model to predict the process behavior, and then, optimizes an economic objective function subject to this model. Although largely implemented in industry, there is not a general agreement about the benefits of implementing RTO due to some limitations discussed in the present work: structural plant/model mismatch, identifiability issues and low frequency of set points update. Some alternative RTO approaches have been proposed in literature to handle the problem of structural plant/model mismatch. However, there is not a sensible comparison evaluating the scope and limitations of these RTO approaches under different aspects. For this reason, the classical two-step method is compared to more recently derivative-based methods (Modifier Adaptation, Integrated System Optimization and Parameter estimation, and Sufficient Conditions of Feasibility and Optimality) using a Monte Carlo methodology. The results of this comparison show that the classical RTO method is consistent, providing a model flexible enough to represent the process topology, a parameter estimation method appropriate to handle measurement noise characteristics and a method to improve the sample information quality. At each iteration, the RTO methodology updates some key parameter of the model, where it is possible to observe identifiability issues caused by lack of measurements and measurement noise, resulting in bad prediction ability. Therefore, four different parameter estimation approaches (Rotational Discrimination, Automatic Selection and Parameter estimation, Reparametrization via Differential Geometry and classical nonlinear Least Square) are evaluated with respect to their prediction accuracy, robustness and speed. The results show that the Rotational Discrimination method is the most suitable to be implemented in a RTO framework, since it requires less a priori information, it is simple to be implemented and avoid the overfitting caused by the Least Square method. The third RTO drawback discussed in the present thesis is the low frequency of set points update, this problem increases the period in which the process operates at suboptimum conditions. An alternative to handle this problem is proposed in this thesis, by integrating the classic RTO and Self-Optimizing control (SOC) using a new Model Predictive Control strategy. The new approach demonstrates that it is possible to reduce the problem of low frequency of set points updates, improving the economic performance. Finally, the practical aspects of the RTO implementation are carried out in an industrial case study, a Vapor Recompression Distillation (VRD) process located in Paulínea refinery from Petrobras. The conclusions of this study suggest that the model parameters are successfully estimated by the Rotational Discrimination method; the RTO is able to improve the process profit in about 3%, equivalent to 2 million dollars per year; and the integration of SOC and RTO may be an interesting control alternative for the VRD process. / O aumento da concorrência motiva a indústria a implementar ferramentas que melhorem a eficiência de seus processos. A automação é uma dessas ferramentas, e o Real Time Optimization (RTO) ou Otimização em Tempo Real, é uma metodologia de automação que considera aspectos econômicos e restrições de processos e equipamentos para atualizar o controle do processo, de acordo com preços de mercado e distúrbios. Basicamente, o RTO usa um modelo fenomenológico em estado estacionário para predizer o comportamento do processo, em seguida, otimiza uma função objetivo econômica sujeita a esse modelo. Embora amplamente utilizado na indústria, não há ainda um consenso geral sobre os benefícios da implementação do RTO, devido a algumas limitações discutidas no presente trabalho: incompatibilidade estrutural entre planta e modelo, problemas de identificabilidade e baixa frequência de atualização dos set points. Algumas metodologias de RTO foram propostas na literatura para lidar com o problema da incompatibilidade entre planta e modelo. No entanto, não há uma comparação que avalie a abrangência e as limitações destas diversas abordagens de RTO, sob diferentes aspectos. Por esta razão, o método clássico de RTO é comparado com metodologias mais recentes, baseadas em derivadas (Modifier Adaptation, Integrated System Optimization and Parameter estimation, and Sufficient Conditions of Feasibility and Optimality), utilizando-se o método de Monte Carlo. Os resultados desta comparação mostram que o método clássico de RTO é coerente, desde que seja proporcionado um modelo suficientemente flexível para se representar a topologia do processo, um método de estimação de parâmetros apropriado para lidar com características de ruído de medição e um método para melhorar a qualidade da informação da amostra. Já os problemas de identificabilidade podem ser observados a cada iteração de RTO, quando o método atualiza alguns parâmetros-chave do modelo, o que é causado principalmente pela ausência de medidas e ruídos. Por esse motivo, quatro abordagens de estimação de parâmetros (Discriminação Rotacional, Seleção