The models used by model predictive controllers (MPCs) to predict future outcomes are usually unconstrained forms like impulse or step responses and discrete state space models. Certain MPC algorithms allow constraints to be imposed on the inputs or outputs of a system; but they may be infeasible as they are not checked for consistency via the process model. Consistent constraint handling methods - which account for their interdependence and disambiguate the language used to specify constraints – would therefore be an attractive aid when using any MPC package. A rigorous and systematic approach to constraint management has been developed, building on the work of Vinson (2000), Lima (2007) and Georgakis et al. (2003) in interpreting constraint interactions. The method supports linear steady-state system models, and provides routines to obtain the following information: <ul> <li> effects of constraint changes on the corresponding input and output constraints, </li><li> feasibility checks for constraints, </li><li> specification of constraint-set size and</li><li> optimal fitting of constraints within the desirable input and output space.</li></ul> Mathematical rigour and unambiguous language for identifying constraint types were key design criteria. The outputs of the program provide guidance when handling constraints, as opposed to rules of thumb and experience, and promote understanding of the system and its constraints. The metrics presented are not specific to any commercial MPC and can be implemented in the user interfaces of such MPCs. The method was applied to laboratory-scale test rigs to illustrate the information obtained. / Dissertation (MEng)--University of Pretoria, 2011. / Chemical Engineering / unrestricted

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A relação entre a Geometria e a Trigonometria vai além da forma clássica em que estas duas áreas da Matemática são apresentadas no Ensino Básico. Existe uma tendência a separá-las por fronteiras rígidas cerceando de certa forma a cooperac~ao entre os métodos e tecnicas de uma e de outra, com o objetivo de resolver determinados problemas matem aticos, cuja solução não está obrigatoriamente inscrita numa destas áreas. Por exemplo, problemas propostos em olimpíadas. Neste trabalho mostra-se algumas dessas possibilidades trabalhando com situações em que a partir de um resultado geométrico obtem-se determinados resultados trigonométricos ou, o contrário. / The relationship between Geometry and Trigonometry goes beyond the classic way in which these two areas of mathematics are presented in high school. There is a tendency to separate them by rigid boundaries, restricting somehow cooperation between the methods and techniques of one of them in the other in order to solve certain mathematical problems, whose solution is not compulsorily insured in a particular area. For example, problems proposed in the Olympics. In this work we will show some possibilities of interaction, working with situations where from geometrical results we obtain certain trigonometric results and otherwise.

No description available.

With the wide deployment of data intensive Internet applications and continued advances in sensing technology and biotechnology, large multidimensional datasets, possibly containing privacy-conscious information have been emerging. Mining such datasets has become increasingly common in business integration, large-scale scientific data analysis, and national security. The proposed research aims at exploring the geometric properties of the multidimensional datasets utilized in statistical learning and data mining, and providing novel techniques and frameworks for mining very large datasets while protecting the desired data privacy. The first main contribution of this research is the development of iVIBRATE interactive visualization-based approach for clustering very large datasets. The iVIBRATE framework uniquely addresses the challenges in handling irregularly shaped clusters, domain-specific cluster definition, and cluster-labeling of the data on disk. It consists of the VISTA visual cluster rendering subsystem, and the Adaptive ClusterMap Labeling subsystem. The second main contribution is the development of ``Best K Plot'(BKPlot) method for determining the critical clustering structures in multidimensional categorical data. The BKPlot method uniquely addresses two challenges in clustering categorical data: How to determine the number of clusters (the best K) and how to identify the existence of significant clustering structures. The method consists of the basic theory, the sample BKPlot theory for large datasets, and the testing method for identifying no-cluster datasets. The third main contribution of this research is the development of the theory of geometric data perturbation and its application in privacy-preserving data classification involving single party or multiparty collaboration. The key of geometric data perturbation is to find a good randomly generated rotation matrix and an appropriate noise component that provides satisfactory balance between privacy guarantee and data quality, considering possible inference attacks. When geometric perturbation is applied to collaborative multiparty data classification, it is challenging to unify the different geometric perturbations used by different parties. We study three protocols under the data-mining-service oriented framework for unifying the perturbations: 1) the threshold-satisfied voting protocol, 2) the space adaptation protocol, and 3) the space adaptation protocol with a trusted party. The tradeoffs between the privacy guarantee, the model accuracy and the cost are studied for the protocols.

