It is known that a linear system x=Ax+Bu can be stabilized by means of a smooth bounded control if and only if it has no eigenvalues with positive real part, and all the uncontrollable modes have a negative real part. The authors investigate, for single-input systems, the question of whether such systems can be stabilized by means of a feedback u= sigma (h(x)), where h is linear and sigma (s) is a saturation function such as sign(s) min( mod s mod ,1). A stabilizing feedback of this particular form exists if A has no multiple eigenvalues, and also in some other special cases such as the double integrator. It is shown that for the multiple integrator of order n, with n>or=3, no saturation of a linear feedback can be globally stabilizing.<>
已知当且仅当线性系统x=Ax+Bu不存在正实部特征值，且所有不可控模态均具有负实部时，可以用光滑有界控制实现稳定。对于单输入系统，作者研究了这样的系统是否可以用反馈u= sigma (h(x))来稳定的问题，其中h是线性的，sigma (s)是一个饱和函数，如sign(s) min(mod s mod,1)。当A没有多重特征值时，存在这种特殊形式的稳定反馈，也存在其他一些特殊情况，如二重积分。证明了对于n阶的多重积分器，当n>或=3时，线性反馈的无饱和可以全局稳定。>
{"title":"On the stabilizability of multiple integrators by means of bounded feedback controls","authors":"H. J. Sussmann, Y. Yang","doi":"10.1109/CDC.1991.261255","DOIUrl":"https://doi.org/10.1109/CDC.1991.261255","url":null,"abstract":"It is known that a linear system x=Ax+Bu can be stabilized by means of a smooth bounded control if and only if it has no eigenvalues with positive real part, and all the uncontrollable modes have a negative real part. The authors investigate, for single-input systems, the question of whether such systems can be stabilized by means of a feedback u= sigma (h(x)), where h is linear and sigma (s) is a saturation function such as sign(s) min( mod s mod ,1). A stabilizing feedback of this particular form exists if A has no multiple eigenvalues, and also in some other special cases such as the double integrator. It is shown that for the multiple integrator of order n, with n>or=3, no saturation of a linear feedback can be globally stabilizing.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"149 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132976082","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 approach to the computer-aided study of multivariable nonlinear and time-varying systems in the time-domain is outlined, the basis of modern input-output (I/O) theory of control systems. A theoretical justification of the approach is given, together with some observations on the representation problem. The concept of k-time sequence matrices is described. A new simulation language which has been specifically designed to implement this I/O methodology is discussed. An example illustrating one of the I/O representations is presented.<>
{"title":"Computer-aided study of nonlinear systems using an input-output approach","authors":"N. Sadaoui, N. Gough, G. Dimirovski","doi":"10.1109/CDC.1991.261867","DOIUrl":"https://doi.org/10.1109/CDC.1991.261867","url":null,"abstract":"An approach to the computer-aided study of multivariable nonlinear and time-varying systems in the time-domain is outlined, the basis of modern input-output (I/O) theory of control systems. A theoretical justification of the approach is given, together with some observations on the representation problem. The concept of k-time sequence matrices is described. A new simulation language which has been specifically designed to implement this I/O methodology is discussed. An example illustrating one of the I/O representations is presented.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130739869","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 show how geometric ideas can be applied in control theory and in particular in robust control in order to give further insight into of fundamental issues. It is shown that stability criteria for control systems can be stated in terms of geometric notions in the Hilbert space. Two ways of modeling uncertainty in robust control have received a considerable amount of attention: uncertainty in the gap metric and coprime factor perturbations. The connection between these two uncertainty descriptions is discussed. A result is given that gives a full characterization of the maximal ball in the gap metric that can be stabilized by a controller.<>
{"title":"Graphs of linear systems and stabilization","authors":"J. Sefton, R. Ober","doi":"10.1109/CDC.1991.261366","DOIUrl":"https://doi.org/10.1109/CDC.1991.261366","url":null,"abstract":"The authors show how geometric ideas can be applied in control theory and in particular in robust control in order to give further insight into of fundamental issues. It is shown that stability criteria for control systems can be stated in terms of geometric notions in the Hilbert space. Two ways of modeling uncertainty in robust control have received a considerable amount of attention: uncertainty in the gap metric and coprime factor perturbations. The connection between these two uncertainty descriptions is discussed. A result is given that gives a full characterization of the maximal ball in the gap metric that can be stabilized by a controller.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133005537","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}
Robustness properties of an adaptive predictive controller are presented. The algorithm is obtained via a receding horizon control strategy by minimizing a quadratic performance index under the constraint that the terminal output sequence matches the reference over a suitable number of steps. The performances of both the nonadaptive and an adaptive version of the algorithm are examined in the case of unmodeled plant dynamics.<>
