A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Model and control of tendon actuated robots

The use of tendons for the transmission of the forces and the movements in robotic devices has been investigated from several researchers all over the world. The interest in this kind of actuation modality is based on the possibility of optimizing the position of the actuators with respect to the moving part of the robot, in the reduced weight, high reliability, simplicity in the mechanic design and, finally, in the reduced cost of the resulting kinematic chain. After a brief discussion about the benefits that the use of tendons can introduce in the motion control of a robotic device, the design and control aspects of the UB Hand 3 anthropomorphic robotic hand are presented. In particular, the tendon-sheaths transmission system adopted in the UB Hand 3 is analyzed and the problem of force control and friction compensation is taken into account. The implementation of a tendon based antagonistic actuated robotic arm is then investigated. With this kind of actuation modality, and by using transmission elements with nonlinear force/compression characteristic, it is possible to achieve simultaneous stiffness and position control, improving in this way the safety of the device during the operation in unknown environments and in the case of interaction with other robots or with humans. The problem of modeling and control of this type of robotic devices is then considered and the stability analysis of proposed controller is reported. At the end, some tools for the realtime simulation of dynamic systems are presented. This realtime simulation environment has been developed with the aim of improving the reliability of the realtime control applications both for rapid prototyping of controllers and as teaching tools for the automatic control courses.

Pattern-based segmentation of digital documents: model and implementation

This thesis proposes a new document model, according to which any document can be segmented in some independent components and transformed in a pattern-based projection, that only uses a very small set of objects and composition rules. The point is that such a normalized document expresses the same fundamental information of the original one, in a simple, clear and unambiguous way. The central part of my work consists of discussing that model, investigating how a digital document can be segmented, and how a segmented version can be used to implement advanced tools of conversion. I present seven patterns which are versatile enough to capture the most relevant documents’ structures, and whose minimality and rigour make that implementation possible. The abstract model is then instantiated into an actual markup language, called IML. IML is a general and extensible language, which basically adopts an XHTML syntax, able to capture a posteriori the only content of a digital document. It is compared with other languages and proposals, in order to clarify its role and objectives. Finally, I present some systems built upon these ideas. These applications are evaluated in terms of users’ advantages, workflow improvements and impact over the overall quality of the output. In particular, they cover heterogeneous content management processes: from web editing to collaboration (IsaWiki and WikiFactory), from e-learning (IsaLearning) to professional printing (IsaPress).

Nonlinear/electromagnetic co-simulation of microwaves and millimeter-waves links

The Ph.D. thesis describes the simulations of different microwave links from the transmitter to the receiver intermediate-frequency ports, by means of a rigorous circuit-level nonlinear analysis approach coupled with the electromagnetic characterization of the transmitter and receiver front ends. This includes a full electromagnetic computation of the radiated far field which is used to establish the connection between transmitter and receiver. Digitally modulated radio-frequency drive is treated by a modulation-oriented harmonic-balance method based on Krylov-subspace model-order reduction to allow the handling of large-size front ends. Different examples of links have been presented: an End-to-End link simulated by making use of an artificial neural network model; the latter allows a fast computation of the link itself when driven by long sequences of the order of millions of samples. In this way a meaningful evaluation of such link performance aspects as the bit error rate becomes possible at the circuit level. Subsequently, a work focused on the co-simulation an entire link including a realistic simulation of the radio channel has been presented. The channel has been characterized by means of a deterministic approach, such as Ray Tracing technique. Then, a 2x2 multiple-input multiple-output antenna link has been simulated; in this work near-field and far-field coupling between radiating elements, as well as the environment factors, has been rigorously taken into account. Finally, within the scope to simulate an entire ultra-wideband link, the transmitting side of an ultrawideband link has been designed, and an interesting Front-End co-design technique application has been setup.

