Generalized Scattering-Based Stabilization of Nonlinear Interconnected Systems

The research presented in this thesis is aimed at development of new methods and techniques for stability analysis and stabilization of interconnections of nonlinear systems, in particular, in the presence of communication delays. Based on the conic systems\u27 formalism, we extend the notion of conicity for the non-planar case where the dimension of the cone\u27s central subspace may be greater than one. One of the advantages of the notion of non-planar conicity is that any dissipative system with a quadratic supply rate can be represented as a non-planar conic system; specifically, its central subspace and radius can be calculated using an algorithm developed in this thesis. For a feedback interconnection of two non-planar conic systems, a graph separation condition for finite-gain L2-stability is established in terms of central subspaces and radii of the subsystems\u27 non-planar cones. Subsequently, a generalized version of the scattering transformation is developed which is applicable to non-planar conic systems. The transformation allows for rendering the dynamics of a non-planar conic system into a prescribed cone with compatible dimensions; the corresponding design algorithm is presented. The ability of the generalized scattering transformation to change the parameters of a system\u27s cone can be used for stabilization of interconnections of non-planar conic systems. For interconnections without communication delays, stabilization is achieved through the design of a scattering transformation that guarantees the fulfilment of the graph separation stability condition. For interconnected systems with communication delays, scattering transformations are designed on both sides of communication channel in a way that guarantees the overall stability through fulfilment of the small gain stability condition. Application to stabilization of bilateral teleoperators with multiple heterogeneous communication delays is briefly discussed. Next, the coupled stability problem is addressed based on the proposed scattering based stabilization techniques. The coupled stability problem is one of the most fundamental problems in robotics. It requires to guarantee stability of a controlled manipulator in contact with an environment whose dynamics are unknown, or at least not known precisely. We present a scattering-based design procedure that guarantees coupled stability while at the same time does not affect the robot\u27s trajectory tracking performance in free space. A detailed design example is presented that demonstrates the capabilities of the scattering-based design approach, as well as its advantages in comparison with more conventional passivity-based approaches. Finally, the generalized scattering-based technique is applied to the problem of stabilization of complex interconnections of dissipative systems with quadratic supply rates in the presence of multiple heterogeneous constant time delays. Our approach is to design local scattering transformations that guarantee the fulfilment of a multi-dimensional small-gain stability condition for the interconnected system. A numerical example is presented that illustrates the capabilities of the proposed design method

A Framework for Stable Robot-Environment Interaction Based on the Generalized Scattering Transformation

This thesis deals with development and experimental evaluation of control algorithms for stabilization of robot-environment interaction based on the conic systems formalism and scattering transformation techniques. A framework for stable robot-environment interaction is presented and evaluated on a real physical system. The proposed algorithm fundamentally generalizes the conventional passivity-based approaches to the coupled stability problem. In particular, it allows for stabilization of not necessarily passive robot-environment interaction. The framework is based on the recently developed non-planar conic systems formalism and generalized scattering-based stabilization methods. A comprehensive theoretical background on the scattering transformation techniques, planar and non-planar conic systems is presented. The dynamics of the robot are estimated using data-driven techniques, which allows the equations for the dynamics of a robot to be obtained in an explicit form. The generalized scattering transformation is used in combination with the Lyapunov-based adaptive trajectory tracking control. It is shown that the original interconnected system is not stable due to its non-passive nature; however, the application of the proposed stabilization algorithm allows stability to be achieved, without affecting the robot’s trajectory tracking performance in free space

Electrically Switchable and Permanently Stable Light Scattering Modes by Dynamic Fingerprint Chiral Textures.

