A representation of nonlinear systems based on the idea of representing the input-output pairs of the system as elements of the kernel of a stable operator has been previously introduced by the authors (1993, 1994). This has been denoted the kernel representation of the system. In this paper it is demonstrated that the kernel representation is a generalization of the left coprime factorization of a general nonlinear system in the sense that it is a dual operator to the right coprime factorization of a nonlinear system. The results obtainable in the linear case linking left and right coprime factorizations are shown to be reproduced within the kernel representation framework.<>
{"title":"Stable kernel representations as nonlinear left coprime factorizations","authors":"A. Paice, A. J. van der Schaft","doi":"10.1109/CDC.1994.411378","DOIUrl":"https://doi.org/10.1109/CDC.1994.411378","url":null,"abstract":"A representation of nonlinear systems based on the idea of representing the input-output pairs of the system as elements of the kernel of a stable operator has been previously introduced by the authors (1993, 1994). This has been denoted the kernel representation of the system. In this paper it is demonstrated that the kernel representation is a generalization of the left coprime factorization of a general nonlinear system in the sense that it is a dual operator to the right coprime factorization of a nonlinear system. The results obtainable in the linear case linking left and right coprime factorizations are shown to be reproduced within the kernel representation framework.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124848293","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 main goal in this work is to develop numerical algorithms for approximating the optimal threshold values of manufacturing systems. The key idea is to construct gradient estimates of the objective function with respect to the threshold values, and to use stochastic recursive algorithms for locating the optimal value. Motivated by designing more feasible methods of solutions, for systems described by differential equations with long run average cost functions, the authors previously developed stochastic optimization algorithms. The main idea is that instead of finding the optimal control of the systems, the authors turn the problem into an optimization problem by focusing their attention to the threshold control type of policies. The underlying problem is then converted to an optimization problem, namely, finding the optimal threshold values. In this paper, after briefly discussing the convergence of the algorithm, the authors concentrate on the rate of convergence issues.<>
{"title":"Further results on approximation of the optimal threshold values for manufacturing systems","authors":"G. Yin, H. Yan","doi":"10.1109/CDC.1994.411217","DOIUrl":"https://doi.org/10.1109/CDC.1994.411217","url":null,"abstract":"The main goal in this work is to develop numerical algorithms for approximating the optimal threshold values of manufacturing systems. The key idea is to construct gradient estimates of the objective function with respect to the threshold values, and to use stochastic recursive algorithms for locating the optimal value. Motivated by designing more feasible methods of solutions, for systems described by differential equations with long run average cost functions, the authors previously developed stochastic optimization algorithms. The main idea is that instead of finding the optimal control of the systems, the authors turn the problem into an optimization problem by focusing their attention to the threshold control type of policies. The underlying problem is then converted to an optimization problem, namely, finding the optimal threshold values. In this paper, after briefly discussing the convergence of the algorithm, the authors concentrate on the rate of convergence issues.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124955024","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 derive stability conditions for model predictive control (MPC) with hard constraints on the inputs and "soft" constraints on the outputs for an infinitely long output horizon. We show that with state feedback MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback the eigenvalues must be strictly inside the unit circle. The online optimization problem defining MPC can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon.<>
{"title":"Stability of model predictive control with soft constraints","authors":"Zheng Manfred Morari","doi":"10.1109/CDC.1994.411277","DOIUrl":"https://doi.org/10.1109/CDC.1994.411277","url":null,"abstract":"We derive stability conditions for model predictive control (MPC) with hard constraints on the inputs and \"soft\" constraints on the outputs for an infinitely long output horizon. We show that with state feedback MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback the eigenvalues must be strictly inside the unit circle. The online optimization problem defining MPC can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125020591","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}
During the last decade, quite a few workers have concerned themselves with the robust stability conditions for discrete-time time-invariant linear systems (DLSs). In this connection, various approaches have been developed. Simple and obvious robust stability sufficient conditions for MIMO DLSs with parameter interval uncertainty are proposed below.<>