No description available.

An ever increasing demand for instant and reliable information on modern communication networks forces codewords to operate in a non-asymptotic regime. To achieve reliability for imperfect channels in this regime, codewords need to be retransmitted from receiver to the transmit buffer, aided by a fast feedback mechanism. Large occupancy of this buffer results in longer communication delays. Therefore, codewords need to be designed carefully to reduce transmit queue-length and thus the delay experienced in this buffer. We first study the consequences of physical layer decisions on the transmit buffer occupancy. We develop an analytical framework to relate physical layer channel to the transmit buffer occupancy. We compute the optimal code-rate for finite-length codewords operating over a correlated channel, under certain communication service guarantees. We show that channel memory has a significant impact on this optimal code-rate. Next, we study the delay in small ad-hoc networks. In particular, we find out what rates can be supported on a small network, when each flow has a certain end-to-end service guarantee. To this end, service guarantee at each intermediate link is characterized. These results are applied to study the potential benefits of setting up a network suitable for network coding in multicast. In particular, we quantify the gains of network coding over classic routing for service provisioned multicast communication over butterfly networks. In the wireless setting, we study the trade-off between communications gains achieved by network coding and the cost to set-up a network enabling network coding. In particular, we show existence of scenarios where one should not attempt to create a network suitable for coding. Insights obtained from these studies are applied to design a distributed rate control algorithm in a large network. This algorithm maximizes sum-utility of all flows, while satisfying per-flow end-to-end service guarantees. We introduce a notion of effective-capacity per communication link that captures the service requirements of flows sharing this link. Each link maintains a price and effective-capacity, and each flow maintains rate and dissatisfaction. Flows and links update their respective variables locally, and we show that their decisions drive the system to an optimal point. We implemented our algorithm on a network simulator and studied its convergence behavior on few networks of practical interest.

Dans cette thèse, nous nous intéressons à la reconnaissance d’images couleur à l’aide d’une nouvelle approche géométrique du domaine fréquentiel. La plupart des méthodes existantes ne traitent que les images en niveaux de gris au travers de descripteurs issus de la transformée de Fourier usuelle. L’extension de telles méthodes aux images multicanaux, comme par exemple les images couleur, consiste généralement à reproduire un traitement identique sur chacun des canaux. Afin d’éviter ce traitement marginal, nous étudions et mettons en perspective les différentes généralisations de la transformée de Fourier pour les images couleur. Ce travail nous oriente vers la transformée de Fourier Clifford pour les images couleur définie dans le cadre des algèbres géométriques. Une étude approfondie de celle-ci nous conduit à définir un algorithme de calcul rapide et à proposer une méthode de corrélation de phase pour les images couleur. Dans un deuxième temps, nous cherchons à généraliser à travers cette transformée de Fourier les définitions des descripteurs de Fourier de la littérature. Nous étudions ainsi les propriétés, notamment l’invariance à la translation, rotation et échelle, des descripteurs existants. Ce travail nous mène à proposer trois nouveaux descripteurs appelés “descripteurs de Fourier couleur généralisés”(GCFD) invariants en translation et en rotation.Les méthodes proposées sont évaluées sur des bases d’images usuelles afin d’estimer l’apport du contenu fréquentiel couleur par rapport aux méthodes niveaux de gris et marginales. Les résultats obtenus à l’aide d’un classifieur SVM montrent le potentiel des méthodes proposées ; les descripteurs GCFD se révèlent être plus compacts, de complexité algorithmique moindre pour des performances de classification au minimum équivalentes. Nous proposons également des heuristiques pour le choix du paramètre de la transformée de Fourier Clifford.Cette thèse constitue un premier pas vers une généralisation des méthodes fréquentielles aux images multicanaux. / In this thesis, we focus on color image recognition using a new geometric approach in the frequency domain. Most existing methods only process grayscale images through descriptors defined from the usual Fourier transform. The extension of these methods to multichannel images such as color images usually consists in reproducing the same processing for each channel. To avoid this marginal processing,we study and compare the different generalizations of color Fourier transforms. This work leads us to use the Clifford Fourier transform for color images defined in the framework of geometric algebra. A detailed study of it leads us to define a fast algorithm and to propose a phase correlation for colorimages. In a second step, with the aim of generalizing Fourier descriptors of the literature with thisFourier transform, we study their properties, including invariance to translation, rotation and scale.This work leads us to propose three new descriptors called “generalized color Fourier descriptors”(GCFD) invariant in translation and in rotation.The proposed methods are evaluated on usual image databases to estimate the contribution of color frequency content compared with grayscale and marginal methods. The results obtained usingan SVM classifier show the potential of the proposed methods ; the GCFD are more compact, have less computational complexity and give better recognition rates. We also propose heuristics for choosing the parameter of the color Clifford Fourier transform.This thesis is a first step towards a generalization of frequency methods to multichannel images.

