A Schwarz lemma for Kahler affine metrics and the canonical potential of a proper convex cone

This is an account of some aspects of the geometry of Kahler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for Kahler affine metrics of Yau s Schwarz lemma for volume forms. By a theorem of Cheng and Yau, there is a canonical Kahler affine Einstein metric on a proper convex domain, and the Schwarz lemma gives a direct proof of its uniqueness up to homothety. The potential for this metric is a function canonically associated to the cone, characterized by the property that its level sets are hyperbolic affine spheres foliating the cone. It is shown that for an n -dimensional cone, a rescaling of the canonical potential is an n -normal barrier function in the sense of interior point methods for conic programming. It is explained also how to construct from the canonical potential Monge-Ampère metrics of both Riemannian and Lorentzian signatures, and a mean curvature zero conical Lagrangian submanifold of the flat para-Kahler space.

OntoTag - A Linguistic and Ontological Annotation Model Suitable for the Semantic Web

OntoTag - A Linguistic and Ontological Annotation Model Suitable for the Semantic Web 1. INTRODUCTION. LINGUISTIC TOOLS AND ANNOTATIONS: THEIR LIGHTS AND SHADOWS Computational Linguistics is already a consolidated research area. It builds upon the results of other two major ones, namely Linguistics and Computer Science and Engineering, and it aims at developing computational models of human language (or natural language, as it is termed in this area). Possibly, its most well-known applications are the different tools developed so far for processing human language, such as machine translation systems and speech recognizers or dictation programs. These tools for processing human language are commonly referred to as linguistic tools. Apart from the examples mentioned above, there are also other types of linguistic tools that perhaps are not so well-known, but on which most of the other applications of Computational Linguistics are built. These other types of linguistic tools comprise POS taggers, natural language parsers and semantic taggers, amongst others. All of them can be termed linguistic annotation tools. Linguistic annotation tools are important assets. In fact, POS and semantic taggers (and, to a lesser extent, also natural language parsers) have become critical resources for the computer applications that process natural language. Hence, any computer application that has to analyse a text automatically and ‘intelligently’ will include at least a module for POS tagging. The more an application needs to ‘understand’ the meaning of the text it processes, the more linguistic tools and/or modules it will incorporate and integrate. However, linguistic annotation tools have still some limitations, which can be summarised as follows: 1. Normally, they perform annotations only at a certain linguistic level (that is, Morphology, Syntax, Semantics, etc.). 2. They usually introduce a certain rate of errors and ambiguities when tagging. This error rate ranges from 10 percent up to 50 percent of the units annotated for unrestricted, general texts. 3. Their annotations are most frequently formulated in terms of an annotation schema designed and implemented ad hoc. A priori, it seems that the interoperation and the integration of several linguistic tools into an appropriate software architecture could most likely solve the limitations stated in (1). Besides, integrating several linguistic annotation tools and making them interoperate could also minimise the limitation stated in (2). Nevertheless, in the latter case, all these tools should produce annotations for a common level, which would have to be combined in order to correct their corresponding errors and inaccuracies. Yet, the limitation stated in (3) prevents both types of integration and interoperation from being easily achieved. In addition, most high-level annotation tools rely on other lower-level annotation tools and their outputs to generate their own ones. For example, sense-tagging tools (operating at the semantic level) often use POS taggers (operating at a lower level, i.e., the morphosyntactic) to identify the grammatical category of the word or lexical unit they are annotating. Accordingly, if a faulty or inaccurate low-level annotation tool is to be used by other higher-level one in its process, the errors and inaccuracies of the former should be minimised in advance. Otherwise, these errors and inaccuracies would be transferred to (and even magnified in) the annotations of the high-level annotation tool. Therefore, it would