Negative dielectric nematic liquid crystals (LCs) doped with two azobenzene materials provide electrically switchable and permanently stable scattering mode light modulators based on dynamic fingerprint chiral textures (DFCT) with inhomogeneously helical axes. These light modulators can be switched between transparent (stable large domains of DFCT) states and scattering (stable small domains of DFCT) states by applying electric fields with different frequencies. The generation of DFCT results from the long flexible side chains of the doped chiral dopant. That is, if the DFCT can be obtained, then the large domains of DFCT reflect an intrinsically stable state. Moreover, the stabilization of the small domains of DFCT are caused by the terminal rigid restricted side chains of the other doped chiral dopant. Experimentally, the required amplitude to switch the light modulator from a scattering (transparent) state to a transparent (scattering) state decreases as the frequency of the applied electric field increases (decreases) within the set limits. This study is the first report on the advantages of the light scattering mode of DFCT, including low operating voltage, permanently stable transmission, wide viewing angle, high contrast, and polarization-independent scattering and transparency.The authors would like to thank the Ministry of Science and Technology (MOST) of Taiwan for financially supporting this research under Grant No. MOST 103-2112-M-008-018-MY3. We are also grateful to Prof. Jy-Shan Hsu (Chung Yuan Christian University, Taiwan) for allowing full equipment usage

Study of Molecular interactions and surface alignment control of liquid crystals

Le contrôle de l’alignement des molécules de cristaux liquides (CL) est d’une importance majeure pour la plupart des applications électro-optique comme les afficheurs, les modulateurs et les atténuateurs variables. Ce contrôle est réalisé plus spécifiquement par les interactions entre les molécules de CL et la surface adjacente. L’alignement par la surface est ainsi un des facteurs clés pour l’amélioration des performances des systèmes basés sur les CL. Cette thèse rapporte une étude expérimentale sur le contrôle de l’alignement des molécules de CL par la surface, et explore des avenues pratiques. Dans un premier temps, des CL nématiques à double fréquence (DF-NLC) et des films minces de mésogènes réactifs (MR) déposés sur la surface intérieure d’une cellule, ont été utilisés pour produire des structures polymères stabilisées en surface. Pour former ces structures, une interpénétration partielle entre les molécules de CL et de MR a été réalisée pendant l’application d’un couple diélectrique (positif ou négatif) sur le système de matériau. Après une courte période d’interpénétration entre la couche de MR et les CL, une exposition UV a été appliquée pour polymériser totalement le système de matériau. Ces systèmes ont démontré un fort potentiel pour le contrôle de l’alignement des CL par la surface. Ils permettent la « programmation » de cellule de CL présentant une diffusion de la lumière électriquement contrôlable, pouvant être utilisé dans des applications telles que des fenêtres intimités et l’éclairage intelligent. Des analyses électro-optiques et microscopiques ont été faites pour caractériser ces structures. Nous avons montré que les modulations de contraste de la lumière diffusée, ainsi que la dépendance de la polarisation et les temps de réponses peuvent être améliorées de façon notable par le contrôle à double fréquence. Dans un deuxième temps, des CL chiraux double fréquence (DF-CLC) ont été utilisé pour produire des structures stabilisées en surface, qui, en addition d’une diffusion contrôlable, ont montré des phénomènes de réflexion résonante. Des couches de MR orientées et partiellement polymérisées furent utilisées comme couche d’alignement pour les DF-CLC. Le rôle du temps de pré-polymérisation des MR sur les propriétés des cellules ont été étudiées par des analyses électro-optiques et spectroscopiques. Nos études morphologiques ont démontré que l’interdiffusion des molécules entre la couche de MR et le volume des CL durant le procédé de programmation génère des agrégats polymères sur les surfaces internes de la cellule, qui sont à l’origine de la diffusion contrôlable de la lumière.The alignment control of liquid crystal (LC) molecules is of great importance for the most of LC based electro-optical applications such as displays, modulators, and variable attenuators. This control realises, particularly, by the interactions between LC molecules and the adjacent surface. This makes the surface alignment one of the key factors for the improvement of LC-based devices’ performance. This PhD thesis reports an experimental study of alignment control of LC molecules by surfaces, and explores the possibility of practical avenues. First, dual frequency nematic LCs (DF-NLC) and thin reactive mesogen (RM) films, cast on internal surfaces of cell substrate, were used to build surface polymer stabilized structures. To form these surface-stabilized structures, a partial interpenetration between the LC and RM molecules was allowed while applying an orienting dielectric torque (positive or negative) to the material system. Then, after a short interpenetration period between the RM layer and the bulk LC, UV exposition was added to definitely cure the material system. These systems demonstrated great potential for the surface alignment control of LCs, enabling the ‘‘programming’’ of LC cells with electrically controllable light scattering, which can be used in privacy windows and smart lighting applications. Electro-optic and microscopic studies were done to characterize these surface-stabilized structures. We showed that the contrasts of light scatter modulation, polarization dependence and response times can be noticeably improved by the dual-frequency control. Afterward, dual frequency chiral LCs (DF-CLC) were used to build surface-stabilized structures, which in addition to the controllable scattering, showed also resonant reflection phenomenon. Partially cured and oriented RM layers were used as alignment layers for DF-CLC. The role of the pre-curing duration of RM in the behavior of the cell was observed by electro-optical and spectroscopic studies. Our morphological studies showed that the molecular interdiffusion between RM layer and bulk LC during the programming process generates polymer aggregates on the cell’s internal surfaces, which are at the origin of formation of controllable light scattering