Automática e Estimação de Parâmetros, Reparametrização via Geometria Diferencial e o clássico Mínimos Quadrados não-lineares) são avaliados em relação à sua capacidade de predição, robustez e velocidade. Os resultados revelam que o método de Discriminação Rotacional é o mais adequado para ser implementado em um ciclo de RTO, já que requer menos informação a priori, é simples de ser implementado e evita o sobreajuste observado no método de Mínimos Quadrados. A terceira desvantagem associada ao RTO é a baixa frequência de atualização dos set points, o que aumenta o período em que o processo opera em condições subotimas. Uma alternativa para lidar com este problema é proposta no presente trabalho, integrando-se o RTO e o Self-Optimizing Control (SOC) através de um novo algoritmo de Model Predictive Control (MPC). Os resultados obtidos com a nova abordagem demonstram que é possível reduzir o problema da baixa frequência de atualização dos set points, melhorando o desempenho econômico do processo. Por fim, os aspectos práticos da implementação do RTO são discutidos em um estudo de caso industrial, que trata de um processo de destilação com bomba de calor, localizado na Refinaria de Paulínia (REPLAN - Petrobras). Os resultados deste estudo sugerem que os parâmetros do modelo são estimados com sucesso pelo método de Discriminação Rotacional; que o RTO é capaz de aumentar o lucro do processo em cerca de 3%, o equivalente a 2 milhões de dólares por ano; e que a integração entre SOC e RTO pode ser uma alternativa interessante para o controle deste processo de destilação.

Both major open-source compilers, GCC and LLVM, have a mature link-time optimization framework usable on most current programs. They are however not free from many performance issues, which prevent them to perform certain analyses and optimizations. We analyze bottlenecks and identify multiple places for improvement, focusing on improving interprocedural points-to analysis. For this purpose, we design a new data structure derived from Bloom filters and use it to significantly improve performance and memory consumption of link-time optimization. Powered by TCPDF (www.tcpdf.org)

The control and optimization of chemical plants is a major area of research as it has the potential to improve both economic output and plant safety. It is often prudent to separate control and optimization tasks of varying complexities and time scales, creating a hierarchical control structure. Within this structure, it is beneficial for one control layer to be able to account for the effects of other layers. A clear example of this, and the basis of this work, is closed-loop dynamic real-time optimization (CL-DRTO), in which an economic optimization method considers both the plant behavior and the effects of an underlying model predictive controller (MPC). This technique can be expanded on to allow its use and methods to be employed in a greater diversity of applications, particularly unstable and uncertain plant environments. First, this work seeks to improve on existing robust MPC techniques, which incorporate plant uncertainty via direct multi-scenario modelling, by also including future MPC behavior through the use of the CL modelling technique of CL-DRTO. This allows the CL robust MPC to account for how future MPC executions will be affected by uncertain plant behavior. Second, Lyapunov MPC (LMPC) is a generally nonconvex technique which focuses on effective control of plants which exhibit open-loop unstable behavior. A new convex LMPC formulation is presented here which can be readily embedded into a CL-DRTO scheme. Next, uncertainty handling is incorporated directly into a CL-DRTO via a robust multi-scenario method to allow for the economic optimization to take uncertain plant behavior into account while also modelling MPC behavior under plant uncertainty. Finally, the robust CL-DRTO method is computationally expensive, so a decomposition method which separates the robust CL-DRTO into its respective scenario subproblems is developed to improve computation time, especially for large optimization problems. / Thesis / Doctor of Philosophy (PhD) / It is common for control and optimization of chemical plants to be performed in a multi-layered hierarchy. The ability to predict the behavior of other layers or the future behavior of the same layer can improve overall plant performance. This thesis presents optimization and control frameworks which use this concept to more effectively control and economically optimize chemical plants which are subject to uncertain behavior or instability. The strategy is shown, in a series of simulated case studies, to effectively control chemical plants with uncertain behavior, control and optimize unstable plant systems, and economically optimize uncertain chemical plants. One of the drawbacks of these strategies is the relatively large computation time required to solve the optimization problems. Therefore, for uncertain systems, the problem is separated into smaller pieces which are then coordinated towards a single solution. This results in reduced computation time.

