A new class of systems, the dynamical systems with controllable singularities, is considered. This class refers to systems that admit introduction of the impulsive control actions during singular phases of their motion, such as changes in dimension, discontinuities in the state, and other nonsmooth types of motion. A well-posed representation of the discontinuous in the limit behavior of these systems is given in terms of differential equations with measure and the corresponding generalized (discontinuous) solution of the new type is introduced. This representation, which admits discontinuity of the entire state, is put into correspondence with the detailed multi-scale system description via a space-time transformation followed by a limit procedure. Finally, using the framework developed, an approach to constructive optimal controller synthesis for this class of systems is presented.
{"title":"Dynamical systems with controllable singularities: multi-scale and limit representations and optimal control","authors":"J. Bentsman, B. Miller","doi":"10.1109/CDC.2001.980435","DOIUrl":"https://doi.org/10.1109/CDC.2001.980435","url":null,"abstract":"A new class of systems, the dynamical systems with controllable singularities, is considered. This class refers to systems that admit introduction of the impulsive control actions during singular phases of their motion, such as changes in dimension, discontinuities in the state, and other nonsmooth types of motion. A well-posed representation of the discontinuous in the limit behavior of these systems is given in terms of differential equations with measure and the corresponding generalized (discontinuous) solution of the new type is introduced. This representation, which admits discontinuity of the entire state, is put into correspondence with the detailed multi-scale system description via a space-time transformation followed by a limit procedure. Finally, using the framework developed, an approach to constructive optimal controller synthesis for this class of systems is presented.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125044960","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}
Several linear and higher order methods to compute nth roots of a given real or complex matrix are presented. These include Newton-like, subspace, and Krylov type methods. As a special case, the matrix sector function and other roots of an identity matrix are computed and shown to be an efficient numerical tool for computing a block eigen-decompsition of a given matrix.
{"title":"Computation of matrix nth roots and the matrix sector function","authors":"M. Hasan, A. Hasan, Khaled B. Ejaz","doi":"10.1109/CDC.2001.980812","DOIUrl":"https://doi.org/10.1109/CDC.2001.980812","url":null,"abstract":"Several linear and higher order methods to compute nth roots of a given real or complex matrix are presented. These include Newton-like, subspace, and Krylov type methods. As a special case, the matrix sector function and other roots of an identity matrix are computed and shown to be an efficient numerical tool for computing a block eigen-decompsition of a given matrix.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129412234","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}
Presents some results concerning robust fault diagnosis of dynamic processes using a parametric identification technique. The first step of the considered approach estimates an equation error model by means of the input-output data acquired from the monitored system. In particular, the equation error term of the model takes into account disturbances, non-linear and time-variant terms, measurement errors, etc. The next step of the method requires a state-space realization of the input-output equation error model which allows us to define an equivalent disturbance distribution matrix related to the error term. Therefore, the eigenstructure assignment results for robust fault diagnosis can be successfully applied. The proposed procedure has been tested by means of a industrial process simulator. In such a manner, sensor, component and actuator faults can be simulated on an single shaft gas turbine. Results from this simulator are also reported.
{"title":"Robust fault diagnosis of dynamic processes using parametric identification with eigenstructure assignment approach","authors":"C. Fantuzzi, S. Simani, S. Beghelli","doi":"10.1109/CDC.2001.980090","DOIUrl":"https://doi.org/10.1109/CDC.2001.980090","url":null,"abstract":"Presents some results concerning robust fault diagnosis of dynamic processes using a parametric identification technique. The first step of the considered approach estimates an equation error model by means of the input-output data acquired from the monitored system. In particular, the equation error term of the model takes into account disturbances, non-linear and time-variant terms, measurement errors, etc. The next step of the method requires a state-space realization of the input-output equation error model which allows us to define an equivalent disturbance distribution matrix related to the error term. Therefore, the eigenstructure assignment results for robust fault diagnosis can be successfully applied. The proposed procedure has been tested by means of a industrial process simulator. In such a manner, sensor, component and actuator faults can be simulated on an single shaft gas turbine. Results from this simulator are also reported.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129788369","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}
In this article we consider a dynamic M-ary detection problem when Markov chains are observed through a Wiener process. These systems are fully specified by a candidate set of parameters, whose elements are: a rate matrix for the Markov chain and a parameter for the observation model. Further, we suppose these parameter sets can switch according to the state of an unobserved Markov chain and thereby produce an observation process generated by time varying (jump stochastic) parameter sets. We estimate the probabilities of each model parameter set explaining the observation. Using the gauge transformation techniques introduced by Clark (1977) and a pointwise matrix product, we compute robust matrix-valued dynamics for the joint probabilities on the augmented state space. In these new dynamics the observation Wiener process appears as a parameter in the fundamental matrix of a linear ordinary differential equation, rather than an integrator in a stochastic integral equation. Finally, by exploiting a duality between causal and anticausal robust detector dynamics, we develop an algorithm to compute smoothed mode probability estimates without stochastic integrations.
