Pub Date : 2009-01-13DOI: 10.1109/TAC.2008.2009485
A. Wills, B. Ninness, S. Gibson
This paper addresses the problem of estimating linear time invariant models from observed frequency domain data. Here an emphasis is placed on deriving numerically robust and efficient methods that can reliably deal with high order models over wide bandwidths. This involves a novel application of the Expectation-Maximisation (EM) algorithm in order to find Maximum Likelihood estimates of state space structures. An empirical study using both simulated and real measurement data is presented to illustrate the efficacy of the EM-based method derived here.
{"title":"Maximum Likelihood estimation of state space models from frequency domain data","authors":"A. Wills, B. Ninness, S. Gibson","doi":"10.1109/TAC.2008.2009485","DOIUrl":"https://doi.org/10.1109/TAC.2008.2009485","url":null,"abstract":"This paper addresses the problem of estimating linear time invariant models from observed frequency domain data. Here an emphasis is placed on deriving numerically robust and efficient methods that can reliably deal with high order models over wide bandwidths. This involves a novel application of the Expectation-Maximisation (EM) algorithm in order to find Maximum Likelihood estimates of state space structures. An empirical study using both simulated and real measurement data is presented to illustrate the efficacy of the EM-based method derived here.","PeriodicalId":407048,"journal":{"name":"2007 European Control Conference (ECC)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133387869","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}
The output feedback H∞ control is addressed for a class of continuous-time Markov jump linear systems with the Markov process taking values in an infinite countable set S. We consider that only an output and the jump parameters are available to the controller. Via a certain Bounded Real Lemma, together with some extensions of Schur complements and of the Projection Lemma, a theorem which characterizes whether there exist or not a full-order solution to the disturbance attenuation problem is devised in terms of two different Linear Matrix Inequality (LMI) feasibility problems. This result connects the so-called projective approach to an LMI problem which is more amenable to computer solution, and hence for design. We conclude the paper with two design algorithms for the construction of such controllers.
{"title":"Output feedback H∞ control of continuous-time infinite Markovian jump linear systems via LMI methods","authors":"M. Todorov, M. Fragoso","doi":"10.1137/060675162","DOIUrl":"https://doi.org/10.1137/060675162","url":null,"abstract":"The output feedback H∞ control is addressed for a class of continuous-time Markov jump linear systems with the Markov process taking values in an infinite countable set S. We consider that only an output and the jump parameters are available to the controller. Via a certain Bounded Real Lemma, together with some extensions of Schur complements and of the Projection Lemma, a theorem which characterizes whether there exist or not a full-order solution to the disturbance attenuation problem is devised in terms of two different Linear Matrix Inequality (LMI) feasibility problems. This result connects the so-called projective approach to an LMI problem which is more amenable to computer solution, and hence for design. We conclude the paper with two design algorithms for the construction of such controllers.","PeriodicalId":407048,"journal":{"name":"2007 European Control Conference (ECC)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116758469","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}
Pub Date : 2007-10-01DOI: 10.1109/WISP.2007.4447643
L. Ángel, J. M. Sebastián, A. Traslosheros, F. Roberti, R. Carelli
This paper describes the visual control of a parallel robot called “RoboTenis”. The system has been designed and built in order to carry out tasks in three dimensions and dynamical environments, thus the system is capable to interact with objects which move up to 1m/s. The control strategy is composed by two intertwined control loops: The internal loop is faster and considers the information from the joins, its sample time is 0.5 ms. Second loop represents the visual servoing system which is external loop to the first mentioned, second loop represents the study purpose, that it is based in the prediction of the object velocity which is obtained form visual information and its sample time is 8.3 ms. Lyapunov stability analysis, system delays and saturation components has been taken into account.