Electrothermal characterization and nonlinear modelling of GaN transistors for telecommunication circuit design

This thesis starts showing the main characteristics and application fields of the AlGaN/GaN HEMT technology, focusing on reliability aspects essentially due to the presence of low frequency dispersive phenomena which limit in several ways the microwave performance of this kind of devices. Based on an equivalent voltage approach, a new low frequency device model is presented where the dynamic nonlinearity of the trapping effect is taken into account for the first time allowing considerable improvements in the prediction of very important quantities for the design of power amplifier such as power added efficiency, dissipated power and internal device temperature. An innovative and low-cost measurement setup for the characterization of the device under low-frequency large-amplitude sinusoidal excitation is also presented. This setup allows the identification of the new low frequency model through suitable procedures explained in detail. In this thesis a new non-invasive empirical method for compact electrothermal modeling and thermal resistance extraction is also described. The new contribution of the proposed approach concerns the non linear dependence of the channel temperature on the dissipated power. This is very important for GaN devices since they are capable of operating at relatively high temperatures with high power densities and the dependence of the thermal resistance on the temperature is quite relevant. Finally a novel method for the device thermal simulation is investigated: based on the analytical solution of the tree-dimensional heat equation, a Visual Basic program has been developed to estimate, in real time, the temperature distribution on the hottest surface of planar multilayer structures. The developed solver is particularly useful for peak temperature estimation at the design stage when critical decisions about circuit design and packaging have to be made. It facilitates the layout optimization and reliability improvement, allowing the correct choice of the device geometry and configuration to achieve the best possible thermal performance.

Analysis of nonlinear diffusion equations of second and fourth order

Wegen der fortschreitenden Miniaturisierung von Halbleiterbauteilen spielen Quanteneffekte eine immer wichtigere Rolle. Quantenphänomene werden gewöhnlich durch kinetische Gleichungen beschrieben, aber manchmal hat eine fluid-dynamische Beschreibung Vorteile: die bessere Nutzbarkeit für numerische Simulationen und die einfachere Vorgabe von Randbedingungen. In dieser Arbeit werden drei Diffusionsgleichungen zweiter und vierter Ordnung untersucht. Der erste Teil behandelt die implizite Zeitdiskretisierung und das Langzeitverhalten einer degenerierten Fokker-Planck-Gleichung. Der zweite Teil der Arbeit besteht aus der Untersuchung des viskosen Quantenhydrodynamischen Modells in einer Raumdimension und dessen Langzeitverhaltens. Im letzten Teil wird die Existenz von Lösungen einer parabolischen Gleichung vierter Ordnung in einer Raumdimension bewiesen, und deren Langzeitverhalten studiert.

Fiber beam-columns models with flexure-shear interaction for nonlinear analysis of reinforced concrete structures

The aim of this study was to develop a model capable to capture the different contributions which characterize the nonlinear behaviour of reinforced concrete structures. In particular, especially for non slender structures, the contribution to the nonlinear deformation due to bending may be not sufficient to determine the structural response. Two different models characterized by a fibre beam-column element are here proposed. These models can reproduce the flexure-shear interaction in the nonlinear range, with the purpose to improve the analysis in shear-critical structures. The first element discussed is based on flexibility formulation which is associated with the Modified Compression Field Theory as material constitutive law. The other model described in this thesis is based on a three-field variational formulation which is associated with a 3D generalized plastic-damage model as constitutive relationship. The first model proposed in this thesis was developed trying to combine a fibre beamcolumn element based on the flexibility formulation with the MCFT theory as constitutive relationship. The flexibility formulation, in fact, seems to be particularly effective for analysis in the nonlinear field. Just the coupling between the fibre element to model the structure and the shear panel to model the individual fibres allows to describe the nonlinear response associated to flexure and shear, and especially their interaction in the nonlinear field. The model was implemented in an original matlab® computer code, for describing the response of generic structures. The simulations carried out allowed to verify the field of working of the model. Comparisons with available experimental results related to reinforced concrete shears wall were performed in order to validate the model. These results are characterized by the peculiarity of distinguishing the different contributions due to flexure and shear separately. The presented simulations were carried out, in particular, for monotonic loading. The model was tested also through numerical comparisons with other computer programs. Finally it was applied for performing a numerical study on the influence of the nonlinear shear response for non slender reinforced concrete (RC) members. Another approach to the problem has been studied during a period of research at the University of California Berkeley. The beam formulation follows the assumptions of the Timoshenko shear beam theory for the displacement field, and uses a three-field variational formulation in the derivation of the element response. A generalized plasticity model is implemented for structural steel and a 3D plastic-damage model is used for the simulation of concrete. The transverse normal stress is used to satisfy the transverse equilibrium equations of at each control section, this criterion is also used for the condensation of degrees of freedom from the 3D constitutive material to a beam element. In this thesis is presented the beam formulation and the constitutive relationships, different analysis and comparisons are still carrying out between the two model presented.

