The subject of this thesis is the design and practical application of a model-based controller with variable structure control (VSC). Robot manipulators are highly non-linear systems, however they form a specific class in the non-linear group. Exact mathematical descriptions of the robot dynamics can be achieved and further, robot manipulators have specific useful properties that can be used for the design of advanced controllers. The inclusion of the inverse dynamic description of the robot manipulator as a feedforward term of the controller (model-based controller) is used to transform two non-linear systems i.e. the controller and the robot, into one linear system. The limitation of this technique arises from the accuracy of the inverse dynamic model. The linearisation only takes place if the model is known exactly. To deal with the uncertainties that arise in the model, a control methodology based on variable structure control is proposed. The design of the controller is based on a Lyapunov approach and engineering considerations of the robot. A candidate Lyapunov function of a pseudo-energy form is selected to start the controller design. The general form of the controller is selected to satisfy the negative definiteness of the Lyapunov function. The initial uncertainties between the actual robot dynamics and the model used in the controller are dealt with using a classical VSC regulator. The deficiencies of this approach are evident however because of the chattering phenomenum. The model uncertainties are examined from an engineering point of view and adjustable bounds are then devised for the VSC regulator, and simulations confirm a reduction in the chattering. Implementation on the SPRINTA robot reveals further limitations in the proposed methodology and the bound adjustment is enhanced to take into account the position of the robot and the tracking errors. Two controllers based on the same principle are then obtained and their performances are compared to a PID controller, for three types of trajectory. Tests reveal the superiority of the devised control methodology over the classic PID controller. The devised controller demonstrates that the inclusion of the robot dynamics and properties in the controller design with adequate engineering considerations lead to improved robot responses.

In this thesis, we study fault tolerant control (FTC) for the decentralized robust servomechanism problem (DRSP) of a colocated large flexible space structure (LFSS) under sensor and actuator failures (SAF). The control objective is to devise a decentralized controller that maintains the stability of the LFSS, tracks a constant reference for healthy outputs, regulates against an unknown constant disturbance for healthy outputs, and is robust against parametric uncertainties, so that ``spillover effects'' do not occur. Two FTC frameworks are considered: An active FTC framework that assumes SAF are known, and a passive FTC framework for which SAF are unknown. The active FTC framework extends existing work on DRSP of a nominal LFSS, and applies a PID controller that has fault-dependent adjustments. Necessary and sufficient conditions for a solution to exist are determined, notably an easy-to-test rank condition. For the passive FTC framework, a PD controller that stabilizes an LFSS under unknown SAF is found. Although perfect tracking and regulation are not attained under the PD controller, by applying high gains, the errors for healthy outputs can be reduced to any desired level. However, outputs with failed sensors and healthy actuators can reach undesirably high magnitude under high gains. To improve performance under low gains, insights on steady-state outputs are applied to develop a feed-forward control that has good performance in tracking, but not regulation. Further analysis on the PD controller reveals a method to diagnose SAF using steady-state outputs. As a result, the PD controller and PID controller are found to have complementary advantages, leading to an 3-stage integrated FTC procedure. First, the PD controller can stabilize the LFSS under unknown SAF (passive FTC). Next, fault diagnosis is performed while the LFSS is stabilized. Finally, a reconfigured PID controller applying diagnosed SAF enables healthy outputs to meet control objectives (active FTC). Three examples, including a benchmark space platform with 200 states obtained by finite-element analysis, are used to illustrate the results throughout this thesis.