be quite useful to find a way to (i) correct or, at least, reduce the errors and the inaccuracies of lower-level linguistic tools; (ii) unify the annotation schemas of different linguistic annotation tools or, more generally speaking, make these tools (as well as their annotations) interoperate. Clearly, solving (i) and (ii) should ease the automatic annotation of web pages by means of linguistic tools, and their transformation into Semantic Web pages (Berners-Lee, Hendler and Lassila, 2001). Yet, as stated above, (ii) is a type of interoperability problem. There again, ontologies (Gruber, 1993; Borst, 1997) have been successfully applied thus far to solve several interoperability problems. Hence, ontologies should help solve also the problems and limitations of linguistic annotation tools aforementioned. Thus, to summarise, the main aim of the present work was to combine somehow these separated approaches, mechanisms and tools for annotation from Linguistics and Ontological Engineering (and the Semantic Web) in a sort of hybrid (linguistic and ontological) annotation model, suitable for both areas. This hybrid (semantic) annotation model should (a) benefit from the advances, models, techniques, mechanisms and tools of these two areas; (b) minimise (and even solve, when possible) some of the problems found in each of them; and (c) be suitable for the Semantic Web. The concrete goals that helped attain this aim are presented in the following section. 2. GOALS OF THE PRESENT WORK As mentioned above, the main goal of this work was to specify a hybrid (that is, linguistically-motivated and ontology-based) model of annotation suitable for the Semantic Web (i.e. it had to produce a semantic annotation of web page contents). This entailed that the tags included in the annotations of the model had to (1) represent linguistic concepts (or linguistic categories, as they are termed in ISO/DCR (2008)), in order for this model to be linguistically-motivated; (2) be ontological terms (i.e., use an ontological vocabulary), in order for the model to be ontology-based; and (3) be structured (linked) as a collection of ontology-based triples, as in the usual Semantic Web languages (namely RDF(S) and OWL), in order for the model to be considered suitable for the Semantic Web. Besides, to be useful for the Semantic Web, this model should provide a way to automate the annotation of web pages. As for the present work, this requirement involved reusing the linguistic annotation tools purchased by the OEG research group (http://www.oeg-upm.net), but solving beforehand (or, at least, minimising) some of their limitations. Therefore, this model had to minimise these limitations by means of the integration of several linguistic annotation tools into a common architecture. Since this integration required the interoperation of tools and their annotations, ontologies were proposed as the main technological component to make them effectively interoperate. From the very beginning, it seemed that the formalisation of the elements and the knowledge underlying linguistic annotations within an appropriate set of ontologies would be a great step forward towards the formulation of such a model (henceforth referred to as OntoTag). Obviously, first, to combine the results of the linguistic annotation tools that operated at the same level, their annotation schemas had to be unified (or, preferably, standardised) in advance. This entailed the unification (id. standardisation) of their tags (both their representation and their meaning), and their format or syntax. Second, to merge the results of the linguistic annotation tools operating at different levels, their respective annotation schemas had to be (a) made interoperable and (b) integrated. And third, in order for the resulting annotations to suit the Semantic Web, they had to be specified by means of an ontology-based vocabulary, and structured by means of ontology-based triples, as hinted above. Therefore, a new annotation scheme had to be devised, based both on ontologies and on this type of triples, which allowed for the combination and the integration of the annotations of any set of linguistic annotation tools. This annotation scheme was considered a fundamental part of the model proposed here, and its development was, accordingly, another major objective of the present work. All these goals, aims and objectives could be re-stated more clearly as follows: Goal 1: Development of a set of ontologies for the formalisation of the linguistic knowledge relating linguistic annotation. Sub-goal 1.1: Ontological formalisation of the EAGLES (1996a; 1996b) de facto standards for morphosyntactic