Inom den automatiserade bearbetande metallindustrin är ett sätt att effektivisera produktionen, och följaktligen stärka konkurrenskraft, att cykeltidsoptimera CNC-maskiner. I avsikt att denna typ av optimeringsarbeten inte ska ske ostrukturerat, utan med systematik, syftar detta arbete till att arbeta fram ett förslag på en projektmetod avsedd för cykeltidsoptimering av CNC-maskiner. Vidare har intervjuer, arbetsuppföljning och observationer vid Scania CV ABs vevaxelproduktion tillsammans med relaterade litterära studier analyserats och filtrerats; och sedan använts för att tillhandahålla svar på arbetets frågeställningar: (1) Kan onödiga aktiviteter i CNC-cykler identifieras och kan dessa i sådant fall minimeras eller uteslutas? (2) Hur kan en projektmetod vara uppbyggd och vad kan den uppbyggnaden innefatta? Åtta stycken täckande aktiviteter i CNC-cyklar med optimeringspotential noterades. Där innefattas exempelvis väntetider, långsamma och onödiga sekvenser samt aktiviteter som kanske parallellt men ej gör det. Även praktisk arbetsgång för cykeltidsoptimering av CNC-maskiner och metoder för annan optimering identifierades. Sammanvägningen av de empiriska resultaten och de relaterade studierna visade att fasindelning och innehållet i en projektmetod kan skilja beroende på om metoden är generell eller specifikt anpassad. Efter att ha arbetat samtliga empiriska resultat och relaterade studier konstruerades ett förslag på projektmetod. Metoden har fem faser (potential, initiering, planering, utförande och avslutning) och presenteras i ett användargränssnitt. Gränssnittet tydliggör vad som ska utföras i respektive fas och hur. I ett utökat arbete kan gränssnittet utvecklas och optimeringsaspekter som kräver mer omfattande lösningar kartläggas samt definieras kopplat till hur de bör hanteras. / Within the automated metalworking industry, one way to make production more effective, and consequently strengthen and maintain competitiveness, is to optimize the cycle time of CNC machines. With the intention that this type of optimization work should not be done unstructured, but systematically, this work aims to develop a proposal for a project method intended for cycle time optimization of CNC machines. Furthermore, interviews, workfollow-up and observations at Scania CV AB's crankshaft production together with related literary studies have been analyzed and filtered; and then used to provide answers to the work's research questions: (1) Can unnecessary activities in CNC cycles be identified and, if so, can these be minimized or excluded? (2) How can a project method be structured and what can that structure include? Eight covering activities in CNC cycles with optimization potential were noted. This includes, for example, waiting times, slow and unnecessary sequences and activities that can take place parallelly but do not. Practical workflow for cycle time optimization of CNC machines and methods for other types optimization were also identified. The balance of the empirical results and the related studies showed that the phasing and content of a project method can differ depending on whether the method is general or specifically adapted. After working through all the empirical results and related studies, a proposal was put together for a project method. The method has five phases (potential, initiation, planning, execution and termination) and is presented in a user interface. The interface clarifies what must be done in each phase and how. In an extended work, the interface can be further developed and optimization aspects that require more comprehensive solutions can be mapped and defined in connection with how they should be handled.