Study of resonant reflection in helicoidal photonic band gap structures

La présente thèse de doctorat rapporte une étude expérimentale sur la réflexion résonante de la lumière dans des structures hélicoïdales à bande photonique interdite. Plusieurs aspects optiques et électro-optiques des cristaux liquides cholestériques sont abordés en concentrant l’attention sur deux effets principaux: l’influence des conditions aux limites (mécaniques et optiques) sur les propriétés optiques des couches de cristaux liquides cholestériques et le contrôle de la bande interdite de ces dernières. On présente un élément à double-rétroaction optique basé sur une cavité de Fabry-Pérot remplie de cristal liquide cholestérique. Les propriétés spectrales et de polarisation de cet élément sont caractérisées expérimentalement et par des simulations théoriques. Un changement mineur dans la structure en haut (cavité de Fabry-Pérot) nous a permis d’obtenir une transmission non-réciproque de la lumière sans application d’un champ externe à l’élément en question. Nous avons observé une transmission non-réciproque de la lumière par un système qui ressemble beaucoup aux structures naturelles observées sur certaines carapaces d’insectes (par exemple, sur les élytres de certains coléoptères): une simple couche de matière transparente linéaire dans son état fondamental. L’effet est défini par deux facteurs principaux: la chiralité et la périodicité de la matière ainsi que les conditions asymétriques aux surfaces limites. Concernant la partie sur le contrôle de la bande interdite, nous présentons la création et l’utilisation du mélange de cristal liquide cholestérique à deux fréquences pour le ‘déroulement’ et la reconstruction dynamique de la structure hélicoïdale. Le processus de reconstruction est accéléré d’un ordre de grandeur par l’application de champs électriques modérés. L’étape suivante du contrôle de la bande interdite est l’accord en longueur d’onde de la bande interdite. Un effet électromécanique est utilisé pour générer et étudier l’auto-adaptation du pas d’hélice de la couche de cristal liquide cholestérique. L’anisotropie négative diélectrique a permis d’assurer la stabilisation de la structure hélicoïdale de la couche pendant l’application du champ électrique qui a aussi changé l’épaisseur de la couche de cristal liquide en pliant un des substrats minces de la cellule. Cette déformation de la couche a généré un d’accord (et des sauts) des longueurs d’onde de la bande interdite. Les études spectrales et morphologiques pendant les changements de la bande interdite sont présentées et discutées.The present PhD thesis reports experimental study of resonant reflection in helicodal photonic band gap structures. Several optical and electro-optical properties of cholesteric liquid crystals are investigated where attention was concentrated on two principal phenomena: the influence of mechanical and optical boundary conditions on optical properties of cholesteric liquid crystal layers and control of photonic band gap of cholesteric liquid crystals. The creation of a double-feedback optical element based on a Fabry-Perot cavity filled with a planar aligned cholesteric liquid crystal mixture is presented. The polarization and spectral properties of this element are characterized experimentally and simulated theoretically. Experimental results are obtained for the transmittance dependence upon the orientation of the linear polarization plane and the polarization state of incident probe beam. A slight change in above mentioned structure (Fabry-Perot cavity) let us obtain a non-reciprocal transmittance of light without applying any external field. We observed an optical non reciprocity in a material system that is very close to natural structures, such as insect skin: a single layer of linear transparent material in its ground state. The process is shown to be defined by two key parameters: the chiral and periodic nature of the material and its asymmetric boundary conditions. In the part of band gap control, we present the creation and the use of dual frequency cholesteric liquid crystal mixtures for the dynamic electrical unwinding and forced (accelerated) restoring of their molecular helix. The restoring process is accelerated almost by an order of magnitude for quite moderate voltages used. The next step of band gap control is the tuning of band gap (wavelength). Strong electromechanical effect was used to generate and study self-adaptation and pitch jumps in a layer of cholesteric liquid crystal. The negative dielectric anisotropy of the material allowed its stabilization by the electric field and important thickness changes, achieved thanks to the use of a very thin substrate, allowed the observation of multiple dynamic jumps at fixed deformation conditions. Spectral and morphological studies of the material during those jumps were performed and are presented