and syntactic annotation, in a way that helps respect the triple structure recommended for annotations in these works (which is isomorphic to the triple structures used in the context of the Semantic Web). Sub-goal 1.2: Incorporation into this preliminary ontological formalisation of other existing standards and standard proposals relating the levels mentioned above, such as those currently under development within ISO/TC 37 (the ISO Technical Committee dealing with Terminology, which deals also with linguistic resources and annotations). Sub-goal 1.3: Generalisation and extension of the recommendations in EAGLES (1996a; 1996b) and ISO/TC 37 to the semantic level, for which no ISO/TC 37 standards have been developed yet. Sub-goal 1.4: Ontological formalisation of the generalisations and/or extensions obtained in the previous sub-goal as generalisations and/or extensions of the corresponding ontology (or ontologies). Sub-goal 1.5: Ontological formalisation of the knowledge required to link, combine and unite the knowledge represented in the previously developed ontology (or ontologies). Goal 2: Development of OntoTag’s annotation scheme, a standard-based abstract scheme for the hybrid (linguistically-motivated and ontological-based) annotation of texts. Sub-goal 2.1: Development of the standard-based morphosyntactic annotation level of OntoTag’s scheme. This level should include, and possibly extend, the recommendations of EAGLES (1996a) and also the recommendations included in the ISO/MAF (2008) standard draft. Sub-goal 2.2: Development of the standard-based syntactic annotation level of the hybrid abstract scheme. This level should include, and possibly extend, the recommendations of EAGLES (1996b) and the ISO/SynAF (2010) standard draft. Sub-goal 2.3: Development of the standard-based semantic annotation level of OntoTag’s (abstract) scheme. Sub-goal 2.4: Development of the mechanisms for a convenient integration of the three annotation levels already mentioned. These mechanisms should take into account the recommendations included in the ISO/LAF (2009) standard draft. Goal 3: Design of OntoTag’s (abstract) annotation architecture, an abstract architecture for the hybrid (semantic) annotation of texts (i) that facilitates the integration and interoperation of different linguistic annotation tools, and (ii) whose results comply with OntoTag’s annotation scheme. Sub-goal 3.1: Specification of the decanting processes that allow for the classification and separation, according to their corresponding levels, of the results of the linguistic tools annotating at several different levels. Sub-goal 3.2: Specification of the standardisation processes that allow (a) complying with the standardisation requirements of OntoTag’s annotation scheme, as well as (b) combining the results of those linguistic tools that share some level of annotation. Sub-goal 3.3: Specification of the merging processes that allow for the combination of the output annotations and the interoperation of those linguistic tools that share some level of annotation. Sub-goal 3.4: Specification of the merge processes that allow for the integration of the results and the interoperation of those tools performing their annotations at different levels. Goal 4: Generation of OntoTagger’s schema, a concrete instance of OntoTag’s abstract scheme for a concrete set of linguistic annotations. These linguistic annotations result from the tools and the resources available in the research group, namely • Bitext’s DataLexica (http://www.bitext.com/EN/datalexica.asp), • LACELL’s (POS) tagger (http://www.um.es/grupos/grupo-lacell/quees.php), • Connexor’s FDG (http://www.connexor.eu/technology/machinese/glossary/fdg/), and • EuroWordNet (Vossen et al., 1998). This schema should help evaluate OntoTag’s underlying hypotheses, stated below. Consequently, it should implement, at least, those levels of the abstract scheme dealing with the annotations of the set of tools considered in this implementation. This includes the morphosyntactic, the syntactic and the semantic levels. Goal 5: Implementation of OntoTagger’s configuration, a concrete instance of OntoTag’s abstract architecture for this set of linguistic tools and annotations. This configuration (1) had to use the schema generated in the previous goal; and (2) should help support or refute the hypotheses of this work as well (see the next section). Sub-goal 5.1: Implementation of the decanting processes that facilitate the classification and separation of the results of those linguistic resources that provide annotations at several different levels (on the one hand, LACELL’s tagger operates at