{"title":"Visual servoing of a parallel robot system","authors":"L. Ángel, J. M. Sebastián, A. Traslosheros, F. Roberti, R. Carelli","doi":"10.1109/WISP.2007.4447643","DOIUrl":"https://doi.org/10.1109/WISP.2007.4447643","url":null,"abstract":"This paper describes the visual control of a parallel robot called “RoboTenis”. The system has been designed and built in order to carry out tasks in three dimensions and dynamical environments, thus the system is capable to interact with objects which move up to 1m/s. The control strategy is composed by two intertwined control loops: The internal loop is faster and considers the information from the joins, its sample time is 0.5 ms. Second loop represents the visual servoing system which is external loop to the first mentioned, second loop represents the study purpose, that it is based in the prediction of the object velocity which is obtained form visual information and its sample time is 8.3 ms. Lyapunov stability analysis, system delays and saturation components has been taken into account.","PeriodicalId":407048,"journal":{"name":"2007 European Control Conference (ECC)","volume":"158 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116325641","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}
Pub Date : 2007-07-09DOI: 10.1109/ACC.2007.4282698
Masayuki Sato, D. Peaucelle
This note addresses the comparison between Sums-Of-Squares (SOS) approach and Slack Variable (SV) approach for the non-negativity check of multiple variable polynomial functions. In the process to compare these methods, we derive a new method of SV approach with use of multiple slack variables, which encompasses the previously proposed method of SV approach with use of a single slack variable. The obtained result is as follows: For the unbounded case, SOS approach and our new SV approach are equivalent; for the bounded case, our new SV approach is less conservative with increased number of decision variables compared to SOS approach. Several numerical examples are shown to illustrate our conclusions.
{"title":"Comparison between SOS approach and Slack Variable approach for non-negativity check of polynomial functions: Multiple variable case","authors":"Masayuki Sato, D. Peaucelle","doi":"10.1109/ACC.2007.4282698","DOIUrl":"https://doi.org/10.1109/ACC.2007.4282698","url":null,"abstract":"This note addresses the comparison between Sums-Of-Squares (SOS) approach and Slack Variable (SV) approach for the non-negativity check of multiple variable polynomial functions. In the process to compare these methods, we derive a new method of SV approach with use of multiple slack variables, which encompasses the previously proposed method of SV approach with use of a single slack variable. The obtained result is as follows: For the unbounded case, SOS approach and our new SV approach are equivalent; for the bounded case, our new SV approach is less conservative with increased number of decision variables compared to SOS approach. Several numerical examples are shown to illustrate our conclusions.","PeriodicalId":407048,"journal":{"name":"2007 European Control Conference (ECC)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130995203","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}
Pub Date : 2007-07-05DOI: 10.23919/ECC.2007.7068319
J. Biggs, W. Holderbaum
In this paper we study constrained optimal control problems on semi-simple Lie groups. These constrained optimal control problems include Riemannian, sub-Riemannian, elastic and mechanical problems. We begin by lifting these problems, through the Maximum Principle, to their associated Hamiltonian formalism. As the base manifold is a Lie group G the cotangent bundle is realized as the direct product G×g* where g* is the dual of the Lie algebra g of G. The solutions to these Hamiltonian vector fields l ∈ g*, are called extremal curves and the projections g(t) ∈ G are the corresponding optimal solutions. The main contribution of this paper is a method for deriving explicit expressions relating the extremal curves l ∈ g* to the optimal solutions g(t) ∈ G for the special cases of the Lie groups SO(4) and SO(1,3). This method uses the double cover property of these Lie groups to decouple them into lower dimensional systems. These lower dimensional systems are then solved in terms of the extremals using a coordinate representation and the systems dynamic constraints. This illustrates that the optimal solutions g(t) ∈ G are explicitly dependent on the extremal curves.
{"title":"Integrating Hamiltonian systems defined on the Lie groups SO(4) and SO(1,3)","authors":"J. Biggs, W. Holderbaum","doi":"10.23919/ECC.2007.7068319","DOIUrl":"https://doi.org/10.23919/ECC.2007.7068319","url":null,"abstract":"In this paper we study constrained optimal control problems on semi-simple Lie groups. These constrained optimal control problems include Riemannian, sub-Riemannian, elastic and mechanical problems. We begin by lifting these problems, through the Maximum Principle, to their associated Hamiltonian formalism. As the base manifold is a Lie group G the cotangent bundle is realized as the direct product G×g* where g* is the dual of the Lie algebra g of G. The solutions to these Hamiltonian vector fields l ∈ g*, are called extremal curves and the projections g(t) ∈ G are the corresponding optimal solutions. The main contribution of this paper is a method for deriving explicit expressions relating the extremal curves l ∈ g* to the optimal solutions g(t) ∈ G for the special cases of the Lie groups SO(4) and SO(1,3). This method uses the double cover property of these Lie groups to decouple them into lower dimensional systems. These lower dimensional systems are then solved in terms of the extremals using a coordinate representation and the systems dynamic constraints. This illustrates that the optimal solutions g(t) ∈ G are explicitly dependent on the extremal curves.","PeriodicalId":407048,"journal":{"name":"2007 European Control Conference (ECC)","volume":"24 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128449992","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}
Pub Date : 2007-07-02DOI: 10.23919/ECC.2007.7068822
N. Faísca, K. I. Kouramas, E. Pistikopoulos
This paper presents a new algorithm for multi-stage decision problems with hard constraints. The algorithm is based upon the concepts of dynamic programming and multi-parametric programming. The multi-stage problem is considered within a framework of dynamic programming where each echelon of problem is formulated and solved as a multi-parametric program. The state-space of a given stage constitutes the parametric space whereas the state-space of the next stage represents the space of control or optimisation variables. The solution of the resulting multi-parametric program is given by the control or the optimization variables as a set of explicit functions of the parameters. The dynamic recursive nature of the multi-stage problem is preserved and a set of sequential and simpler multi-parametric programs which are constrained by a reduced number of inequalities is obtained. This results in a reduction in the complexity of the overall problem. The underlying theory is described in detail and numerical examples are presented to illustrate the potential of this new approach.