Nonlinear Observers for Sensorless Control of Permanent Magnet Synchronous Motors

In this thesis, the industrial application of control a Permanent Magnet Synchronous Motor in a sensorless configuration has been faced, and in particular the task of estimating the unknown “parameters” necessary for the application of standard motor control algorithms. In literature several techniques have been proposed to cope with this task, among them the technique based on model-based nonlinear observer has been followed. The hypothesis of neglecting the mechanical dynamics from the motor model has been applied due to practical and physical considerations, therefore only the electromagnetic dynamics has been used for the observers design. First observer proposed is based on stator currents and Stator Flux dynamics described in a generic rotating reference frame. Stator flux dynamics are known apart their initial conditions which are estimated, with speed that is also unknown, through the use of the Adaptive Theory. The second observer proposed is based on stator currents and Rotor Flux dynamics described in a self-aligning reference frame. Rotor flux dynamics are described in the stationary reference frame exploiting polar coordinates instead of classical Cartesian coordinates, by means the estimation of amplitude and speed of the rotor flux. The stability proof is derived in a Singular Perturbation Framework, which allows for the use the current estimation errors as a measure of rotor flux estimation errors. The stability properties has been derived using a specific theory for systems with time scale separation, which guarantees a semi-global practical stability. For the two observer ideal simulations and real simulations have been performed to prove the effectiveness of the observers proposed, real simulations on which the effects of the Inverter nonlinearities have been introduced, showing the already known problems of the model-based observers for low speed applications.

Model reduction techniques in flexible multibody dynamics with application to engine cranktrain simulation

The development of a multibody model of a motorbike engine cranktrain is presented in this work, with an emphasis on flexible component model reduction. A modelling methodology based upon the adoption of non-ideal joints at interface locations, and the inclusion of component flexibility, is developed: both are necessary tasks if one wants to capture dynamic effects which arise in lightweight, high-speed applications. With regard to the first topic, both a ball bearing model and a journal bearing model are implemented, in order to properly capture the dynamic effects of the main connections in the system: angular contact ball bearings are modelled according to a five-DOF nonlinear scheme in order to grasp the crankshaft main bearings behaviour, while an impedance-based hydrodynamic bearing model is implemented providing an enhanced operation prediction at the conrod big end locations. Concerning the second matter, flexible models of the crankshaft and the connecting rod are produced. The well-established Craig-Bampton reduction technique is adopted as a general framework to obtain reduced model representations which are suitable for the subsequent multibody analyses. A particular component mode selection procedure is implemented, based on the concept of Effective Interface Mass, allowing an assessment of the accuracy of the reduced models prior to the nonlinear simulation phase. In addition, a procedure to alleviate the effects of modal truncation, based on the Modal Truncation Augmentation approach, is developed. In order to assess the performances of the proposed modal reduction schemes, numerical tests are performed onto the crankshaft and the conrod models in both frequency and modal domains. A multibody model of the cranktrain is eventually assembled and simulated using a commercial software. Numerical results are presented, demonstrating the effectiveness of the implemented flexible model reduction techniques. The advantages over the conventional frequency-based truncation approach are discussed.

Model reduction of stochastic groundwater flow and transport processes

This work presents a comprehensive methodology for the reduction of analytical or numerical stochastic models characterized by uncertain input parameters or boundary conditions. The technique, based on the Polynomial Chaos Expansion (PCE) theory, represents a versatile solution to solve direct or inverse problems related to propagation of uncertainty. The potentiality of the methodology is assessed investigating different applicative contexts related to groundwater flow and transport scenarios, such as global sensitivity analysis, risk analysis and model calibration. This is achieved by implementing a numerical code, developed in the MATLAB environment, presented here in its main features and tested with literature examples. The procedure has been conceived under flexibility and efficiency criteria in order to ensure its adaptability to different fields of engineering; it has been applied to different case studies related to flow and transport in porous media. Each application is associated with innovative elements such as (i) new analytical formulations describing motion and displacement of non-Newtonian fluids in porous media, (ii) application of global sensitivity analysis to a high-complexity numerical model inspired by a real case of risk of radionuclide migration in the subsurface environment, and (iii) development of a novel sensitivity-based strategy for parameter calibration and experiment design in laboratory scale tracer transport.

