{"title":"Symbolic models for nonlinear control systems affected by disturbances","authors":"A. Borri, G. Pola, M. D. Benedetto","doi":"10.1080/00207179.2012.686672","DOIUrl":"https://doi.org/10.1080/00207179.2012.686672","url":null,"abstract":"Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for analysis and synthesis of complex systems. In fact, symbolic models enable the use of well known algorithms in the context of supervisory control and algorithmic game theory, for controller synthesis. Since the 1990s many researchers faced the problem of identifying classes of dynamical and control systems that admit symbolic models. In this paper we make further progress along this research line by focusing on control systems affected by disturbances. Our main contribution is to show that incrementally globally asymptotically stable nonlinear control systems with disturbances admit symbolic models. When specializing these results to linear systems, we show that these symbolic models can be easily constructed.","PeriodicalId":433215,"journal":{"name":"2008 47th IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130713264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Pathirana, A. Bishop, A. Savkin, S. Ekanayake, T. Black
{"title":"A method for stereo-vision based tracking for robotic applications","authors":"P. Pathirana, A. Bishop, A. Savkin, S. Ekanayake, T. Black","doi":"10.1017/S0263574709005827","DOIUrl":"https://doi.org/10.1017/S0263574709005827","url":null,"abstract":"Vision based tracking of an object using the ideas of perspective projection inherently consists of nonlinearly modelled measurements although the underlying dynamic system that encompasses the object and the vision sensors can be linear. Based on a necessary stereo vision setting, we introduce an appropriate measurement conversion techniques which subsequently facilitate using a linear filter. Linear filter together with the aforementioned measurement conversion approach conforms a robust linear filter that is based on the set values state estimation ideas; a particularly rich area in the robust control literature. We provide a rigorously theoretical analysis to ensure bounded state estimation errors formulated in terms of an ellipsoidal set in which the actual state is guaranteed to be included to an arbitrary high probability. Using computer simulations as well as a practical implementation consisting of a robotic manipulator, we demonstrate our linear robust filter significantly outperforms the traditionally used extended Kalman filter under this stereo vision scenario.","PeriodicalId":433215,"journal":{"name":"2008 47th IEEE Conference on Decision and Control","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114199331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Coprime factor model reduction for continuous-time uncertain systems","authors":"Li Li","doi":"10.1109/CDC.2008.4738772","DOIUrl":"https://doi.org/10.1109/CDC.2008.4738772","url":null,"abstract":"The paper considers the problem of coprime factor model reduction for a class of continuous-time uncertain systems with structured norm bounded uncertainty. The proposed method is applicable to the uncertain systems which may be robustly unstable, overcoming the robust stability restriction in the balanced truncation approach. A systematic approach is presented to construct a contractive coprime factor for the underlying uncertain system, based on the use of LMIs. This enables the balanced truncation to be applied to the contractive coprime factor to obtain the reduced uncertain system. Error bound on the L2-induced norm of the resulting coprime factor is derived.","PeriodicalId":433215,"journal":{"name":"2008 47th IEEE Conference on Decision and Control","volume":"281 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131474193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bahman Tahayori, L. Johnston, I. Mareels, P. Farrell
{"title":"Revisiting the Bloch equation through averaging","authors":"Bahman Tahayori, L. Johnston, I. Mareels, P. Farrell","doi":"10.1109/CDC.2008.4739243","DOIUrl":"https://doi.org/10.1109/CDC.2008.4739243","url":null,"abstract":"A novel approach to finding an approximate analytic solution to the Bloch equation is developed in this paper. The method is based on time scaling and averaging of the Bloch equation after transformation to a rotating frame of reference. In order to accomplish the scaling, a novel time scaled magnetisation vector is introduced. The resultant time scaled system is subsequently approximated through averaging, a technique that to the best of our knowledge, has not previously been applied in the nuclear magnetic resonance context. Our proposed method of approximating the solution to the Bloch equation is valid for continuous wave excitation as well as the traditional pulse excitation with an arbitrary envelope, making this a widely applicable technique unlike previously proposed methods. Comparison of the approximate analytic solution and simulation results clearly indicates that the error is negligible when the field inhomogeneities are small compared to the excitation field amplitude. Extremum seeking techniques may be applied to determine the optimal excitation, given the form of the approximate solution. This result is applicable to a range of research areas including nuclear magnetic resonance, magnetic resonance imaging and optical resonance problems.","PeriodicalId":433215,"journal":{"name":"2008 47th IEEE Conference on Decision and Control","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132669729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Gain bounds for multiple model switched adaptive control of general MIMO LTI systems","authors":"D. Buchstaller, M. French","doi":"10.1109/CDC.2008.4738838","DOIUrl":"https://doi.org/10.1109/CDC.2008.4738838","url":null,"abstract":"For the class of MIMO minimal LTI systems controlled by an estimation based multiple model switched adaptive controller (EMMSAC), bounds are obtained for the closed loop lp gain, 1 ¿ p ¿ ¿, from the input and output disturbances to the internal signals.","PeriodicalId":433215,"journal":{"name":"2008 