In this thesis, we study fault tolerant control (FTC) for the decentralized robust servomechanism problem (DRSP) of a colocated large flexible space structure (LFSS) under sensor and actuator failures (SAF). The control objective is to devise a decentralized controller that maintains the stability of the LFSS, tracks a constant reference for healthy outputs, regulates against an unknown constant disturbance for healthy outputs, and is robust against parametric uncertainties, so that ``spillover effects'' do not occur. Two FTC frameworks are considered: An active FTC framework that assumes SAF are known, and a passive FTC framework for which SAF are unknown. The active FTC framework extends existing work on DRSP of a nominal LFSS, and applies a PID controller that has fault-dependent adjustments. Necessary and sufficient conditions for a solution to exist are determined, notably an easy-to-test rank condition. For the passive FTC framework, a PD controller that stabilizes an LFSS under unknown SAF is found. Although perfect tracking and regulation are not attained under the PD controller, by applying high gains, the errors for healthy outputs can be reduced to any desired level. However, outputs with failed sensors and healthy actuators can reach undesirably high magnitude under high gains. To improve performance under low gains, insights on steady-state outputs are applied to develop a feed-forward control that has good performance in tracking, but not regulation. Further analysis on the PD controller reveals a method to diagnose SAF using steady-state outputs. As a result, the PD controller and PID controller are found to have complementary advantages, leading to an 3-stage integrated FTC procedure. First, the PD controller can stabilize the LFSS under unknown SAF (passive FTC). Next, fault diagnosis is performed while the LFSS is stabilized. Finally, a reconfigured PID controller applying diagnosed SAF enables healthy outputs to meet control objectives (active FTC). Three examples, including a benchmark space platform with 200 states obtained by finite-element analysis, are used to illustrate the results throughout this thesis.

Inference of regulatory networks has received attention of researchers from many fields. The challenge offered by this problem is its being a typical modeling problem under insufficient information about the process. Hence, we need to derive the apriori unavailable information from the empirical observations. Modeling by inference consists of selecting or defining the most appropriate model structure and inferring the parameters. An appropriate model structure should have the following properties. The model parameters should be inferable. Given the observation and the model class, all parameters used in the model should have a unique solution restriction of the solution space). The forward model should be accurately computable (restriction of the solution space). The model should be capable of exhibiting the essential qualitative features of the system (limit of the restriction). The model should be relevant with the process (limit of the restriction). A piecewise linear formulation, described by a switching state transition matrix and a switching state transition vector with a Boolean function indicating the switching conditions is proposed for the inference of gene regulatory networks. This thesis mainly concerns using a formulation of switching networks obeying all the above mentioned requirements and developing an inference algorithm for estimating the parameters of the formulation. The methodologies used or developed during this study are applicable to various fields of science and engineering.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 127-131).

Thesis (Ph.D.)--University of Western Australia, 2007.

Thesis (M.E.)--University of Canterbury, 2008. / Typescript (photocopy). "August 2008." Includes bibliographical references (p. [123]-126). Also available via the World Wide Web.