the morphosyntactic level and, minimally, also at the semantic level; on the other hand, FDG operates at the morphosyntactic and the syntactic levels and, minimally, at the semantic level as well). Sub-goal 5.2: Implementation of the standardisation processes that allow (i) specifying the results of those linguistic tools that share some level of annotation according to the requirements of OntoTagger’s schema, as well as (ii) combining these shared level results. In particular, all the tools selected perform morphosyntactic annotations and they had to be conveniently combined by means of these processes. Sub-goal 5.3: Implementation of the merging processes that allow for the combination (and possibly the improvement) of the annotations and the interoperation of the tools that share some level of annotation (in particular, those relating the morphosyntactic level, as in the previous sub-goal). Sub-goal 5.4: Implementation of the merging processes that allow for the integration of the different standardised and combined annotations aforementioned, relating all the levels considered. Sub-goal 5.5: Improvement of the semantic level of this configuration by adding a named entity recognition, (sub-)classification and annotation subsystem, which also uses the named entities annotated to populate a domain ontology, in order to provide a concrete application of the present work in the two areas involved (the Semantic Web and Corpus Linguistics). 3. MAIN RESULTS: ASSESSMENT OF ONTOTAG’S UNDERLYING HYPOTHESES The model developed in the present thesis tries to shed some light on (i) whether linguistic annotation tools can effectively interoperate; (ii) whether their results can be combined and integrated; and, if they can, (iii) how they can, respectively, interoperate and be combined and integrated. Accordingly, several hypotheses had to be supported (or rejected) by the development of the OntoTag model and OntoTagger (its implementation). The hypotheses underlying OntoTag are surveyed below. Only one of the hypotheses (H.6) was rejected; the other five could be confirmed. H.1 The annotations of different levels (or layers) can be integrated into a sort of overall, comprehensive, multilayer and multilevel annotation, so that their elements can complement and refer to each other. • CONFIRMED by the development of: o OntoTag’s annotation scheme, o OntoTag’s annotation architecture, o OntoTagger’s (XML, RDF, OWL) annotation schemas, o OntoTagger’s configuration. H.2 Tool-dependent annotations can be mapped onto a sort of tool-independent annotations and, thus, can be standardised. • CONFIRMED by means of the standardisation phase incorporated into OntoTag and OntoTagger for the annotations yielded by the tools. H.3 Standardisation should ease: H.3.1: The interoperation of linguistic tools. H.3.2: The comparison, combination (at the same level and layer) and integration (at different levels or layers) of annotations. • H.3 was CONFIRMED by means of the development of OntoTagger’s ontology-based configuration: o Interoperation, comparison, combination and integration of the annotations of three different linguistic tools (Connexor’s FDG, Bitext’s DataLexica and LACELL’s tagger); o Integration of EuroWordNet-based, domain-ontology-based and named entity annotations at the semantic level. o Integration of morphosyntactic, syntactic and semantic annotations. H.4 Ontologies and Semantic Web technologies (can) play a crucial role in the standardisation of linguistic annotations, by providing consensual vocabularies and standardised formats for annotation (e.g., RDF triples). • CONFIRMED by means of the development of OntoTagger’s RDF-triple-based annotation schemas. H.5 The rate of errors introduced by a linguistic tool at a given level, when annotating, can be reduced automatically by contrasting and combining its results with the ones coming from other tools, operating at the same level. However, these other tools might be built following a different technological (stochastic vs. rule-based, for example) or theoretical (dependency vs. HPS-grammar-based, for instance) approach. • CONFIRMED by the results yielded by the evaluation of OntoTagger. H.6 Each linguistic level can be managed and annotated independently. • REJECTED: OntoTagger’s experiments and the dependencies observed among the morphosyntactic annotations, and between them and the syntactic annotations. In fact, Hypothesis H.6 was already rejected when OntoTag’s ontologies were developed. We observed then that several linguistic units stand on an interface between levels, belonging thereby to both of them (such as morphosyntactic units, which belong to both the morphological level and the syntactic level). Therefore, the annotations of these levels overlap and cannot be handled independently when merged into a unique multileveled annotation. 