Solving optimal control problems with state constraints using nonlinear programming and simulation tools

This paper illustrates how nonlinear programming and simulation tools, which are available in packages such as MATLAB and SIMULINK, can easily be used to solve optimal control problems with state- and/or input-dependent inequality constraints. The method presented is illustrated with a model of a single-link manipulator. The method is suitable to be taught to advanced undergraduate and Master's level students in control engineering.

State constraints in optimal impulsive controls

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimality conditions for infinite horizon control problems with state constraints

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Necessary conditions of optimality for state constrained infinite horizon differential inclusions

This article presents and discusses necessary conditions of optimality for infinite horizon dynamic optimization problems with inequality state constraints and set inclusion constraints at both endpoints of the trajectory. The cost functional depends on the state variable at the final time, and the dynamics are given by a differential inclusion. Moreover, the optimization is carried out over asymptotically convergent state trajectories. The novelty of the proposed optimality conditions for this class of problems is that the boundary condition of the adjoint variable is given as a weak directional inclusion at infinity. This improves on the currently available necessary conditions of optimality for infinite horizon problems. © 2011 IEEE.

A Novel Approach to Context-Aware Content-Based Middleware

La computación ubicua está extendiendo su aplicación desde entornos específicos hacia el uso cotidiano; el Internet de las cosas (IoT, en inglés) es el ejemplo más brillante de su aplicación y de la complejidad intrínseca que tiene, en comparación con el clásico desarrollo de aplicaciones. La principal característica que diferencia la computación ubicua de los otros tipos está en como se emplea la información de contexto. Las aplicaciones clásicas no usan en absoluto la información de contexto o usan sólo una pequeña parte de ella, integrándola de una forma ad hoc con una implementación específica para la aplicación. La motivación de este tratamiento particular se tiene que buscar en la dificultad de compartir el contexto con otras aplicaciones. En realidad lo que es información de contexto depende del tipo de aplicación: por poner un ejemplo, para un editor de imágenes, la imagen es la información y sus metadatos, tales como la hora de grabación o los ajustes de la cámara, son el contexto, mientras que para el sistema de ficheros la imagen junto con los ajustes de cámara son la información, y el contexto es representado por los metadatos externos al fichero como la fecha de modificación o la de último acceso. Esto significa que es difícil compartir la información de contexto, y la presencia de un middleware de comunicación que soporte el contexto de forma explícita simplifica el desarrollo de aplicaciones para computación ubicua. Al mismo tiempo el uso del contexto no tiene que ser obligatorio, porque si no se perdería la compatibilidad con las aplicaciones que no lo usan, convirtiendo así dicho middleware en un middleware de contexto. SilboPS, que es nuestra implementación de un sistema publicador/subscriptor basado en contenido e inspirado en SIENA [11, 9], resuelve dicho problema extendiendo el paradigma con dos elementos: el Contexto y la Función de Contexto. El contexto representa la información contextual propiamente dicha del mensaje por enviar o aquella requerida por el subscriptor para recibir notificaciones, mientras la función de contexto se evalúa usando el contexto del publicador y del subscriptor. Esto permite desacoplar la lógica de gestión del contexto de aquella de la función de contexto, incrementando de esta forma la flexibilidad de la comunicación entre varias aplicaciones. De hecho, al utilizar por defecto un contexto vacío, las aplicaciones clásicas y las que manejan el contexto pueden usar el mismo SilboPS, resolviendo de esta forma la incompatibilidad entre las dos categorías. En cualquier caso la posible incompatibilidad semántica sigue existiendo ya que depende de la interpretación que cada aplicación hace de los datos y no puede ser solucionada por una tercera parte agnóstica. El entorno IoT conlleva retos no sólo de contexto, sino también de escalabilidad. La cantidad de sensores, el volumen de datos que producen y la cantidad de aplicaciones que podrían estar interesadas en manipular esos datos está en continuo aumento. Hoy en día la respuesta a esa necesidad es la computación en la nube, pero requiere que las aplicaciones sean no sólo capaces de escalar, sino de hacerlo de forma elástica [22]. Desgraciadamente no hay ninguna primitiva de sistema distribuido de slicing que soporte un particionamiento del estado interno [33] junto con un cambio en caliente, además de que los sistemas cloud actuales como OpenStack u OpenNebula no ofrecen directamente una monitorización elástica. Esto implica que hay un problema bilateral: cómo puede una aplicación escalar de forma elástica y cómo monitorizar esa aplicación para saber cuándo escalarla horizontalmente. E-SilboPS es la versión elástica de SilboPS y se adapta perfectamente como solución para el problema de monitorización, gracias al paradigma publicador/subscriptor basado en contenido y, a diferencia de otras soluciones [5], permite escalar eficientemente, para cumplir con la carga de trabajo sin sobre-provisionar o sub-provisionar recursos. Además está basado en un algoritmo recientemente diseñado que muestra como añadir elasticidad a una aplicación con distintas restricciones sobre el estado: sin estado, estado aislado con coordinación externa y estado compartido con coordinación general. Su evaluación enseña como se pueden conseguir notables speedups, siendo el nivel de red el principal factor limitante: de hecho la eficiencia calculada (ver Figura 5.8) demuestra cómo se comporta cada configuración en comparación con las adyacentes. Esto permite conocer la tendencia actual de todo el sistema, para saber