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Στη διπλωματική εργασία αυτή ασχοληθήκαμε με την πρόβλεψη της εξόδου μη-γραμμικών συστημάτων με τη χρήση αναδρομικών αλγορίθμων που χρησιμοποιούν συναρτήσεις πυρήνα. Παρουσιάζεται ο δικός μας αναδρομικός αλγόριθμος πρόβλεψης και βλέπουμε πως αποδίδει σε σχέση με έναν άλλο ήδη υπάρχων και ιδιαίτερα δημοφιλή αλγόριθμο. Στο πρώτο κεφάλαιο δίνουμε μια σύντομη περιγραφή του προβλήματος που καλούμαστε να λύσουμε. Στη συνέχεια δείχνουμε πως οι συναρτήσεις πυρήνα μπορούν να χρησιμοποιηθούν για να μας βοηθήσουν να λύσουμε το πρόβλημα αυτό. Στο δεύτερο κεφάλαιο αναλύουμε περισσότερο τις συναρτήσεις πυρήνα και τις ιδιότητες που τις χαρακτηρίζουν. Παρουσιάζουμε τα βασικά θεωρήματα και βλέπουμε πώς διαμορφώνεται το πρόβλημα της πρόβλεψης με την εφαρμογή αυτών. Επιπλέον παρουσιάζουμε πως το πρόβλημα μας μετατρέπεται στο γνωστό πρόβλημα γραμμικών ελαχίστων τετραγώνων στην περίπτωση που χρησιμοποιήσουμε γραμμικό πυρήνα. Στο τρίτο κεφάλαιο παρουσιάζουμε τον αλγόριθμο μας, αναλύοντας το συλλογισμό που μας οδήγησε σε αυτόν. Δίνουμε επίσης μια περιγραφή ενός άλλου αλγορίθμου που χρησιμοποιείται ήδη για την επίλυση τέτοιων προβλημάτων. Στο τέταρτο κεφάλαιο γίνονται μια σειρά από προσομοιώσεις σε MATLAB οπού βλέπουμε πόσο καλά μπορεί να κάνει την πρόβλεψη των εξόδων μη-γραμικών συστημάτων ο αλγόριθμός μας. Επίσης αντιπαραθέτουμε και την απόδοση του ανταγωνιστικού αλγορίθμου. Στα πειράματα μας εξετάζουμε το σφάλμα πρόβλεψης των προαναφερθέντων αλγορίθμων, την ταχύτητα σύγκλισης τους καθώς και την σθεναρότητα τους. Τέλος παρουσιάζουμε τα συμπεράσματα μας εξηγώντας γιατί πιστεύουμε ότι η δικία μας προσέγγιση υπερτερεί της άλλης. / This dissertation deals with the problem of predicting the output of non-linear systems using recursive kernel methods. We will present our own prediction algorithm and see how it performs in relation to a widely used alternative algorithm. In the first chapter we provide a short description of the problem of non-linear prediction. We then describe how kernel methods could help us solve this problem. In the second chapter we further analyze kernel functions and their properties. We present the basic theorems and see how these affect and transform the problem at hand. Furthermore, we explain how this problem results in the linear least squares problem in case we use the linear kernel. In the third chapter we present our algorithm and reasoning that led to it. We also describe a different algorithm that is already used to predict such signals. In the fourth chapter we perform a series of simulations in the Matlab environment were we evaluate how well the two approaches predict the output. In this evaluation we consider the complexity, the error and robustness of the algorithms. Finally we present our conclusion and explain why our algorithm is superior to the alternative.

Ο έλεγχος μη γραμμικών δειγματοληπτικών συστημάτων αποτελεί μια σημαντική πρόκληση, στην ανάλυση και σχεδιασμό ελεγκτών συστημάτων, με μεγάλη πρακτική εφαρμογή. Σε αυτή την μελέτη παρουσιάζουμε ένα από τα πιο σημαντικά εργαλεία ανάλυσης και σχεδιασμού, για μια γενική κατηγορία μη γραμικών δειγματοληπτικών συστημάτων (nonlinear sampled-data control). Παρουσιάζεται μια γενίκευση και ενοποίηση των γνωστών αποτελεσμάτων σχεδίασης εξομοίωσης (Emulation Design), διαθέσιμων στην βιβλιογραφία, θεωρώντας την διατήρηση των γενικευμένων ανισώσεων διάχυσης (Dissipation inequalities) υπό δειγματοληψίας, στο πλαίσιο του σχεδιασμού εξομοιωτών ελεγκτών δυναμικής κατάστασης ανάδρασης (dynamic state feedback controllers). Στην συνέχεια παρουσιάζονται δύο παραδείγματα μελέτης εφαρμογής των αποτελεσμάτων της γενικής μελέτης σχετικά με την διατήρηση των ιδιοτήτων διαχυτικότητας (dissipativity properties), ευστάθειας (stability), εισόδου-σε-κατάσταση σταθερότητας (input-to-state stability) και παθητικότητας (passivity), όταν ο ελεγκτής διακριτού χρόνου ενός συστήματος σχεδιάζεται με εξομοίωση. / The current diploma thesis is about a general and unified framework of a sampled-data nonlinear system using the emulation design.