Real-time optimization (RTO) is a supervisory strategy in the hierarchical industrial process automation architecture in which economically optimal set-point targets are computed for the lower level advanced control system, which is typically model predictive control (MPC). Due to highly volatile market conditions, recent developments have considered transforming the conventional steady-state RTO to dynamic RTO (DRTO) to permit economic optimization during transient operation. Published DRTO literature optimizes plant input trajectories without taking into account the presence of the plant control system, constituting an open-loop DRTO (OL-DRTO) approach. The goal of this research is to develop a design framework for a DRTO system that optimizes process economics based on a closed-loop response prediction. We focus, in particular, on DRTO applied to a continuous process operation regulated under constrained MPC. We follow a two-layer DRTO/MPC configuration due to its close tie to the industrial process automation architecture. We first analyze the effects of optimizing MPC closed-loop response dynamics at the DRTO level. A rigorous DRTO problem structure proposed in this thesis is in the form of a multilevel dynamic optimization problem, as it embeds a sequence of MPC optimization subproblems to be solved in order to generate the closed-loop prediction in the DRTO formulation, denoted here as a closed-loop DRTO (CL-DRTO) strategy. A simultaneous solution approach is applied in which the convex MPC optimization subproblems are replaced by their necessary and sufficient, Karush-Kuhn-Tucker (KKT) optimality conditions, resulting in the reformulation of the original multilevel problem as a single-level mathematical program with complementarity constraints (MPCC) with the complementarities handled using an exact penalty formulation. Performance analysis is carried out, and process conditions under which the CL-DRTO strategy significantly outperforms the traditional open-loop counterpart are identified. The multilevel DRTO problem with a rigorous inclusion of the future MPC calculations significantly increases the size and solution time of the economic optimization problem. Next, we identify and analyze multiple closed-loop approximation techniques, namely, a hybrid formulation, a bilevel programming formulation, and an input clipping formulation applied to an unconstrained MPC algorithm. Performance analysis based on a linear dynamic system shows that the proposed approximation techniques are able to substantially reduce the size and solution time of the rigorous CL-DRTO problem, while largely retaining its original performance. Application to an industrially-based case study of a polystyrene production described by a nonlinear differential-algebraic equation (DAE) system is also presented. Often large-scale industrial systems comprise multi-unit subsystems regulated under multiple local controllers that require systematic coordination between them. Utilization of closed-loop prediction in the CL-DRTO formulation is extended for application as a higher-level, centralized supervisory control strategy for coordination of a distributed MPC system. The advantage of the CL-DRTO coordination formulation is that it naturally considers interaction between the underlying MPC subsystems due to the embedded controller optimization subproblems while optimizing the overall process dynamics. In this case, we take advantage of the bilevel formulation to perform closed-loop prediction in two DRTO coordination schemes, with variations in the coordinator objective function based on dynamic economics and target tracking. Case study simulations demonstrate excellent performance in which the proposed coordination schemes minimize the impact of disturbance propagation originating from the upstream subsystem dynamics, and also reduce the magnitude of constraint violation through appropriate adjustment of the controller set-point trajectories. / Thesis / Doctor of Philosophy (PhD)

Estratégias de otimização em tempo real (RTO: Real Time Optimization) são utilizadas para avaliar e determinar as condições ótimas operacionais de uma planta em estado estacionario, maximizando a produtividade econômica do processo sujeita a restrições operacionais. Esse problema de otimização engloba toda a planta e pode ser resolvido utilizando um só modelo para todo o processo que maximize o lucro bruto operacional considerando os preços de mercado das correntes de entrada e saída do processo. No entanto, na prática, essa abordagem centralizada muitas vezes não pode ser aplicada, devido ao tamanho e complexidade do problema de otimização, a que é muito difícil que todas as unidades da planta estejam em estado estacionário ao mesmo tempo e a que as unidades de processo não estão sincronizadas já que em muitos processos não existe armazenamento intermediário. Uma solução é utilizar uma estrutura distribuída, na qual o problema de otimização deve ser decomposto em subproblemas com reduzida complexidade numérica. Tal decomposição, no entanto, exige que o preço das correntes de entrada e saída de cada subproblema sejam adequadamente determinados. Com este proposito, neste trabalho, serão