{"title":"Robustness of an adaptive predictive controller","authors":"David W. Clarke, E. Mosca, R. Scattolini","doi":"10.1109/CDC.1991.261471","DOIUrl":"https://doi.org/10.1109/CDC.1991.261471","url":null,"abstract":"Robustness properties of an adaptive predictive controller are presented. The algorithm is obtained via a receding horizon control strategy by minimizing a quadratic performance index under the constraint that the terminal output sequence matches the reference over a suitable number of steps. The performances of both the nonadaptive and an adaptive version of the algorithm are examined in the case of unmodeled plant dynamics.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133011650","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 investigate aspects of subspace-based state-space identification techniques from a statistical perspective. They concentrate their efforts on a simple approach which is based on finding the range-space of the observability matrix of a state-space representation. The system description is then found using the shift-invariance property of the observability matrix. It is shown that this results in a consistent system description for multivariable output-error models if the measurement noise is white in time and independent from output to output. The asymptotic covariance of the estimated poles of the system is also derived. In the test case studied, the subspace technique performs comparably with the statistically efficient PE (prediction error) method, whereas the instrumental variable method does notably worse. Hence, the subspace technique may be a strong candidate for determining initial values for the optimization in the efficient PE method.<>
{"title":"A statistical perspective on state-space modeling using subspace methods","authors":"M. Viberg, B. Ottersten, B. Wahlberg, L. Ljung","doi":"10.1109/CDC.1991.261612","DOIUrl":"https://doi.org/10.1109/CDC.1991.261612","url":null,"abstract":"The authors investigate aspects of subspace-based state-space identification techniques from a statistical perspective. They concentrate their efforts on a simple approach which is based on finding the range-space of the observability matrix of a state-space representation. The system description is then found using the shift-invariance property of the observability matrix. It is shown that this results in a consistent system description for multivariable output-error models if the measurement noise is white in time and independent from output to output. The asymptotic covariance of the estimated poles of the system is also derived. In the test case studied, the subspace technique performs comparably with the statistically efficient PE (prediction error) method, whereas the instrumental variable method does notably worse. Hence, the subspace technique may be a strong candidate for determining initial values for the optimization in the efficient PE method.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133608912","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 learning and computing processes in a recursive neural network of the Hopfield type are identified as slow and fast phenomena. The corresponding dynamical equations are cast to fit into the framework of the theory of singular perturbations and time scales. The issues of degeneration and asymptotic expansions arising in obtaining approximate solutions are addressed.<>
{"title":"Singular perturbations and time scales in artificial neural networks","authors":"K. L. Moore, D. Naidu","doi":"10.1109/CDC.1991.261077","DOIUrl":"https://doi.org/10.1109/CDC.1991.261077","url":null,"abstract":"The learning and computing processes in a recursive neural network of the Hopfield type are identified as slow and fast phenomena. The corresponding dynamical equations are cast to fit into the framework of the theory of singular perturbations and time scales. The issues of degeneration and asymptotic expansions arising in obtaining approximate solutions are addressed.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"182 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133322354","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 novel technique for obtaining reduced-order dynamic models from high-order models is proposed. The technique uses Schur decomposition, which is an efficient and stable numerical procedure. Based on different assumptions about system modes, two methods for obtaining reduced-order models are developed. In the first method, the reduced model is derived directly from the Schur form. In the second method, it is necessary, in addition, to solve some algebraic equations to derive the reduced model. The order-reduction methods are applied to a discrete dynamic model.<>