{"title":"Cyclic representations and robust stability sufficient conditions for discrete-time stationary linear systems","authors":"E.K. Kornoushenko, A. Bernstein","doi":"10.1109/CDC.1994.411764","DOIUrl":"https://doi.org/10.1109/CDC.1994.411764","url":null,"abstract":"During the last decade, quite a few workers have concerned themselves with the robust stability conditions for discrete-time time-invariant linear systems (DLSs). In this connection, various approaches have been developed. Simple and obvious robust stability sufficient conditions for MIMO DLSs with parameter interval uncertainty are proposed below.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125192186","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 framework of hybrid control systems can be used to examine digital control systems. This paper shows how digital control systems can be modeled as hybrid control systems. A technique for designing interfaces for hybrid control systems is presented. An example is employed to demonstrate how this technique, as well as a DES controller design methodology developed earlier, can be applied to improve a digital control system.<>
{"title":"Digital control from a hybrid perspective","authors":"J. Stiver, P. Antsaklis, M. Lemmon","doi":"10.1109/CDC.1994.411617","DOIUrl":"https://doi.org/10.1109/CDC.1994.411617","url":null,"abstract":"The framework of hybrid control systems can be used to examine digital control systems. This paper shows how digital control systems can be modeled as hybrid control systems. A technique for designing interfaces for hybrid control systems is presented. An example is employed to demonstrate how this technique, as well as a DES controller design methodology developed earlier, can be applied to improve a digital control system.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126127362","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}
An estimation problem over discrete-continuous observations is considered for an impulse component. A filtering procedure is suggested to design filtering equations over discrete-continuous observations (DCO) proceeding from the known filtering equations over continuous ones. This paper aims to obtain filtering equations over DCO with a vector impulse component. The ellipsoidal guaranteed estimation problem is selected as an example that illustrates the difference between filtering equations in scalar and vector distribution. Indeed, the obtained ellipsoidal estimation equations contain discontinuous regular functions in righthand sides. To define a solution uniquely and therefore to use a filtering procedure is possible if a transfer function in an observation equation is a symmetric matrix one. Then a right-hand side of each filtering equation satisfies the one-side solvability condition which is equivalent to the one-side Frobenius condition ensuring uniqueness. A vibrosolution, defined as a unique limit, to a system of ellipsoidal filtering equations is thus to be a pair of ellipsoid parameters optimal in the given sense. In case of scalar distribution the one-side solvability condition is always satisfied.<>
{"title":"Ellipsoidal estimation over observations with a vector impulse component","authors":"M. Basin","doi":"10.1109/CDC.1994.411170","DOIUrl":"https://doi.org/10.1109/CDC.1994.411170","url":null,"abstract":"An estimation problem over discrete-continuous observations is considered for an impulse component. A filtering procedure is suggested to design filtering equations over discrete-continuous observations (DCO) proceeding from the known filtering equations over continuous ones. This paper aims to obtain filtering equations over DCO with a vector impulse component. The ellipsoidal guaranteed estimation problem is selected as an example that illustrates the difference between filtering equations in scalar and vector distribution. Indeed, the obtained ellipsoidal estimation equations contain discontinuous regular functions in righthand sides. To define a solution uniquely and therefore to use a filtering procedure is possible if a transfer function in an observation equation is a symmetric matrix one. Then a right-hand side of each filtering equation satisfies the one-side solvability condition which is equivalent to the one-side Frobenius condition ensuring uniqueness. A vibrosolution, defined as a unique limit, to a system of ellipsoidal filtering equations is thus to be a pair of ellipsoid parameters optimal in the given sense. In case of scalar distribution the one-side solvability condition is always satisfied.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126152405","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}
Studies the sensitivity of Lyapunov equations which are encountered in generalized state-space systems of the form E/spl chi/(/spl kappa/+1)=A/spl chi/(/spl kappa/), where E is nonsingular, and the system stable. The authors treat this problem and show that the results of the generalized continuous-time case extend to the discrete-time case. Furthermore, the authors derive bounds on the perturbations in the system so that the perturbed system is stable.<>
{"title":"Sensitivity analysis of the discrete generalized Lyapunov equation","authors":"R. Aripirala, V. Syrmos, P. Misra","doi":"10.1109/CDC.1994.411051","DOIUrl":"https://doi.org/10.1109/CDC.1994.411051","url":null,"abstract":"Studies the sensitivity of Lyapunov equations which are encountered in generalized state-space systems of the form E/spl chi/(/spl kappa/+1)=A/spl chi/(/spl kappa/), where E is nonsingular, and the system stable. The authors treat this problem and show that the results of the generalized continuous-time case extend to the discrete-time case. Furthermore, the authors derive bounds on the perturbations in the system so that the perturbed system is stable.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123566627","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}
Extends the work of Bridges, Dawson and Gao (1993) and Hu and Dawson (1993) to design an adaptive controller for rigid-link electrically-driven (RLED) robot manipulators specifically actuated with brushless direct current (BLDC) motors. In particular the adaptive controller presented in the second paper is tailored to handle the multi-link dynamics of a rigid-link robot as opposed to a simple inertial load. Furthermore, the linear electrical dynamics of brushed DC motors used in the development of the first paper, are replaced with the multiple input nonlinear dynamics of BLDC motors. The result is an adaptive controller that guarantees globally asymptotic convergence of the link position tracking error in spite of parametric uncertainty throughout the entire electro-mechanical model.<>