{"title":"Robust M-ary detection filters for continuous-time jump Markov systems","authors":"R. Elliott, W. P. Malcolm","doi":"10.1109/CDC.2001.981143","DOIUrl":"https://doi.org/10.1109/CDC.2001.981143","url":null,"abstract":"In this article we consider a dynamic M-ary detection problem when Markov chains are observed through a Wiener process. These systems are fully specified by a candidate set of parameters, whose elements are: a rate matrix for the Markov chain and a parameter for the observation model. Further, we suppose these parameter sets can switch according to the state of an unobserved Markov chain and thereby produce an observation process generated by time varying (jump stochastic) parameter sets. We estimate the probabilities of each model parameter set explaining the observation. Using the gauge transformation techniques introduced by Clark (1977) and a pointwise matrix product, we compute robust matrix-valued dynamics for the joint probabilities on the augmented state space. In these new dynamics the observation Wiener process appears as a parameter in the fundamental matrix of a linear ordinary differential equation, rather than an integrator in a stochastic integral equation. Finally, by exploiting a duality between causal and anticausal robust detector dynamics, we develop an algorithm to compute smoothed mode probability estimates without stochastic integrations.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128577307","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}
In this paper, the problem of the stabilization of a class of discrete-time nonlinear systems with time delay is addressed. We investigate the Lyapunov approach to deduce general conditions for stabilizing the closed-loop system and derive stabilizing state feedback control laws.
{"title":"On stabilization of discrete time nonlinear systems with time delay","authors":"W. Aggoune, G. Sallet","doi":"10.1109/CDC.2001.981151","DOIUrl":"https://doi.org/10.1109/CDC.2001.981151","url":null,"abstract":"In this paper, the problem of the stabilization of a class of discrete-time nonlinear systems with time delay is addressed. We investigate the Lyapunov approach to deduce general conditions for stabilizing the closed-loop system and derive stabilizing state feedback control laws.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128434715","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}
A new, easily computable, upper bound on the real structured singular value /spl mu/ is derived under the assumption of a nonrepeated largest singular value. The condition under which real /spl mu/ is (strictly) less than the largest singular value is used to embed the structured uncertainty set in a larger related set. This is then used to derive an upper bound strictly less than the largest singular value without the use of scaling matrices.
{"title":"A new upper bound for the real structured singular value","authors":"S. K. Gungah, U. Malik, I. Jaimoukha, G. Halikias","doi":"10.1109/CDC.2001.980106","DOIUrl":"https://doi.org/10.1109/CDC.2001.980106","url":null,"abstract":"A new, easily computable, upper bound on the real structured singular value /spl mu/ is derived under the assumption of a nonrepeated largest singular value. The condition under which real /spl mu/ is (strictly) less than the largest singular value is used to embed the structured uncertainty set in a larger related set. This is then used to derive an upper bound strictly less than the largest singular value without the use of scaling matrices.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127185080","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}
We study discrete-time Markov decision processes with denumerable state space and bounded costs per stage. It is assumed that the decision maker exhibits a constant sensitivity to risk, and that the performance of a control policy is measured by a (long-run) risk-sensitive average cost criterion. Besides standard continuity-compactness conditions, the basic structural constraint on the decision model is that the transition law satisfies a simultaneous Doeblin condition. Within this framework, the main objective is to study the existence of bounded solutions to the risk-sensitive average cost optimality equation. Our main result guarantees a bounded solution to the optimality equation only if the risk sensitivity coefficient /spl lambda/ is small enough and, via a detailed example, it can be shown that such a conclusion cannot be extended to arbitrary values of /spl lambda/. Our results are in opposition to previous claims in the literature, but agree with recent results obtained via a direct probabilistic analysis. A key analysis tool developed in the paper is the definition of an appropriate operator with contractive properties, analogous to the dynamic programming operator in Bellman's equation, and a family of (value) functions with a discounted stochastic games interpretation.
{"title":"Markov decision processes with risk-sensitive criteria: dynamic programming operators and discounted stochastic games","authors":"R. Cavazos-Cadena, E. Fernández-Gaucherand","doi":"10.1109/CDC.2001.980564","DOIUrl":"https://doi.org/10.1109/CDC.2001.980564","url":null,"abstract":"We study discrete-time Markov decision processes with denumerable state space and bounded costs per stage. It is assumed that the decision maker exhibits a constant sensitivity to risk, and that the performance of a control policy is measured by a (long-run) risk-sensitive average cost criterion. Besides standard continuity-compactness conditions, the basic structural constraint on the decision model is that the transition law satisfies a simultaneous Doeblin condition. Within this framework, the main objective is to study the existence of bounded solutions to the risk-sensitive average cost optimality equation. Our main result guarantees a bounded solution to the optimality equation only if the risk sensitivity coefficient /spl lambda/ is small enough and, via a detailed example, it can be shown that such a conclusion cannot be extended to arbitrary values of /spl lambda/. Our results are in opposition to previous claims in the literature, but agree with recent results obtained via a direct probabilistic analysis. A key analysis tool developed in the paper is the definition of an appropriate operator with contractive properties, analogous to the dynamic programming operator in Bellman's equation, and a family of (value) functions with a discounted stochastic games interpretation.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"128 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129983882","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 paper presents a novel approach to output feedback stabilization with L/sub 2/ disturbance attenuation for nonlinear systems in the presence of dynamic uncertainties. A new method of state-dependent scaling unifies treatment of nonlinear and linear gains in the output feedback design. The effect of disturbance on the controlled output, which is allowed to be any function of output measurements, can be attenuated to an arbitrarily small level with global asymptotic stability if the plant belongs to a wide class of interconnected systems whose uncertain components unnecessarily have finite linear-gain. The uncertain dynamics is not limited to input-to-state stable systems either. The approach is not only a natural extension of popular approaches in robust linear control, but also advantageous to numerical computation. The design procedure proposed in the paper consists of novel recursive calculation of robust observer gain as well as feedback gain.