4. OTHER MAIN RESULTS AND CONTRIBUTIONS First, interoperability is a hot topic for both the linguistic annotation community and the whole Computer Science field. The specification (and implementation) of OntoTag’s architecture for the combination and integration of linguistic (annotation) tools and annotations by means of ontologies shows a way to make these different linguistic annotation tools and annotations interoperate in practice. Second, as mentioned above, the elements involved in linguistic annotation were formalised in a set (or network) of ontologies (OntoTag’s linguistic ontologies). • On the one hand, OntoTag’s network of ontologies consists of − The Linguistic Unit Ontology (LUO), which includes a mostly hierarchical formalisation of the different types of linguistic elements (i.e., units) identifiable in a written text; − The Linguistic Attribute Ontology (LAO), which includes also a mostly hierarchical formalisation of the different types of features that characterise the linguistic units included in the LUO; − The Linguistic Value Ontology (LVO), which includes the corresponding formalisation of the different values that the attributes in the LAO can take; − The OIO (OntoTag’s Integration Ontology), which  Includes the knowledge required to link, combine and unite the knowledge represented in the LUO, the LAO and the LVO;  Can be viewed as a knowledge representation ontology that describes the most elementary vocabulary used in the area of annotation. • On the other hand, OntoTag’s ontologies incorporate the knowledge included in the different standards and recommendations for linguistic annotation released so far, such as those developed within the EAGLES and the SIMPLE European projects or by the ISO/TC 37 committee: − As far as morphosyntactic annotations are concerned, OntoTag’s ontologies formalise the terms in the EAGLES (1996a) recommendations and their corresponding terms within the ISO Morphosyntactic Annotation Framework (ISO/MAF, 2008) standard; − As for syntactic annotations, OntoTag’s ontologies incorporate the terms in the EAGLES (1996b) recommendations and their corresponding terms within the ISO Syntactic Annotation Framework (ISO/SynAF, 2010) standard draft; − Regarding semantic annotations, OntoTag’s ontologies generalise and extend the recommendations in EAGLES (1996a; 1996b) and, since no stable standards or standard drafts have been released for semantic annotation by ISO/TC 37 yet, they incorporate the terms in SIMPLE (2000) instead; − The terms coming from all these recommendations and standards were supplemented by those within the ISO Data Category Registry (ISO/DCR, 2008) and also of the ISO Linguistic Annotation Framework (ISO/LAF, 2009) standard draft when developing OntoTag’s ontologies. Third, we showed that the combination of the results of tools annotating at the same level can yield better results (both in precision and in recall) than each tool separately. In particular, 1. OntoTagger clearly outperformed two of the tools integrated into its configuration, namely DataLexica and FDG in all the combination sub-phases in which they overlapped (i.e. POS tagging, lemma annotation and morphological feature annotation). As far as the remaining tool is concerned, i.e. LACELL’s tagger, it was also outperformed by OntoTagger in POS tagging and lemma annotation, and it did not behave better than OntoTagger in the morphological feature annotation layer. 2. As an immediate result, this implies that a) This type of combination architecture configurations can be applied in order to improve significantly the accuracy of linguistic annotations; and b) Concerning the morphosyntactic level, this could be regarded as a way of constructing more robust and more accurate POS tagging systems. Fourth, Semantic Web annotations are usually performed by humans or else by machine learning systems. Both of them leave much to be desired: the former, with respect to their annotation rate; the latter, with respect to their (average) precision and recall. In this work, we showed how linguistic tools can be wrapped in order to annotate automatically Semantic Web pages using ontologies. This entails their fast, robust and accurate semantic annotation. As a way of example, as mentioned in Sub-goal 5.5, we developed a particular OntoTagger module for the recognition, classification and labelling of named entities, according to the MUC and ACE tagsets (Chinchor, 1997; Doddington et al., 2004). These