Presented is a state-space characterization of transmission zeros of 'singular' linear multivariable system models (E, A, B, C, D), where E is a singular matrix. The characterization is based on defining the transmission zeros as the finite zeros of the transfer function matrix of the given 5-tuple. Based on the proposed characterization, a numerical algorithm is developed for computation of the transmission zeros of singular systems. Several numerical examples are included to illustrate the proposed scheme.<>
给出了“奇异”线性多变量系统模型(E, a, B, C, D)的传输零点的状态空间表征，其中E是一个奇异矩阵。该表征是基于将传递零点定义为给定5元组的传递函数矩阵的有限零点。在此基础上，提出了一种计算奇异系统传输零点的数值算法。文中给出了几个数值算例来说明所提出的方案。
{"title":"Characterization and computation of transmission zeros of singular multivariable systems","authors":"P. Misra, G. Gu, P. Van Dooren","doi":"10.1109/CDC.1990.203596","DOIUrl":"https://doi.org/10.1109/CDC.1990.203596","url":null,"abstract":"Presented is a state-space characterization of transmission zeros of 'singular' linear multivariable system models (E, A, B, C, D), where E is a singular matrix. The characterization is based on defining the transmission zeros as the finite zeros of the transfer function matrix of the given 5-tuple. Based on the proposed characterization, a numerical algorithm is developed for computation of the transmission zeros of singular systems. Several numerical examples are included to illustrate the proposed scheme.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114163740","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 problems of constructing model reference adaptive control systems for distributed parameter systems of the parabolic type are considered. Although the distributed parameter systems are infinite-dimensional, the proposed control scheme is constructed from finite-dimensional compensators instead of infinite-dimensional ones. It is shown that the resulting control systems are uniformly bounded for any bounded reference signal which the output of the process must follow, and that the tracking error converges to a small residual region whose amplitude is determined freely. Some simulation results are presented which show the effectiveness and simplicity of the proposed method.<>
{"title":"Model reference adaptive control for distributed parameter systems of parabolic type by finite dimensional controller","authors":"Y. Miyasato","doi":"10.1109/CDC.1990.203853","DOIUrl":"https://doi.org/10.1109/CDC.1990.203853","url":null,"abstract":"The problems of constructing model reference adaptive control systems for distributed parameter systems of the parabolic type are considered. Although the distributed parameter systems are infinite-dimensional, the proposed control scheme is constructed from finite-dimensional compensators instead of infinite-dimensional ones. It is shown that the resulting control systems are uniformly bounded for any bounded reference signal which the output of the process must follow, and that the tracking error converges to a small residual region whose amplitude is determined freely. Some simulation results are presented which show the effectiveness and simplicity of the proposed method.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114427610","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 time efficient digital integration method for the solution of the orifice mass flow rate equations common in internal combustion engine breathing process simulation is discussed. Local linearization followed by development of a standard singular perturbation model is used to synthesize digital integrating factors that are applied to the original nonlinear differential equations. This approach results in a method suitable for high-speed flow rate integration over the entire flow rate operating range. Analytical development of the method and simulation results are summarized.<>
{"title":"Application of singular perturbation theory to compressible mass flow rate integration","authors":"B. Powell","doi":"10.1109/CDC.1990.203490","DOIUrl":"https://doi.org/10.1109/CDC.1990.203490","url":null,"abstract":"A time efficient digital integration method for the solution of the orifice mass flow rate equations common in internal combustion engine breathing process simulation is discussed. Local linearization followed by development of a standard singular perturbation model is used to synthesize digital integrating factors that are applied to the original nonlinear differential equations. This approach results in a method suitable for high-speed flow rate integration over the entire flow rate operating range. Analytical development of the method and simulation results are summarized.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114436317","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 case of a multilayer perceptron (MLP) used for position control of a two-link robot is reported. Simulation results as well as the computational burden on neurocontrollers designed for robot control are presented. Such issues as the number of layers and number of nodes per layer are discussed. It is concluded that a neural network can be used to approximate a dynamical model of a robot. However, the error associated with this model is not nearly as good as that of conventional controllers, specifically a computed torque controller.<>