{"title":"Output feedback disturbance attenuation with robustness to nonlinear uncertain dynamics via state-dependent scaling","authors":"H. Ito, Zhong-Ping Jiang","doi":"10.1109/CDC.2001.980693","DOIUrl":"https://doi.org/10.1109/CDC.2001.980693","url":null,"abstract":"The paper presents a novel approach to output feedback stabilization with L/sub 2/ disturbance attenuation for nonlinear systems in the presence of dynamic uncertainties. A new method of state-dependent scaling unifies treatment of nonlinear and linear gains in the output feedback design. The effect of disturbance on the controlled output, which is allowed to be any function of output measurements, can be attenuated to an arbitrarily small level with global asymptotic stability if the plant belongs to a wide class of interconnected systems whose uncertain components unnecessarily have finite linear-gain. The uncertain dynamics is not limited to input-to-state stable systems either. The approach is not only a natural extension of popular approaches in robust linear control, but also advantageous to numerical computation. The design procedure proposed in the paper consists of novel recursive calculation of robust observer gain as well as feedback gain.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130086799","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}
We describe all symmetries of a single-input nonlinear control system that is not feedback linearizable and whose first-order approximation is controllable, around an equilibrium point. For a system such that a feedback transformation bringing it into the canonical form is analytic, we prove that the set of all local symmetries of the system is exhausted by exactly two 1-parameter families of symmetries if the system is odd, and by exactly one 1-parameter family otherwise. We also prove that the form of the set of symmetries is completely described by the canonical form of the system: possessing a nonstationary symmetry, a 1-parameter family of symmetries, or being odd corresponds, respectively, to the fact that the drift vector field of the canonical form is periodic, does not depend on the first variable, or is odd. If the feedback transformation bringing the system to its canonical form is formal, we show an analogous result for an infinitesimal symmetry: its existence is equivalent to the fact that the drift vector field of the formal canonical form does not depend on the first variable. We illustrate our results by studying the symmetries of a variable-length pendulum.
{"title":"How many symmetries does admit a nonlinear single-input control system around an equilibrium?","authors":"W. Respondek, I. Tall","doi":"10.1109/CDC.2001.981165","DOIUrl":"https://doi.org/10.1109/CDC.2001.981165","url":null,"abstract":"We describe all symmetries of a single-input nonlinear control system that is not feedback linearizable and whose first-order approximation is controllable, around an equilibrium point. For a system such that a feedback transformation bringing it into the canonical form is analytic, we prove that the set of all local symmetries of the system is exhausted by exactly two 1-parameter families of symmetries if the system is odd, and by exactly one 1-parameter family otherwise. We also prove that the form of the set of symmetries is completely described by the canonical form of the system: possessing a nonstationary symmetry, a 1-parameter family of symmetries, or being odd corresponds, respectively, to the fact that the drift vector field of the canonical form is periodic, does not depend on the first variable, or is odd. If the feedback transformation bringing the system to its canonical form is formal, we show an analogous result for an infinitesimal symmetry: its existence is equivalent to the fact that the drift vector field of the formal canonical form does not depend on the first variable. We illustrate our results by studying the symmetries of a variable-length pendulum.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128918876","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}
Summary form only given. We study an inventory control problem, under a stochastic demand process and with risk (i.e., variance) sensitive optimality criteria. Using convexity and semimodularity-type arguments, we present sufficient conditions for an optimal base-stock policy to exist, in the finite horizon problem. For the infinite horizon case, we show that there exists an ultimately stationary base-stock optimal policy.
{"title":"Risk-sensitive inventory control problems","authors":"G. Avila-Godoy, E. Fernández-Gaucherand","doi":"10.1109/CDC.2001.980925","DOIUrl":"https://doi.org/10.1109/CDC.2001.980925","url":null,"abstract":"Summary form only given. We study an inventory control problem, under a stochastic demand process and with risk (i.e., variance) sensitive optimality criteria. Using convexity and semimodularity-type arguments, we present sufficient conditions for an optimal base-stock policy to exist, in the finite horizon problem. For the infinite horizon case, we show that there exists an ultimately stationary base-stock optimal policy.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128922093","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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