tagsets were further specified by means of a domain ontology, namely the Cinema Named Entities Ontology (CNEO). This module was applied to the automatic annotation of ten different web pages containing cinema reviews (that is, around 5000 words). In addition, the named entities annotated with this module were also labelled as instances (or individuals) of the classes included in the CNEO and, then, were used to populate this domain ontology. • The statistical results obtained from the evaluation of this particular module of OntoTagger can be summarised as follows. On the one hand, as far as recall (R) is concerned, (R.1) the lowest value was 76,40% (for file 7); (R.2) the highest value was 97, 50% (for file 3); and (R.3) the average value was 88,73%. On the other hand, as far as the precision rate (P) is concerned, (P.1) its minimum was 93,75% (for file 4); (R.2) its maximum was 100% (for files 1, 5, 7, 8, 9, and 10); and (R.3) its average value was 98,99%. • These results, which apply to the tasks of named entity annotation and ontology population, are extraordinary good for both of them. They can be explained on the basis of the high accuracy of the annotations provided by OntoTagger at the lower levels (mainly at the morphosyntactic level). However, they should be conveniently qualified, since they might be too domain- and/or language-dependent. It should be further experimented how our approach works in a different domain or a different language, such as French, English, or German. • In any case, the results of this application of Human Language Technologies to Ontology Population (and, accordingly, to Ontological Engineering) seem very promising and encouraging in order for these two areas to collaborate and complement each other in the area of semantic annotation. Fifth, as shown in the State of the Art of this work, there are different approaches and models for the semantic annotation of texts, but all of them focus on a particular view of the semantic level. Clearly, all these approaches and models should be integrated in order to bear a coherent and joint semantic annotation level. OntoTag shows how (i) these semantic annotation layers could be integrated together; and (ii) they could be integrated with the annotations associated to other annotation levels. Sixth, we identified some recommendations, best practices and lessons learned for annotation standardisation, interoperation and merge. They show how standardisation (via ontologies, in this case) enables the combination, integration and interoperation of different linguistic tools and their annotations into a multilayered (or multileveled) linguistic annotation, which is one of the hot topics in the area of Linguistic Annotation. And last but not least, OntoTag’s annotation scheme and OntoTagger’s annotation schemas show a way to formalise and annotate coherently and uniformly the different units and features associated to the different levels and layers of linguistic annotation. This is a great scientific step ahead towards the global standardisation of this area, which is the aim of ISO/TC 37 (in particular, Subcommittee 4, dealing with the standardisation of linguistic annotations and resources).

Metodología de Diseño y Análisis de Sistemas Teleoperados Considerando Dinámica No Lineal

Cuando la separación física entre el sistema local y remoto es relativamente corta, el retardo no es perceptible; sin embargo, cuando el manipulador local y el manipulador remoto se encuentran a una distancia lejana uno del otro, el retardo de tiempo ya no es insignificante e influye negativamente en la realización de la tarea. El retardo de tiempo en un sistema de control introduce un atraso de fase que a su vez degrada el rendimiento del sistema y puede causar inestabilidad. Los sistemas de teleoperación pueden sacar provecho de la posibilidad de estar presente en dos lugares simultáneamente, sin embargo, el uso de Internet y otras redes de conmutación de paquetes, tales como Internet2, impone retardos de tiempo variables, haciendo que los esquemas de control ya establecidos elaboren soluciones para hacer frente a inestabilidades causadas por estos retardos de tiempo variables. En este trabajo de tesis se presenta el modelado y análisis de un sistema de teloperación bilateral no lineal de n grados de libertad controlado por convergencia de estado. La comunicación entre el sitio local y remoto se realiza mediante un canal de comunicación con retardo de tiempo. El análisis presentado en este trabajo considera que el retardo puede ser constante o variable. Los principales objetivos de este trabajo son; 1) Desarrollar una arquitectura de control