47th IEEE Conference on Decision and Control","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117008316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Construction of Lyapunov-Krasovskii functional for time-varying delay systems","authors":"Yassine Ariba, F. Gouaisbaut","doi":"10.1109/CDC.2008.4738942","DOIUrl":"https://doi.org/10.1109/CDC.2008.4738942","url":null,"abstract":"This paper provides some new techniques to construct a Lyapunov-Krasovskii functional for time varying delay systems. The construction is based on a partitioning scheme of the time-varying delay leading to a new type of Lyapunov-Krasovskii functional. This functional is depending on an augmented state and also on an integral quadratic constraint added to reduce the conservatism of the proposed methodology. This approach is then extended to the robust case. Finally, some examples support our approach.","PeriodicalId":433215,"journal":{"name":"2008 47th IEEE Conference on Decision and Control","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121266782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Using polynomial semi-separable kernels to construct infinite-dimensional Lyapunov functions","authors":"M. Peet, A. Papachristodoulou","doi":"10.1109/CDC.2008.4739245","DOIUrl":"https://doi.org/10.1109/CDC.2008.4739245","url":null,"abstract":"In this paper, we introduce the class of semi-separable kernel functions for use in constructing Lyapunov functions for distributed-parameter systems such as delay-differential equations. We then consider the subset of semi-separable kernel functions defined by polynomials. We show that the set of such kernels which define positive forms can be parameterized by positive semidefinite matrices. In the particular case of linear time-delay systems, we show how to construct the derivative of Lyapunov functions defined by piecewise continuous semi-separable kernels and give numerical examples which illustrate some advantages over standard polynomial kernel functions.","PeriodicalId":433215,"journal":{"name":"2008 47th IEEE Conference on Decision and Control","volume":"292 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126019471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust synchronization in networks of cyclic feedback systems","authors":"A. Hamadeh, G. Stan, J. Gonçalves","doi":"10.1109/CDC.2008.4739052","DOIUrl":"https://doi.org/10.1109/CDC.2008.4739052","url":null,"abstract":"This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The result uses incremental versions of the small gain theorem and dissipativity theory to arrive at an upper bound on the norm of the synchronization error between corresponding states, giving a measure of the degree of convergence of the solutions. This error bound is shown to be a function of the difference between the parameters of the interconnected systems, and disappears in the case where the systems are identical, thus retrieving an earlier synchronization result.","PeriodicalId":433215,"journal":{"name":"2008 47th IEEE Conference on Decision and Control","volume":"186 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121268933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Howes, L. Eccleston, J. Gonçalves, G. Stan, S. Warnick
{"title":"Dynamical structure analysis of sparsity and minimality heuristics for reconstruction of biochemical networks","authors":"R. Howes, L. Eccleston, J. Gonçalves, G. Stan, S. Warnick","doi":"10.1109/CDC.2008.4739364","DOIUrl":"https://doi.org/10.1109/CDC.2008.4739364","url":null,"abstract":"Network reconstruction, i.e. obtaining network structure from input-output information, is a central theme in systems biology. A variety of approaches aim to obtaining structural information from available data. Previous work has introduced dynamical structure functions as a tool for posing and solving the network reconstruction problem. Even for linear time invariant systems, reconstruction requires specific additional information not generated in the typical system identification process. This paper demonstrates that such extra information can be obtained through a limited sequence of system identification experiments on structurally modified systems, analogous to gene silencing and overexpression experiments. In the absence of such extra information, we discuss whether combined assumptions of network sparsity and minimality contribute to the recovery of the network dynamical structure. We provide sufficient conditions for a transfer function to have a completely decoupled minimal realization, and demonstrate that every transfer function is arbitrarily close to one that admits a perfectly decoupled minimal realization. This indicates that the assumptions of sparsity and minimality alone do not lend insight into the network structure.","PeriodicalId":433215,"journal":{"name":"2008 47th IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132943230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrea Lecchini-Visintini, J. Lygeros, J. Maciejowski
{"title":"On the approximate domain optimization of deterministic and expected value criteria","authors":"Andrea Lecchini-Visintini, J. Lygeros, J. Maciejowski","doi":"10.1109/CDC.2008.4738753","DOIUrl":"https://doi.org/10.1109/CDC.2008.4738753","url":null,"abstract":"We define the concept of approximate domain optimizer for deterministic and expected value optimization criteria. Roughly speaking, a candidate optimizer is an approximate domain optimizer if only a small fraction of the optimization domain is more than a little better than it. We show how this concept relates to commonly used approximate optimizer notions for the case of Lipschitz criteria. We then show how random extractions from an appropriate probability distribution can generate approximate domain optimizers with high confidence. Finally, we discuss how such random extractions can be performed using Markov Chain Monte Carlo methods.","PeriodicalId":433215,"journal":{"name":"2008 47th IEEE Conference on Decision and Control","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124553202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}