si la siguiente configuración compensará el coste que tiene con la ganancia que lleva en el throughput de notificaciones. Se tiene que prestar especial atención en la evaluación de los despliegues con igual coste, para ver cuál es la mejor solución en relación a una carga de trabajo dada. Como último análisis se ha estimado el overhead introducido por las distintas configuraciones a fin de identificar el principal factor limitante del throughput. Esto ayuda a determinar la parte secuencial y el overhead de base [26] en un despliegue óptimo en comparación con uno subóptimo. Efectivamente, según el tipo de carga de trabajo, la estimación puede ser tan baja como el 10 % para un óptimo local o tan alta como el 60 %: esto ocurre cuando se despliega una configuración sobredimensionada para la carga de trabajo. Esta estimación de la métrica de Karp-Flatt es importante para el sistema de gestión porque le permite conocer en que dirección (ampliar o reducir) es necesario cambiar el despliegue para mejorar sus prestaciones, en lugar que usar simplemente una política de ampliación. ABSTRACT The application of pervasive computing is extending from field-specific to everyday use. The Internet of Things (IoT) is the shiniest example of its application and of its intrinsic complexity compared with classical application development. The main characteristic that differentiates pervasive from other forms of computing lies in the use of contextual information. Some classical applications do not use any contextual information whatsoever. Others, on the other hand, use only part of the contextual information, which is integrated in an ad hoc fashion using an application-specific implementation. This information is handled in a one-off manner because of the difficulty of sharing context across applications. As a matter of fact, the application type determines what the contextual information is. For instance, for an imaging editor, the image is the information and its meta-data, like the time of the shot or camera settings, are the context, whereas, for a file-system application, the image, including its camera settings, is the information and the meta-data external to the file, like the modification date or the last accessed timestamps, constitute the context. This means that contextual information is hard to share. A communication middleware that supports context decidedly eases application development in pervasive computing. However, the use of context should not be mandatory; otherwise, the communication middleware would be reduced to a context middleware and no longer be compatible with non-context-aware applications. SilboPS, our implementation of content-based publish/subscribe inspired by SIENA [11, 9], solves this problem by adding two new elements to the paradigm: the context and the context function. Context represents the actual contextual information specific to the message to be sent or that needs to be notified to the subscriber, whereas the context function is evaluated using the publisher’s context and the subscriber’s context to decide whether the current message and context are useful for the subscriber. In this manner, context logic management is decoupled from context management, increasing the flexibility of communication and usage across different applications. Since the default context is empty, context-aware and classical applications can use the same SilboPS, resolving the syntactic mismatch that there is between the two categories. In any case, the possible semantic mismatch is still present because it depends on how each application interprets the data, and it cannot be resolved by an agnostic third party. The IoT environment introduces not only context but scaling challenges too. The number of sensors, the volume of the data that they produce and the number of applications that could be interested in harvesting such data are growing all the time. Today’s response to the above need is cloud computing. However, cloud computing applications need to be able to scale elastically [22]. Unfortunately there is no slicing, as distributed system primitives that support internal state partitioning [33] and hot swapping and current cloud systems like OpenStack or OpenNebula do not provide elastic monitoring out of the box. This means there is a two-sided problem: 1) how to scale an application elastically and 2) how to monitor the application and know when it should scale in or out. E-SilboPS is the elastic version of SilboPS. I t is the solution for the monitoring problem thanks to its content-based publish/subscribe nature and, unlike other solutions [5], it scales efficiently so as to meet workload demand without overprovisioning or underprovisioning. Additionally, it is based on a newly designed algorithm that shows how to add elasticity in an application with different state constraints: stateless, isolated stateful with external coordination and shared stateful with general coordination. Its evaluation shows that it is able to achieve remarkable speedups where the network layer is the main limiting factor: the calculated efficiency (see Figure 5.8) shows how each configuration performs with respect to adjacent configurations. This provides insight into the actual trending of the whole system in order to predict if the next configuration would offset its cost against the resulting gain in notification throughput. Particular attention has been paid to the evaluation of same-cost deployments in order to find out which one is the best for the given workload demand. Finally, the overhead introduced by the different configurations has been estimated to identify the primary limiting factor for throughput. This helps to determine the intrinsic sequential part and base overhead [26] of an optimal versus a suboptimal deployment. Depending on the type of workload, this can be as low as 10% in a local optimum or as high as 60% when an overprovisioned configuration is deployed for a given workload demand. This Karp-Flatt metric estimation is important for system management because it indicates the direction (scale in or out) in which the deployment has to be changed in order to improve its performance instead of simply using a scale-out policy.