{"title":"A neural network-based controller for a two-link robot","authors":"M. Jamshidi, B. Horne, N. Vadiee","doi":"10.1109/CDC.1990.203395","DOIUrl":"https://doi.org/10.1109/CDC.1990.203395","url":null,"abstract":"A case of a multilayer perceptron (MLP) used for position control of a two-link robot is reported. Simulation results as well as the computational burden on neurocontrollers designed for robot control are presented. Such issues as the number of layers and number of nodes per layer are discussed. It is concluded that a neural network can be used to approximate a dynamical model of a robot. However, the error associated with this model is not nearly as good as that of conventional controllers, specifically a computed torque controller.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114466103","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 problems encountered in a highway automation project are considered. The overall system consists of N+1 vehicles (the platoon); each vehicle is driven by the same input, and the state of the k-th vehicle affects the dynamics of the (k+1)-th vehicle; furthermore, the dynamics of each vehicle is affected by its (local) state-feedback controller. Under very general conditions, it is shown that, for sufficient slowly varying inputs, the local feedbacks can be designed so that the platoon maintains its cohesion.<>
{"title":"Control of an interconnection of nonlinear dynamical systems","authors":"S. Sheikholeslam, C. Desoer","doi":"10.1109/CDC.1990.203504","DOIUrl":"https://doi.org/10.1109/CDC.1990.203504","url":null,"abstract":"The problems encountered in a highway automation project are considered. The overall system consists of N+1 vehicles (the platoon); each vehicle is driven by the same input, and the state of the k-th vehicle affects the dynamics of the (k+1)-th vehicle; furthermore, the dynamics of each vehicle is affected by its (local) state-feedback controller. Under very general conditions, it is shown that, for sufficient slowly varying inputs, the local feedbacks can be designed so that the platoon maintains its cohesion.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114517179","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 algorithm for computing the solution to H/sub infinity / problems with time domain constraints over a finite horizon is presented. This problem is transformed into a convex finite-dimensional optimization problem. Some of the characteristics of the optimal solution are established, namely, the degree of the optimal solution and its behavior in the special case in which the constraints are not binding, in order to gain further insight into the nature of the optimization problem, including the fact that it is in general nondifferentiable. An example is presented in which the technique provides better time responses with only slight deterioration of the robustness properties as compared with the unconstrained H/sub infinity /-optimal solution. Although all the results were obtained for single input-single output systems, they extend naturally to multivariable systems.<>
{"title":"H/sub infinity / optimization with time domain constraints over a finite horizon","authors":"Athanasios Sideris, H. Rotstein","doi":"10.1109/CDC.1990.203930","DOIUrl":"https://doi.org/10.1109/CDC.1990.203930","url":null,"abstract":"An algorithm for computing the solution to H/sub infinity / problems with time domain constraints over a finite horizon is presented. This problem is transformed into a convex finite-dimensional optimization problem. Some of the characteristics of the optimal solution are established, namely, the degree of the optimal solution and its behavior in the special case in which the constraints are not binding, in order to gain further insight into the nature of the optimization problem, including the fact that it is in general nondifferentiable. An example is presented in which the technique provides better time responses with only slight deterioration of the robustness properties as compared with the unconstrained H/sub infinity /-optimal solution. Although all the results were obtained for single input-single output systems, they extend naturally to multivariable systems.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122070129","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 authors present a stability bound on additive perturbations in the plant state matrix for systems with piecewise-constant, periodic output feedback. The bound does not require the calculation of the matrix exponential, but instead uses the matrix measure as an upper limit on its norm. This limit and a special norm based on the closed-loop eigenvectors are used to show that if the stability bound is satisfied, all the eigenvalues of the closed-loop discrete-time state matrix have magnitude less than one. It is also shown that if the stability bound is satisfied for two extreme perturbations, then the system is stable for all of the intermediate perturbations. Use of the stability bound is demonstrated by a numerical example.<>
{"title":"A stability bound for systems with periodic output feedback","authors":"J. L. Rawson, C. Hsu","doi":"10.1109/CDC.1990.203450","DOIUrl":"https://doi.org/10.1109/CDC.1990.203450","url":null,"abstract":"The authors present a stability bound on additive perturbations in the plant state matrix for systems with piecewise-constant, periodic output feedback. The bound does not require the calculation of the matrix exponential, but instead uses the matrix measure as an upper limit on its norm. This limit and a special norm based on the closed-loop eigenvectors are used to show that if the stability bound is satisfied, all the eigenvalues of the closed-loop discrete-time state matrix have magnitude less than one. It is also shown that if the stability bound is satisfied for two extreme perturbations, then the system is stable for all of the intermediate perturbations. Use of the stability bound is demonstrated by a numerical example.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116753161","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}
Problems of designing robust observers in the frequency domain are formulated and solved. Using the factorization approach, a characterization of all observers is derived. This enables the description of all achievable transfer functions of estimate errors in terms of a RH/sub infinity /-parameter matrix. It is shown that the problem of designing optimally robust observers can therefore be transformed into the well-known model matching problem that can be solved with H/sub infinity /-optimization techniques. It is shown that the proposed methods can be used to solve the problem of finding exact unknown input observers.<>