Hierarchical Assemblies of Soft Matters From Polymers and Liquid Crystals on Structured Surfaces

Hierarchical, multifunctional materials hold important keys to numerous advanced technologies, including electronics, optics, and medicine. This thesis encompasses generation of hierarchical structures with novel morphologies and functions through self-assembly directed by lithographically fabricated templates. Here, two soft materials, amphiphilic random copolymers of photopolymerized acryloyl chloride (ranPAC) and smectic-A liquid crystal (SmA-LC) molecule, 4\u27(5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,12-heptadecaflu-orododecyloxy)-biphenyl-4-carboxylic acid ethyl ester, are synthesized as model systems to investigate the governing principles at the topographic surface/interface. The ranPAC can self-organize into nanomicelles with high regularity and stability, typically not possible in random copolymer systems. The morphology can be controlled by the photopolymerization conditions and solvent; the crosslinked shell makes the micelles robust against drying and storage. Using SU-8 micropillar arrays with spatially controlled surface chemistry as templates, we construct hierarchical microporous structures with tunable pore size and symmetry (e.g. square array), and uncover a new evaporative assembly method. By functionalizing the ranPAC nanovesicles with cationic poly(ethyleneimines), we encapsulate the anticancer drug, doxorubicin hydrochloride, and mRNA at a high payload, which are delivered to HEK 293T cells in vitro at a low cytotoxicity level. SmA-LC are characterized by arrangement of molecules into thin layers with the long molecular axis parallel to the layer normal, forming a close-packed hexagonal array of topological defects known as focal conic domains (FCDs) in a thin film. Using a series of SU-8 micropillar arrays with different size, shape, height, and symmetry as topological templates, we investigate the epitaxial and hierarchical assemblies of FCDs; whether the system favors confinement or pillar edge-pinning depends on balance of the elastic energy of LCs and the surface energy imposed by the template. The conservation of toric FCD (TFCD) textures over large LC thickness manifests a remarkably unique outcome of the epitaxial growth of TFCDs. On shorter pillars, however, the system favors the pinning of FCD centers near pillar edges while avoiding the opposing effect of confinement, leading to the break of the underlying symmetry of the pillar lattice, exhibiting tunable eccentricity, and a nontrivial yet organized array of defects balancing the elastic energy of LCs and the surface energy imposed by the template

Liquid crystal blue phases: stability, field effects and alignment

The blue phases are fascinating structures in liquid crystals, fluids that exhibit cubic structures that have true crystalline order. The blue phases were discovered in the 1970s and were the subject of extensive research in the 1980s, when a deep understanding of many of their properties was established. The discovery that the blue phases could be stabilised to exist over wide temperature ranges meant that they became more than scientific curiosities and led to a recent resurgence in research into them as they offer some promise in applications. This paper considers some important aspects of the blue phases that are recurrent topics in their research. It describes factors affecting blue phase stability, demonstrating on the role of the bend elastic constant; field effects, including the Kerr effect, electrostriction and relaxation phenomena; and alignment, in particular production and control of blue phase monodomains. The dependence of these phenomena on the physical properties of the liquid crystalline system, including the twist and bend elastic constants and the dielectric anisotropy, is emphasised wherever possible. The paper links work carried out in the 1980s with contemporary research, using a few key examples to show how there is still much to understand in this beautiful topic

Thermoacoustic tomography arising in brain imaging

We study the mathematical model of thermoacoustic and photoacoustic tomography when the sound speed has a jump across a smooth surface. This models the change of the sound speed in the skull when trying to image the human brain. We derive an explicit inversion formula in the form of a convergent Neumann series under the assumptions that all singularities from the support of the source reach the boundary