A signature of the T → R transition in human hemoglobin

Allosteric effects in hemoglobin arise from the equilibrium between at least two energetic states of the molecule: a tense state, T, and a relaxed state, R. The two states differ from each other in the number and energy of the interactions between hemoglobin subunits. In the T state, constraints between subunits oppose the structural changes resulting from ligand binding. In the R state, these constraints are released, thus enhancing ligand-binding affinity. In the present work, we report the presence of four sites in hemoglobin that are structurally stabilized in the R relative to the T state. These sites are Hisα103(G10) and Hisα122(H5) in each α subunit of hemoglobin. They are located at the α1β1 and α2β2 interfaces of the hemoglobin tetramer, where the histidine side chains form hydrogen bonds with specific residues from the β chains. We have measured the solvent exchange rates of side chain protons of Hisα103(G10) and Hisα122(H5) in both deoxygenated and ligated hemoglobin by NMR spectroscopy. The exchange rates were found to be higher in the deoxygenated-T than in ligated-R state. Analysis of exchange rates in terms of the local unfolding model revealed that the structural stabilization free energy at each of these two histidines is larger by ≈1.5 kcal/(mol tetramer) in the R relative to the T state. The location of these histidines at the intradimeric α1β1 and α2β2 interfaces also suggests a role for these interfaces in the allosteric equilibrium of hemoglobin.

Desenvolvimento de um controlador preditivo estocástico para processos da indústria química.

O sucesso de estratégias de controle preditivo baseado em modelo (MPC, na sigla em inglês) tanto em ambiente industrial quanto acadêmico tem sido marcante. No entanto, ainda há diversas questões em aberto na área, especialmente quando a hipótese simplificadora de modelo perfeito é abandonada. A consideração explícita de incertezas levou a importantes progressos na área de controle robusto, mas esta ainda apresenta alguns problemas: a alta demanda computacional e o excesso de conservadorismo são questões que podem ter prejudicado a aplicação de estratégias de controle robusto na prática. A abordagem de controle preditivo estocástico (SMPC, na sigla em inglês) busca a redução do conservadorismo através da incorporação de informação estatística dos ruídos. Como processos na indústria química sempre estão sujeito a distúrbios, seja devido a diferenças entre planta e modelo ou a distúrbios não medidos, está técnica surge como uma interessante alternativa para o futuro. O principal objetivo desta tese é o desenvolvimento de algoritmos de SMPC que levem em conta algumas das especificidades de tais processos, as quais não foram adequadamente tratadas na literatura até o presente. A contribuição mais importante é a inclusão de ação integral no controlador através de uma descrição do modelo em termos de velocidade. Além disso, restrições obrigatórias (hard) nas entradas associadas a limites físicos ou de segurança e restrições probabilísticas nos estados normalmente advindas de especificações de produtos também são consideradas na formulação. Duas abordagens foram seguidas neste trabalho, a primeira é mais direta enquanto a segunda fornece garantias de estabilidade em malha fechada, contudo aumenta o conservadorismo. Outro ponto interessante desenvolvido nesta tese é o controle por zonas de sistemas sujeitos a distúrbios. Essa forma de controle é comum na indústria devido à falta de graus de liberdade, sendo a abordagem proposta a primeira contribuição da literatura a unir controle por zonas e SMPC. Diversas simulações de todos os controladores propostos e comparações com modelos da literatura são exibidas para demonstrar o potencial de aplicação das técnicas desenvolvidas.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