no lineal garantizando la estabilidad del sistema teleoperado, 2) Evaluar la estabilidad del sistema considerando el retardo en la comunicación, y 3) Implementación de los algoritmos desarrollados para probar el desempeño de los mismos en un sistema experimental de 3 grados de libertad. A través de la teoría de Estabilidad de Lyapunov y el funcional Lyapunov-Krasovskii, se demuestra que el sistema de lazo cerrado es asintóticamente estable. Estas conclusiones de estabilidad se han obtenido mediante la integración de la función de Lyapunov y aplicando el Lema de Barbalat. Se demuestra también que se logra sincronizar las posiciones del manipulador local y remoto cuando el operador humano no mueve el manipulador local y el manipulador remoto se mueve libremente. El esquema de control propuesto se ha validado mediante simulación y en forma experimental empleando un sistema de teleoperación real desarrollado en esta tesis doctoral y que consta de un un manipulador serie planar de tres grados de libertad, un manipulador local, PHANTOM Omni, el cual es un dispositivo haptico fabricado que consta de 3 grados de libertad (en fuerza) y que proporciona realimentación de fuerza en los ejes x,y,z. El control en tiempo real se ha diseñado usando el Sistema Operativo en Tiempo Real QuaRC de QUARC en el lado local y el Simulink Real-Time Windows TargetTM en el lado remoto. Para finalizar el resumen se destaca el impacto de esta tesis en el mundo científico a través de los resultados publicados: 2 artículos en revistas con índice de impacto , 1 artículo en una revista indexada en Sistemas, Cibernética e Informática, 7 artículos en congresos y ha obtenido un premio en la 9a. Conferencia Iberoamericana en Sistemas, Cibernética e Informática, 2010. ABSTRACT When the physical separation between the local and remote system is relatively short, the delay is not noticeable; however, when the local manipulator and the remote manipulator are at a far distance from each other, the time delay is no longer negligible and negatively influences the performance of the task. The time delay in a control system introduces a phase delay which in turn degrades the system performance and cause instability. Teleoperation systems can benefit from the ability to be in two places simultaneously, however, the use of Internet and other packet switched networks, such as Internet2, imposes varying time delays, making established control schemes to develop solutions to address these instabilities caused by different time delays. In this thesis work we present a modeling and analysis of a nonlinear bilateral teloperation system of n degrees of freedom controlled by state convergence strategy. Communication between the local and remote site is via a communication channel with time delay. The analysis presented in this work considers that the time-delay can be constant or variable. The main objectives of this work are; 1) Develop a nonlinear control schemes to ensure the stability of the teleoperated system, 2) Evaluate the system stability considering the delay in communication, and 3) Implementation of algorithms developed to test the performance of the teleoperation system in an experimental system of 3 degrees of freedom. Through the Theory of Stability of Lyapunov and the functional Lyapunov-Krasovskii, one demonstrates that the closed loop system is asymptotically stable.. The conclusions about stability were obtained by integration of the Lyapunov function and applying Barbalat Lemma. It further shows that the positions of the local and remote manipulator are synchronize when the human operator stops applying a constant force and the remote manipulator does not interact with the environment. The proposed control scheme has been validated by means of simulation and in experimental form using a developed system of real teleoperation in this doctoral thesis, which consists of a series planar manipulator of three degrees of freedom, a local manipulator, PHANTOM Omni, which is an haptic device that consists of 3 degrees of freedom (in force) and that provide feeback force in x-axis, and, z. The control in real time has been designed using the Operating system in Real time QuaRC of Quanser in the local side and the Simulink Real-Time Windows Target in the remote side. In order to finalize the summary, the highlights impact of this thesis in the scientific world are shows through the published results: 2 articles in Journals with impact factor, one article in a indexed Journal on Systemics, Cybernetics and Informatics, 7 articles in Conferences and has won an award in 9a. Conferencia Iberoamericana en Sistemas, Cibernética e Informática, 2010.