Robust Nonlinear Output Regulation by Identification Tools

The present thesis focuses on the problem of robust output regulation for minimum phase nonlinear systems by means of identification techniques. Given a controlled plant and an exosystem (an autonomous system that generates eventual references or disturbances), the control goal is to design a proper regulator able to process the only measure available, i.e the error/output variable, in order to make it asymptotically vanishing. In this context, such a regulator can be designed following the well known “internal model principle” that states how it is possible to achieve the regulation objective by embedding a replica of the exosystem model in the controller structure. The main problem shows up when the exosystem model is affected by parametric or structural uncertainties, in this case, it is not possible to reproduce the exact behavior of the exogenous system in the regulator and then, it is not possible to achieve the control goal. In this work, the idea is to find a solution to the problem trying to develop a general framework in which coexist both a standard regulator and an estimator able to guarantee (when possible) the best estimate of all uncertainties present in the exosystem in order to give “robustness” to the overall control loop.

Gene therapy for a novel mouse model of Canavan disease

Canavan disease (CD) is a rare leukodystrophy caused by loss-of-function mutations in the gene encoding aspartoacylase (ASPA), an oligodendrocyte-enriched enzyme. It is characterised by the accumulation of the ASPA substrate N-acetylaspartate (NAA) in brain, blood and urine, leading to a spongiform vacuolisation of the brain, severe motoric and cognitive impairments and premature death. To date, no therapy is available due to the lack of a gene-transfer system allowing transgene expression in oligodendrocytes (OLs) and the restoration of the missing enzyme. Hence, the aim of this study was to establish a novel gene-transfer system and its preclinical evaluation in a CD animal model.rnIn the first part of this thesis, a novel ASPA mouse mutant was generated. A βgeo cassette (including the genes encoding β-galactosidase and neomycin) flanked by frt sites was inserted into intron 1 of the intact aspa gene. Additionally, exon 2 was flanked by loxP sites for optional conditional deletion of the targeted locus. The resulting ASPA-deficient aspalacZ/lacZ-mouse was found to be an accurate model of CD and an important tool to identify novel aspects of its complex pathology. Homozygous mutants showed a CD-like histopathology, neurological impairment, behavioural deficits as well as a reduced body weight. Additionally, MRI data revealed changes in brain metabolite composition. rnRecombinant adeno-associated viral (rAAV) vectors have become a versatile tool for gene transfer to the central nervous system because they are efficient, non-toxic and replication-deficient. Based on the natural neurotropism of AAV vectors, AAV-based gene delivery has entered the clinics for the treatment of neurodegenerative diseases. However, the lack of AAV vectors with oligodendroglial tropism has precluded gene therapy for leukodystrophies. In the second part of this work, it was shown that the transduction profile of established AAV serotypes can be targeted towards OLs in a transcriptional approach, using the oligodendrocyte-specific myelin basic protein (MBP) promoter to drive transgene expression in OLs.rnIn the last part of this work, the therapeutic efficacy of AAV-mediated aspa gene transfer to OLs of juvenile aspalacZ/lacZ mice was evaluated. AAV-aspa injections into multiple sites of the brain parenchyma resulted in transduction of OLs in the grey and white matter throughout the brain. Histological abnormalities in the brain of ASPA-deficient mice were ameliorated and accompanied by a reduction of NAA levels. Furthermore, the treatment resulted in normalisation of body weight, motor function and nest-building behaviour. These data provide a proof-of-concept for a successful gene therapy of Canavan disease. This might pave the way towards translation into clinical application and serve as the basis for the genetic treatment of other leukodystrophies.

Stochastic local volatility model for fx markets

Questa tesi verte sullo studio di un modello a volatilità stocastica e locale, utilizzato per valutare opzioni esotiche nei mercati dei cambio. La difficoltà nell'implementare un modello di tal tipo risiede nella calibrazione della leverage surface e uno degli scopi principali di questo lavoro è quello di mostrarne la procedura.

