Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

Riabilitazione e valutazione di pazienti con deficit neurologici mediante l'utilizzo di realtà virtuale, feedback aumentati, sensori inerziali e tecnologie video a basso costo.

La neuroriabilitazione è un processo attraverso cui individui affetti da patologie neurologiche mirano al conseguimento di un recupero completo o alla realizzazione del loro potenziale ottimale benessere fisico, mentale e sociale. Elementi essenziali per una riabilitazione efficace sono: una valutazione clinica da parte di un team multidisciplinare, un programma riabilitativo mirato e la valutazione dei risultati conseguiti mediante misure scientifiche e clinicamente appropriate. Obiettivo principale di questa tesi è stato sviluppare metodi e strumenti quantitativi per il trattamento e la valutazione motoria di pazienti neurologici. I trattamenti riabilitativi convenzionali richiedono a pazienti neurologici l’esecuzione di esercizi ripetitivi, diminuendo la loro motivazione. La realtà virtuale e i feedback sono in grado di coinvolgerli nel trattamento, permettendo ripetibilità e standardizzazione dei protocolli. È stato sviluppato e valutato uno strumento basato su feedback aumentati per il controllo del tronco. Inoltre, la realtà virtuale permette l’individualizzare il trattamento in base alle esigenze del paziente. Un’applicazione virtuale per la riabilitazione del cammino è stata sviluppata e testata durante un training su pazienti di sclerosi multipla, valutandone fattibilità e accettazione e dimostrando l'efficacia del trattamento. La valutazione quantitativa delle capacità motorie dei pazienti viene effettuata utilizzando sistemi di motion capture. Essendo il loro uso nella pratica clinica limitato, una metodologia per valutare l’oscillazione delle braccia in soggetti parkinsoniani basata su sensori inerziali è stata proposta. Questi sono piccoli, accurati e flessibili ma accumulano errori durante lunghe misurazioni. È stato affrontato questo problema e i risultati suggeriscono che, se il sensore è sul piede e le accelerazioni sono integrate iniziando dalla fase di mid stance, l’errore e le sue conseguenze nella determinazione dei parametri spaziali sono contenuti. Infine, è stata presentata una validazione del Kinect per il tracking del cammino in ambiente virtuale. Risultati preliminari consentono di definire il campo di utilizzo del sensore in riabilitazione.

Management control systems : subcomponents, optimal design and the role of time as a contingency

Management Control System (MCS) research is undergoing turbulent times. For a long time related to cybernetic instruments of management accounting only, MCS are increasingly seen as complex systems comprising not only formal accounting-driven instruments, but also informal mechanisms of control based on organizational culture. But not only have the means of MCS changed; researchers increasingly ap-ply MCS to organizational goals other than strategy implementation.rnrnTaking the question of "How do I design a well-performing MCS?" as a starting point, this dissertation aims at providing a comprehensive and integrated overview of the "current-state" of MCS research. Opting for a definition of MCS, broad in terms of means (all formal as well as informal MCS instruments), but focused in terms of objectives (behavioral control only), the dissertation contributes to MCS theory by, a) developing an integrated (contingency) model of MCS, describing its contingencies, as well as its subcomponents, b) refining the equifinality model of Gresov/Drazin (1997), c) synthesizing research findings from contingency and configuration research concerning MCS, taking into account case studies on research topics such as ambi-dexterity, equifinality and time as a contingency.

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Quality assurance of simulated patient feedback in communication training for fourth-year medical students

Introduction In our program, simulated patients (SPs) give feedback to medical students in the course of communication skills training. To ensure effective training, quality control of the SPs’ feedback should be implemented. At other institutions, medical students evaluate the SPs’ feedback for quality control (Bouter et al., 2012). Thinking about implementing quality control for SPs’ feedback in our program, we wondered whether the evaluation by students would result in the same scores as evaluation by experts. Methods Consultations simulated by 4th-year medical students with SPs were video taped including the SP’s feedback to the students (n=85). At the end of the training sessions students rated the SPs’ performance using a rating instrument called Bernese Assessment for Role-play and Feedback (BARF) containing 11 items concerning feedback quality. Additionally the videos were evaluated by 3 trained experts using the BARF. Results The experts showed a high interrater agreement when rating identical feedbacks (ICCunjust=0.953). Comparing the rating of students and experts, high agreement was found with regard to the following items: 1. The SP invited the student to reflect on the consultation first, Amin (= minimal agreement) 97% 2. The SP asked the student what he/she liked about the consultation, Amin = 88%. 3. The SP started with positive feedback, Amin = 91%. 4. The SP was comparing the student with other students, Amin = 92%. In contrast the following items showed differences between the rating of experts and students: 1. The SP used precise situations for feedback, Amax (=maximal agreement) 55%, Students rated 67 of SPs’ feedbacks to be perfect with regard to this item (highest rating on a 5 point Likert scale), while only 29 feedbacks were rated this way by the experts. 2. The SP gave precise suggestions for improvement, Amax 75%, 62 of SPs’ feedbacks obtained the highest rating from students, while only 44 of SPs’ feedbacks achieved the highest rating in the view of the experts. 3. The SP speaks about his/her role in the third person, Amax 60%. Students rated 77 feedbacks with the highest score, while experts judged only 43 feedbacks this way. Conclusion Although evaluation by the students was in agreement with that of experts concerning some items, students rated the SPs’ feedback more often with the optimal score than experts did. Moreover it seems difficult for students to notice when SPs talk about the role in the first instead of the third person. Since precision and talking about the role in the third person are important quality criteria of feedback, this result should be taken into account when thinking about students’ evaluation of SPs’ feedback for quality control. Bouter, S., E. van Weel-Baumgarten, and S. Bolhuis. 2012. Construction and Validation of the Nijmegen Evaluation of the Simulated Patient (NESP): Assessing Simulated Patients’ Ability to Role-Play and Provide Feedback to Students. Academic Medicine: Journal of the Association of American Medical Colleges

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

Fuzzy Optimal Control for Double Inverted Pendulum

In this paper a fuzzy optimal control for stabilizing an upright position a double inverted pendulum (DIP) is developed and compared. Modeling is based on Euler-Lagrange equations. This results in a complicated nonlinear fast reaction, unstable multivariable system. Firstly, the mathematical models of double pendulum system are presented. The weight variable fuzzy input is gained by combining the fuzzy control theory with the optimal control theory. Simulation results show that the controller, which the upper pendulum is considered as main control variable, has high accuracy, quick convergence speed and higher precision.

Direct Visual Servoing Framework based on Optimal Control for Redundant Joint Structures

This paper presents a new framework based on optimal control to define new dynamic visual controllers to carry out the guidance of any serial link structure. The proposed general method employs optimal control to obtain the desired behaviour in the joint space based on an indicated cost function which determines how the control effort is distributed over the joints. The proposed approach allows the development of new direct visual controllers for any mechanical joint system with redundancy. Finally, authors show experimental results and verifications on a real robotic system for some derived controllers obtained from the control framework.

Automatic control; principles of feedback and their application in machine control.

Photocopy (negative)

On the necessary condition for optimal control of nonlinear systems.

"Prepared under contract Nonr-225(11) (NR-041-086) for Office of Naval Research."

Practical scheme for error control using feedback

We describe a scheme for quantum-error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols [for example, Ahn Phys. Rev. A 65, 042301 (2001)], is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit flips. We also consider implementation in a solid-state quantum-computation architecture and estimate the maximal error rate that could be corrected with current technology.