{"title":"Adaptive control of rigid-link electrically-driven robots actuated with brushless DC motors","authors":"M. Bridges, D. Dawson","doi":"10.1109/CDC.1994.411145","DOIUrl":"https://doi.org/10.1109/CDC.1994.411145","url":null,"abstract":"Extends the work of Bridges, Dawson and Gao (1993) and Hu and Dawson (1993) to design an adaptive controller for rigid-link electrically-driven (RLED) robot manipulators specifically actuated with brushless direct current (BLDC) motors. In particular the adaptive controller presented in the second paper is tailored to handle the multi-link dynamics of a rigid-link robot as opposed to a simple inertial load. Furthermore, the linear electrical dynamics of brushed DC motors used in the development of the first paper, are replaced with the multiple input nonlinear dynamics of BLDC motors. The result is an adaptive controller that guarantees globally asymptotic convergence of the link position tracking error in spite of parametric uncertainty throughout the entire electro-mechanical model.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123701922","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 consider a single-input-single-output nonlinear system which can be represented globally by an explicit input-output model. The system is input-output linearizable by feedback and is required to satisfy a minimum phase condition. The nonlinearities are not required to satisfy any global growth condition. The model depends linearly on unknown parameters which belong to a known compact, convex set. We design a semiglobal adaptive output feedback controller which ensures that the output of the system tracks any given reference signal which is bounded and has bounded derivatives up to the (n+l)th order, where n is the order of the system. The reference signal and its derivatives are assumed to belong to a known compact set. It is also assumed to be sufficiently rich to satisfy a persistence of excitation condition. The design process is simple. First we assume that the output and its derivatives are available for feedback and design the adaptive controller as a state feedback controller in appropriate coordinates. Then we saturate the controller outside a domain of interest and use a high-gain observer to estimate the derivatives of the output. We prove, via asymptotic analysis, that when the speed of the high-gain observer is sufficiently high, the adaptive output feedback controller recovers the performance achieved under the state feedback one.<>
{"title":"Adaptive output feedback control of nonlinear systems represented by input-output models","authors":"H. Khalil","doi":"10.1109/CDC.1994.411021","DOIUrl":"https://doi.org/10.1109/CDC.1994.411021","url":null,"abstract":"We consider a single-input-single-output nonlinear system which can be represented globally by an explicit input-output model. The system is input-output linearizable by feedback and is required to satisfy a minimum phase condition. The nonlinearities are not required to satisfy any global growth condition. The model depends linearly on unknown parameters which belong to a known compact, convex set. We design a semiglobal adaptive output feedback controller which ensures that the output of the system tracks any given reference signal which is bounded and has bounded derivatives up to the (n+l)th order, where n is the order of the system. The reference signal and its derivatives are assumed to belong to a known compact set. It is also assumed to be sufficiently rich to satisfy a persistence of excitation condition. The design process is simple. First we assume that the output and its derivatives are available for feedback and design the adaptive controller as a state feedback controller in appropriate coordinates. Then we saturate the controller outside a domain of interest and use a high-gain observer to estimate the derivatives of the output. We prove, via asymptotic analysis, that when the speed of the high-gain observer is sufficiently high, the adaptive output feedback controller recovers the performance achieved under the state feedback one.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125511173","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 one investigates an approach for system identification in closed loop starting from the pole placement control design using an R-S-T controller. A convenient re-parametrization of the prefilter (T) leads to error equations which are linear in the plant parameter errors and with a regressor which depends exclusively upon the external reference signals. This allows to derive parameter estimation algorithms which are asymptotically unbiased in the presence of noise. A convergence analysis of the parameter estimation algorithm in a stochastic environment using the ODE approach is presented. Simulations illustrate the potentiality of the proposed approach.<>
{"title":"An approach for closed loop system identification","authors":"I. Dore Landau, F. Rolland","doi":"10.1109/CDC.1994.411602","DOIUrl":"https://doi.org/10.1109/CDC.1994.411602","url":null,"abstract":"In this paper one investigates an approach for system identification in closed loop starting from the pole placement control design using an R-S-T controller. A convenient re-parametrization of the prefilter (T) leads to error equations which are linear in the plant parameter errors and with a regressor which depends exclusively upon the external reference signals. This allows to derive parameter estimation algorithms which are asymptotically unbiased in the presence of noise. A convergence analysis of the parameter estimation algorithm in a stochastic environment using the ODE approach is presented. Simulations illustrate the potentiality of the proposed approach.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126738777","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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