Multifunctional polyether architectures : versatile materials for surface attachment and functionalization

Chapter 1 of this thesis comprises a review of polyether polyamines, i.e., combinations of polyether scaffolds with polymers bearing multiple amino moieties. Focus is laid on controlled or living polymerization methods. Furthermore, fields in which the combination of cationic, complexing, and pH-sensitive properties of the polyamines and biocompatibility and water-solubility of polyethers promise enormous potential are presented. Applications include stimuli-responsive polymers with a lower critical solution temperature (LCST) and/or the ability to gel, preparation of shell cross-linked (SCL) micelles, gene transfection, and surface functionalization.rnIn Chapter 2, multiaminofunctional polyethers relying on the class of glycidyl amine comonomers for anionic ring-opening polymerization (AROP) are presented. In Chapter 2.1, N,N-diethyl glycidyl amine (DEGA) is introduced for copolymerization with ethylene oxide (EO). Copolymer microstructure is assessed using online 1H NMR kinetics, 13C NMR triad sequence analysis, and differential scanning calorimetry (DSC). The concurrent copolymerization of EO and DEGA is found to result in macromolecules with a gradient structure. The LCSTs of the resulting copolymers can be tailored by adjusting DEGA fraction or pH value of the environment. Quaternization of the amino moieties by methylation results in polyelectrolytes. Block copolymers are used for PEGylated gold nanoparticle formation. Chapter 2.2 deals with a glycidyl amine monomer with a removable protecting group at the amino moiety, for liberation of primary amines at the polyether backbone, which is N,N-diallyl glycidyl amine (DAGA). Its allyl groups are able to withstand the harsh basic conditions of AROP, but can be cleaved homogeneously after polymerization. Gradient as well as block copolymers poly(ethylene glycol)-PDAGA (PEG-PDAGA) are obtained. They are analyzed regarding their microstructure, LCST behavior, and cleavage of the protecting groups. rnChapter 3 describes applications of multi(amino)functional polyethers for functionalization of inorganic surfaces. In Chapter 3.1, they are combined with an acetal-protected catechol initiator, leading to well-defined PEG and heteromultifunctional PEG analogues. After deprotection, multifunctional PEG ligands capable of attaching to a variety of metal oxide surfaces are obtained. In a cooperative project with the Department of Inorganic and Analytical Chemistry, JGU Mainz, their potential is demonstrated on MnO nanoparticles, which are promising candidates as T1 contrast agents in magnetic resonance imaging. The MnO nanoparticles are solubilized in aqueous solution upon ligand exchange. In Chapter 3.2, a concept for passivation and functionalization of glass surfaces towards gold nanorods is developed. Quaternized mPEG-b-PqDEGA diblock copolymers are attached to negatively charged glass surfaces via the cationic PqDEGA blocks. The PEG blocks are able to suppress gold nanorod adsorption on the glass in the flow cell, analyzed by dark field microscopy.rnChapter 4 highlights a straightforward approach to poly(ethylene glycol) macrocycles. Starting from commercially available bishydroxy-PEG, cyclic polymers are available by perallylation and ring-closing metathesis in presence of Grubbs’ catalyst. Purification of cyclic PEG is carried out using α-cyclodextrin. This cyclic sugar derivative forms inclusion complexes with remaining unreacted linear PEG in aqueous solution. Simple filtration leads to pure macrocycles, as evidenced by SEC and MALDI-ToF mass spectrometry. Cyclic polymers from biocompatible precursors are interesting materials regarding their increased blood circulation time compared to their linear counterparts.rnIn the Appendix, A.1, a study of the temperature-dependent water-solubility of polyether copolymers is presented. Macroscopic cloud points, determined by turbidimetry, are compared with microscopic aggregation phenomena, monitored by continuous wave electron paramagnetic resonance (CW EPR) spectroscopy in presence of the amphiphilic spin probe and model drug (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO). These thermoresponsive polymers are promising candidates for molecular transport applications. The same techniques are applied in Chapter A.2 to explore the pH-dependence of the cloud points of PEG-PDEGA copolymers in further detail. It is shown that the introduction of amino moieties at the PEG backbone allows for precise manipulation of complex phase transition modes. In Chapter A.3, multi-hydroxyfunctional polysilanes are presented. They are obtained via copolymerization of the acetal-protected dichloro(isopropylidene glyceryl propyl ether)methylsilane monomer. The hydroxyl groups are liberated through acidic work-up, yielding versatile access to new multifunctional polysilanes.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.