{"title":"Robust observer design via factorization approach","authors":"X. Ding, P. Frank, L. Guo","doi":"10.1109/CDC.1990.203508","DOIUrl":"https://doi.org/10.1109/CDC.1990.203508","url":null,"abstract":"Problems of designing robust observers in the frequency domain are formulated and solved. Using the factorization approach, a characterization of all observers is derived. This enables the description of all achievable transfer functions of estimate errors in terms of a RH/sub infinity /-parameter matrix. It is shown that the problem of designing optimally robust observers can therefore be transformed into the well-known model matching problem that can be solved with H/sub infinity /-optimization techniques. It is shown that the proposed methods can be used to solve the problem of finding exact unknown input observers.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117080129","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}
It is shown how a generalization of E. Cartan's results (1908, 1914) on absolute equivalence of differential systems provides necessary and sufficient conditions for local dynamic feedback linearization of control systems. The authors prove that the only extended systems which should ever be considered are those obtained by partial prolongation. The problem of dynamic feedback linearizability of a system with p controls is essentially the problem of characterizing the absolute equivalence class of the contact system. It is shown that the problem of absolute equivalence and hence of linearizability may always be reduced to a problem of G-structures after taking partial prolongations of the original system. The approach used first 'sorts' systems with a diffeomorphism group which properly contains the dynamic feedback transformations. If a system is not linearizable by the larger transformation group, then it is not linearizable by a subgroup. If it proves linearizable by the larger group, then the analysis must be refined to show that the subgroup is sufficient. A brief description of the notion of absolute equivalence and a characterization of the absolute equivalence class of the contact system are given.<>
{"title":"Dynamic feedback linearization","authors":"W. Shadwick, W. Sluis","doi":"10.1109/CDC.1990.203991","DOIUrl":"https://doi.org/10.1109/CDC.1990.203991","url":null,"abstract":"It is shown how a generalization of E. Cartan's results (1908, 1914) on absolute equivalence of differential systems provides necessary and sufficient conditions for local dynamic feedback linearization of control systems. The authors prove that the only extended systems which should ever be considered are those obtained by partial prolongation. The problem of dynamic feedback linearizability of a system with p controls is essentially the problem of characterizing the absolute equivalence class of the contact system. It is shown that the problem of absolute equivalence and hence of linearizability may always be reduced to a problem of G-structures after taking partial prolongations of the original system. The approach used first 'sorts' systems with a diffeomorphism group which properly contains the dynamic feedback transformations. If a system is not linearizable by the larger transformation group, then it is not linearizable by a subgroup. If it proves linearizable by the larger group, then the analysis must be refined to show that the subgroup is sufficient. A brief description of the notion of absolute equivalence and a characterization of the absolute equivalence class of the contact system are given.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128234506","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 Levinson-type algorithms have not been applied to the linear minimum mean square error (LMMSE) estimation of parameters of an autoregressive system with exogenous inputs (ARX system) because the Yule-Walker equation in such a case is not a block-Toeplitz system, but is composed of block-Toeplitz submatrices. A new algorithm called the order-recursive algorithm (ORA) is developed to solve such systems, and it is applied to other LMMSE estimation problems of ARX systems. The resulting algorithm operates efficiently and recursively in the order of either the lagged output part or the exogenous input part. Meanwhile, it generates a set of LMMSE ARX models of different order as by-products. As a result, the ORA can be useful in many fields, including linear filtering of ARX and ARMA (autoregressive moving average) processes, system identification, model reduction, and adaptive control.<>
{"title":"A fast order-recursive algorithm for Toeplitz submatrix systems with applications to estimation of ARX systems","authors":"J. Pan, W. Levine","doi":"10.1109/CDC.1990.203307","DOIUrl":"https://doi.org/10.1109/CDC.1990.203307","url":null,"abstract":"The Levinson-type algorithms have not been applied to the linear minimum mean square error (LMMSE) estimation of parameters of an autoregressive system with exogenous inputs (ARX system) because the Yule-Walker equation in such a case is not a block-Toeplitz system, but is composed of block-Toeplitz submatrices. A new algorithm called the order-recursive algorithm (ORA) is developed to solve such systems, and it is applied to other LMMSE estimation problems of ARX systems. The resulting algorithm operates efficiently and recursively in the order of either the lagged output part or the exogenous input part. Meanwhile, it generates a set of LMMSE ARX models of different order as by-products. As a result, the ORA can be useful in many fields, including linear filtering of ARX and ARMA (autoregressive moving average) processes, system identification, model reduction, and adaptive control.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128313627","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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