The main body of this thesis consists of six appended papers. In the  first two, different  cooperative surveillance problems are considered. The second two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.In Papers A and B,  a combinatorial optimization based framework to cooperative surveillance missions using multiple Unmanned Ground Vehicles (UGVs) is proposed. In particular, Paper A  considers the the Minimum Time UGV Surveillance Problem (MTUSP) while Paper B treats the Connectivity Constrained UGV Surveillance Problem (CUSP). The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from  a point on a waypoint-path and such that the time for executing the search in parallel is minimized.  The connectivity constrained formulation  extends the MTUSP by additionally requiring the induced information graph to be  kept recurrently connected  at the time instants when the UGVs  perform the surveillance mission.  In these two papers, the NP-hardness of  both these problems are shown and decomposition techniques are proposed that allow us to find an approximative solution efficiently in an algorithmic manner.Paper C addresses the problem of designing a real time, high performance trajectory planner for an aerial vehicle that uses information about terrain and enemy threats, to fly low and avoid radar exposure on the way to a given target. The high-level framework augments Receding Horizon Control (RHC) with a graph based terminal cost that captures the global characteristics of the environment.  An important issue with RHC is to make sure that the greedy, short term optimization does not lead to long term problems, which in our case boils down to two things: not getting into situations where a collision is unavoidable, and making sure that the destination is actually reached. Hence, the main contribution of this paper is to present a trajectory planner with provable safety and task completion properties. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In Paper D, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for  online  trajectory optimization are illustrated by a missile guidance example.In Paper E, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotic systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a  unicycle robot model, equipped with a set of range-measuring sensors. Finally, in Paper F, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented  by  a proof  that the region of contraction is infinitely thin. Moreover, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature. / QC 20100622 / TAIS, AURES

<p>The main body of this thesis consists of four appended papers. The first two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.</p><p>The first paper addresses the problem of designing a real time, high performance trajectory planner for aerial vehicles. The main contribution is two-fold. Firstly, by augmenting a novel safety maneuver at the end of the planned trajectory, this paper extends previous results by having provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method is shown to have finite time task completion. Moreover, in the second part of the paper, the problem of simultaneous arrival of multiple aerial vehicles is considered. By using a time-scale separation principle, one is able to adopt standard Laplacian control to this consensus problem, which is neither unconstrained, nor first order.</p><p>Direct methods for trajectory optimization are traditionally based on<i> a</i> <i>priori </i>temporal discretization and collocation methods. In the second paper, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example.</p><p>In the third paper, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotics systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors.</p><p>Finally, in the fourth paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. However, assuming <i>a</i> <i>priori </i>bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.</p>

The main body of this thesis consists of four appended papers. The first two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively. The first paper addresses the problem of designing a real time, high performance trajectory planner for aerial vehicles. The main contribution is two-fold. Firstly, by augmenting a novel safety maneuver at the end of the planned trajectory, this paper extends previous results by having provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method is shown to have finite time task completion. Moreover, in the second part of the paper, the problem of simultaneous arrival of multiple aerial vehicles is considered. By using a time-scale separation principle, one is able to adopt standard Laplacian control to this consensus problem, which is neither unconstrained, nor first order. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In the second paper, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example. In the third paper, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotics systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors. Finally, in the fourth paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. However, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature. / QC 20101108