{"title":"A dynamic programming approach for constrained multi-stage problems via multi-parametric programming","authors":"N. Faísca, K. I. Kouramas, E. Pistikopoulos","doi":"10.23919/ECC.2007.7068822","DOIUrl":"https://doi.org/10.23919/ECC.2007.7068822","url":null,"abstract":"This paper presents a new algorithm for multi-stage decision problems with hard constraints. The algorithm is based upon the concepts of dynamic programming and multi-parametric programming. The multi-stage problem is considered within a framework of dynamic programming where each echelon of problem is formulated and solved as a multi-parametric program. The state-space of a given stage constitutes the parametric space whereas the state-space of the next stage represents the space of control or optimisation variables. The solution of the resulting multi-parametric program is given by the control or the optimization variables as a set of explicit functions of the parameters. The dynamic recursive nature of the multi-stage problem is preserved and a set of sequential and simpler multi-parametric programs which are constrained by a reduced number of inequalities is obtained. This results in a reduction in the complexity of the overall problem. The underlying theory is described in detail and numerical examples are presented to illustrate the potential of this new approach.","PeriodicalId":407048,"journal":{"name":"2007 European Control Conference (ECC)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114972636","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}
Pub Date : 2007-07-02DOI: 10.23919/ECC.2007.7068302
Gareth Lee, Parisa A. Bahri, S. Shastri, Anthony Zaknich
The paper investigates the feasibility of developing a classification framework, based on support vector machines, with the correct properties to act as a decision support system for an industrial process plant, such as the Tennessee Eastman process. The system would provide support to the technicians who monitor plants by signalling the occurrence of abnormal plant measurements marking the onset of a fault condition. To be practical such a system must meet strict standards, in terms of low detection latency, a very low rate of false positive detection and high classification accuracy. Experiments were conducted on examples generated by a simulation of the Tennessee Eastman process and these were preprocessed and classified using a support vector machine. Experiments also considered the efficacy of preprocessing observations using Fisher Discriminant Analysis and a strategy for combining the decisions from a bank of classifiers to improve accuracy when dealing with multiple fault categories.
{"title":"A multi-category decision support framework for the Tennessee Eastman problem","authors":"Gareth Lee, Parisa A. Bahri, S. Shastri, Anthony Zaknich","doi":"10.23919/ECC.2007.7068302","DOIUrl":"https://doi.org/10.23919/ECC.2007.7068302","url":null,"abstract":"The paper investigates the feasibility of developing a classification framework, based on support vector machines, with the correct properties to act as a decision support system for an industrial process plant, such as the Tennessee Eastman process. The system would provide support to the technicians who monitor plants by signalling the occurrence of abnormal plant measurements marking the onset of a fault condition. To be practical such a system must meet strict standards, in terms of low detection latency, a very low rate of false positive detection and high classification accuracy. Experiments were conducted on examples generated by a simulation of the Tennessee Eastman process and these were preprocessed and classified using a support vector machine. Experiments also considered the efficacy of preprocessing observations using Fisher Discriminant Analysis and a strategy for combining the decisions from a bank of classifiers to improve accuracy when dealing with multiple fault categories.","PeriodicalId":407048,"journal":{"name":"2007 European Control Conference (ECC)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115134835","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}
Pub Date : 2007-07-02DOI: 10.23919/ECC.2007.7068899
S. Lopes, F. Fontes
The main purpose of necessary conditions of optimality (NCO) is to identify a `small' set of candidates to minimizers among the overall set of admissible solutions. However, for certain optimal control problems with state constraints, it might happen that the set of all admissible solutions coincides with the set of candidates satisfying the NCO. This phenomenon is known as the degeneracy phenomenon and there has been some literature proposing stronger forms of NCO that can be informative in such cases: the so-called nondegenerate NCO. The nondegenerate NCO proposed here are valid under a different set of hypothesis and under a constraint qualification of an integral-type that, in relation to some previous literature, is easier to verify.