{"title":"Discrete multivariable systems order reduction via Schur decomposition","authors":"C. Bottura, C. J. Munaro","doi":"10.1109/CDC.1991.261494","DOIUrl":"https://doi.org/10.1109/CDC.1991.261494","url":null,"abstract":"A novel technique for obtaining reduced-order dynamic models from high-order models is proposed. The technique uses Schur decomposition, which is an efficient and stable numerical procedure. Based on different assumptions about system modes, two methods for obtaining reduced-order models are developed. In the first method, the reduced model is derived directly from the Schur form. In the second method, it is necessary, in addition, to solve some algebraic equations to derive the reduced model. The order-reduction methods are applied to a discrete dynamic model.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133151587","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 shown by means of a lightly damped oscillator example with uncertain stiffness that small gain modeling of constant real parameter uncertainty can be extremely conservative. This example was chosen to highlight inherent drawbacks of small-gain principles applied to the analysis of robust controllers for lightly damped flexible structures. If, for this class of problems, uncertainty in the stiffness operator, which may be relatively large, is modeled as a small gain H/sub infinity / block, then the arbitrary phase characteristics of the uncertainty block can contribute to a significant perturbation of the damping operator, which may be relatively small. An alternative uncertainty modeling approach involving positive real transfer functions and the positivity theorem is shown to be significantly less conservative.<>
{"title":"Small gain versus positive real modeling of real parameter uncertainty","authors":"D. Bernstein, W. Haddad, D. Hyland","doi":"10.2514/3.20872","DOIUrl":"https://doi.org/10.2514/3.20872","url":null,"abstract":"The authors shown by means of a lightly damped oscillator example with uncertain stiffness that small gain modeling of constant real parameter uncertainty can be extremely conservative. This example was chosen to highlight inherent drawbacks of small-gain principles applied to the analysis of robust controllers for lightly damped flexible structures. If, for this class of problems, uncertainty in the stiffness operator, which may be relatively large, is modeled as a small gain H/sub infinity / block, then the arbitrary phase characteristics of the uncertainty block can contribute to a significant perturbation of the damping operator, which may be relatively small. An alternative uncertainty modeling approach involving positive real transfer functions and the positivity theorem is shown to be significantly less conservative.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128915384","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}
Two classical problems involving discrete-time systems are analyzed. The first one concerns the quadratic stabilizability with uncertainties in convex bounded domains, which naturally covers the important class of interval matrices. In that problem, there is no need to introduce any kind of matching conditions, which is an important improvement compared with other results available in the literature. The second problem is defined by simply adding to the first problem some prespecified closed-loop transfer function H/sub infinity / norm bound. Assuming the state is available for feedback, the geometry of both problems is thoroughly analyzed. They turn out to be convex on the parameter space.<>
{"title":"Convex analysis of discrete-time uncertain H/sub infinity / control problems","authors":"P. Peres, J. Geromel, S. R. Souza","doi":"10.1109/CDC.1991.261360","DOIUrl":"https://doi.org/10.1109/CDC.1991.261360","url":null,"abstract":"Two classical problems involving discrete-time systems are analyzed. The first one concerns the quadratic stabilizability with uncertainties in convex bounded domains, which naturally covers the important class of interval matrices. In that problem, there is no need to introduce any kind of matching conditions, which is an important improvement compared with other results available in the literature. The second problem is defined by simply adding to the first problem some prespecified closed-loop transfer function H/sub infinity / norm bound. Assuming the state is available for feedback, the geometry of both problems is thoroughly analyzed. They turn out to be convex on the parameter space.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131408461","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}
Multi-input multi-output (MIMO) process identification is studied, where the purpose of identification is control system design. An identification procedure is presented by which one can estimate not only a nominal parametric process model, but also an upper bound of the model errors in the frequency domain. The basic steps of this method consists of high-order model estimation and subsequent model reduction. In this framework, fundamental problems such as input design and model structure selection can easily be solved. The method is also numerically simple and reliable. A simulation example is given to illustrate the method.<>
{"title":"Multivariable process identification based on frequency domain measures","authors":"Y.C. Zhu, A. Backx, P. Eykhoff","doi":"10.1109/CDC.1991.261311","DOIUrl":"https://doi.org/10.1109/CDC.1991.261311","url":null,"abstract":"Multi-input multi-output (MIMO) process identification is studied, where the purpose of identification is control system design. An identification procedure is presented by which one can estimate not only a nominal parametric process model, but also an upper bound of the model errors in the frequency domain. The basic steps of this method consists of high-order model estimation and subsequent model reduction. In this framework, fundamental problems such as input design and model structure selection can easily be solved. The method is also numerically simple and reliable. A simulation example is given to illustrate the method.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":"282 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131689363","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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