Problem of Hydroelectric Resources Management: Numerical Approach

In this work we analyze an optimal control problem for a system of two hydroelectric power stations in cascade with reversible turbines. The objective is to optimize the profit of power production while respecting the system’s restrictions. Some of these restrictions translate into state constraints and the cost function is nonconvex. This increases the complexity of the optimal control problem. The problem is solved numerically and two different approaches are adopted. These approaches focus on global optimization techniques (Chen-Burer algorithm) and on a projection estimation refinement method (PERmethod). PERmethod is used as a technique to reduce the dimension of the problem. Results and execution time of the two procedures are compared.

Design of a state observer using decay rate LMI constraints for fault detection in mechanical systems

Nowadays, one of the most important concerns for many companies is to maintain the operation of their systems without sudden equipment break down. Because of this, new techniques for fault detection and location in mechanical systems subject to dynamic loads have been developed. This paper studies of the influence of the decay rate in the design of state observers using LMI for fault detection in mechanical systems. This influence is analyzed by the performance index proposed by Huh and Stein for the condition of a state observer. An example is presented to illustrate the methodology discussed.

Influence of spatial constraints in non-crystalline regions on the polymer dynamics in semi-crystalline polyethylene: a solid state NMR study

A broad variety of solid state NMR techniques were used to investigate the chain dynamics in several polyethylene (PE) samples, including ultrahigh molecular weight PEs (UHMW-PEs) and low molecular weight PEs (LMW-PEs). Via changing the processing history, i.e. melt/solution crystallization and drawing processes, these samples gain different morphologies, leading to different molecular dynamics. Due to the long chain nature, the molecular dynamics of polyethylene can be distinguished in local fluctuation and long range motion. With the help of NMR these different kinds of molecular dynamics can be monitored separately. In this work the local chain dynamics in non-crystalline regions of polyethylene samples was investigated via measuring 1H-13C heteronuclear dipolar coupling and 13C chemical shift anisotropy (CSA). By analyzing the motionally averaged 1H-13C heteronuclear dipolar coupling and 13C CSA, the information about the local anisotropy and geometry of motion was obtained. Taking advantage of the big difference of the 13C T1 relaxation time in crystalline and non-crystalline regions of PEs, the 1D 13C MAS exchange experiment was used to investigate the cooperative chain motion between these regions. The different chain organizations in non-crystalline regions were used to explain the relationship between the local fluctuation and the long range motion of the samples. In a simple manner the cooperative chain motion between crystalline and non-crystalline regions of PE results in the experimentally observed diffusive behavior of PE chain. The morphological influences on the diffusion motion have been discussed. The morphological factors include lamellar thickness, chain organization in non-crystalline regions and chain entanglements. Thermodynamics of the diffusion motion in melt and solution crystallized UHMW-PEs is discussed, revealing entropy-controlled features of the chain diffusion in PE. This thermodynamic consideration explains the counterintuitive relationship between the local fluctuation and the long range motion of the samples. Using the chain diffusion coefficient, the rates of jump motion in crystals of the melt crystallized PE have been calculated. A concept of "effective" jump motion has been proposed to explain the difference between the values derived from the chain diffusion coefficients and those in literatures. The observations of this thesis give a clear demonstration of the strong relationship between the sample morphology and chain dynamics. The sample morphologies governed by the processing history lead to different spatial constraints for the molecular chains, leading to different features of the local and long range chain dynamics. The knowledge of the morphological influence on the microscopic chain motion has many implications in our understanding of the alpha-relaxation process in PE and the related phenomena such as crystal thickening, drawability of PE, the easy creep of PE fiber, etc.