{"title":"Nondegenerate necessary conditions for optimal control problem with state constraints: Integral-type constraint qualification","authors":"S. Lopes, F. Fontes","doi":"10.23919/ECC.2007.7068899","DOIUrl":"https://doi.org/10.23919/ECC.2007.7068899","url":null,"abstract":"The main purpose of necessary conditions of optimality (NCO) is to identify a `small' set of candidates to minimizers among the overall set of admissible solutions. However, for certain optimal control problems with state constraints, it might happen that the set of all admissible solutions coincides with the set of candidates satisfying the NCO. This phenomenon is known as the degeneracy phenomenon and there has been some literature proposing stronger forms of NCO that can be informative in such cases: the so-called nondegenerate NCO. The nondegenerate NCO proposed here are valid under a different set of hypothesis and under a constraint qualification of an integral-type that, in relation to some previous literature, is easier to verify.","PeriodicalId":407048,"journal":{"name":"2007 European Control Conference (ECC)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115163479","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}
Pub Date : 2007-07-02DOI: 10.23919/ECC.2007.7069070
P. Albertos
This Panel session aims to discuss some issues about the so-called Intelligent control, these control architectures based on the use of Artificial Intelligence (and more recently denoted under the general umbrella of Soft Computing) techniques. The first problem is the definition of the term itself, and the second problem is the variety of alternatives, broadening the scope of the session. Thus, the discussion will be certainly biased by the Panelists' preferences. The audience could motivate the inclusion of additional topics.
{"title":"Lights and shadows of the Intelligent control","authors":"P. Albertos","doi":"10.23919/ECC.2007.7069070","DOIUrl":"https://doi.org/10.23919/ECC.2007.7069070","url":null,"abstract":"This Panel session aims to discuss some issues about the so-called Intelligent control, these control architectures based on the use of Artificial Intelligence (and more recently denoted under the general umbrella of Soft Computing) techniques. The first problem is the definition of the term itself, and the second problem is the variety of alternatives, broadening the scope of the session. Thus, the discussion will be certainly biased by the Panelists' preferences. The audience could motivate the inclusion of additional topics.","PeriodicalId":407048,"journal":{"name":"2007 European Control Conference (ECC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123114043","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}
Pub Date : 2007-07-02DOI: 10.23919/ECC.2007.7069063
M. Xiao, N. Kazantzis, C. Kravaris
The present research study provides a concrete set of conditions under which a nonlinear discrete-time observer exists that induces linear estimation error dynamics for nonlinear discrete-time continuous (C0) systems. The problem under consideration is mathematically addressed through the existence of a homeomorphism in the state space that maps the orbits of a linear system with an output injection onto the observing system, which indicates the existence of an invariant attracting manifold for the extended system. Within this framework, the discrete-time version of the well-known Hartman-Grobman Theorem can be naturally reproduced as a special case. The performance of the proposed nonlinear discrete-time observer is evaluated using a nonlinear dynamical chaotic system of the Lozi-type.
{"title":"A new nonlinear discrete-time observer design method with linearizable error dynamics","authors":"M. Xiao, N. Kazantzis, C. Kravaris","doi":"10.23919/ECC.2007.7069063","DOIUrl":"https://doi.org/10.23919/ECC.2007.7069063","url":null,"abstract":"The present research study provides a concrete set of conditions under which a nonlinear discrete-time observer exists that induces linear estimation error dynamics for nonlinear discrete-time continuous (C0) systems. The problem under consideration is mathematically addressed through the existence of a homeomorphism in the state space that maps the orbits of a linear system with an output injection onto the observing system, which indicates the existence of an invariant attracting manifold for the extended system. Within this framework, the discrete-time version of the well-known Hartman-Grobman Theorem can be naturally reproduced as a special case. The performance of the proposed nonlinear discrete-time observer is evaluated using a nonlinear dynamical chaotic system of the Lozi-type.","PeriodicalId":407048,"journal":{"name":"2007 European Control Conference (ECC)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121825322","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}
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