aplicadas técnicas de decomposição em uma unidade de produção de propeno da refinaria REPLAN (Refinaria de Paulínia, São Paulo) da PETROBRAS. Essa unidade será modelada, simulada e otimizada no software orientado a equações EMSO (Environment for Modeling, Simulation and Optimization). Com o objetivo de testar as técnicas de decomposição, a unidade será decomposta em três divisões que são: depropanizadora, deetanizadora e C3 splitter. Mostra-se que duas técnicas tradicionais chamadas de relaxação Lagrangiana e Lagrangeano aumentado não conseguem convergir em uma solução devido a duas causas. A primeira causa é que o processo estudado contém divisões indiferentes, o que significa que não existe dependência linear entre a função objetivo e as restrições complicadoras. A segunda causa é que os subproblemas de otimização que representam cada uma das divisões da unidade têm funções objetivos lineares, neste caso, a restrição ativa de cada subproblema irá ser sempre a capacidade de produção máxima ou mínima de cada divisão e não uma vazão intermediária. Uma técnica alternativa, Pricing Interprocess Streams Using Slack Auctions, também foi aplicada ao processo estudado. Essa técnica define uma folga de recurso entre as correntes 2 intermediárias das divisões e utiliza leilões para ajustar o preço dos produtos intermediários. Mostra-se que esse último abordagem também apresenta problemas na sua aplicação, porque todas as divisões estudadas têm dois produtos diferentes, isso significa que a técnica produzirá sempre a vazão máxima do produto final (vazão que tem preço de mercado) de cada divisão e não assim do produto intermediário (vazão que vai de uma divisão para outra). Identificados os problemas nessas técnicas de decomposição, é proposta uma modificação do algoritmo de relaxação Lagrangeana. Para o qual é considerada uma nova variável denominada limite de produção disponível (LPD) e uma restrição para as vazões de carga de cada uma das divisões, a qual será atualizada a cada iteração. Essa modificação no algoritmo consegue superar os problemas apresentados para a resolução do problema de otimização para a unidade estudada considerando uma estrutura distribuída. / Real time optimization strategies (RTO) are used to evaluate and determine the optimum operating conditions of a plant, maximizing the economic productivity of the process which is subject to operational constraints. This optimization framework encompasses the entire plant, and can be solved using one model for the entire process that maximizes the operating gross profit considering the market prices of input and output stream`s process. However, in practice this centralized approach often cannot be applied due to the size and complexity of the optimization problem. One solution is to use a distributed structure, in which the optimization problem must be broken into sub-problems with reduced numerical complexity. Such decomposition, however, requires that the price of input and output stream of each sub-problem should be adequately determined. With this purpose, in this work, decomposition techniques is applied in a propylene production unit at the refinery REPLAN (Refinaria de Paulínia, São Paulo) owned by PETROBRAS. This unit is modeled, simulated and optimized in an equation oriented software EMSO (Environment for Modeling, Simulation and Optimization). In order to test the decomposition techniques, the unit is decomposed into three divisions, which are depropanizer, deethanizer and C3 splitter. It is shown that two traditional techniques called Lagrangian relaxation and augmented Lagrangian cannot converge on a solution due to two causes. The first cause is that the studied process contains indifferent divisions, which means that there is no linear dependence between the objective function and the complicating constraints. The second cause is that the optimization sub-problem that represent each divisions has linear objective functions, in this case, the active constraint of each sub-problem will always be the maximum or minimum production capacity of each division and not an intermediate flow rate. An alternative technique Pricing Interprocess Streams Using Slack Auctions was also applied to the studied process. This technique defines a resource slack between the intermediary streams and use auctions for adjusting the price of intermediary products. It is shown that this technique also presents problems in its applications because all divisions studied has two different products, this means that this technique will always produce the maximum flow rate of the final product (flow rate that has a market price) of each division, and not the intermediate product (flow rate that goes from one division another). Identified problems in these decomposition 4 techniques, the proposed approach extended the Lagrangian relaxation algorithm, in which a new variable called \"available production limit\" (LPD) and a restriction to the feed flow rate from each divisions are considered, which will be updated at every iteration. This change in the algorithm can overcome the issues presented for solving the optimization problem for the unit studied considering a distributed structure.