The paper describes a procedure for improving the robustness margins of robust filters via parameter scaling. The scaling parameter is chosen as the square-root factor of the inverse of a positive-definite solution to certain matrix inequalities. This choice is motivated by the desire to generate an estimator dynamics with a stable closed-loop matrix whose maximum singular value is bounded by unity; a step that enhances the robustness of the filters.
{"title":"Design of robust filters with improved robustness margins via parameter scaling","authors":"M. Terra, A. H. Sayed","doi":"10.1109/CDC.2001.980180","DOIUrl":"https://doi.org/10.1109/CDC.2001.980180","url":null,"abstract":"The paper describes a procedure for improving the robustness margins of robust filters via parameter scaling. The scaling parameter is chosen as the square-root factor of the inverse of a positive-definite solution to certain matrix inequalities. This choice is motivated by the desire to generate an estimator dynamics with a stable closed-loop matrix whose maximum singular value is bounded by unity; a step that enhances the robustness of the filters.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"383 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":"121770202","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 we define a notion of mesh stability for a class of interconnected nonlinear systems. Intuitively mesh stability is the property of damping disturbance propagation. We derive a set of sufficient conditions to assure mesh stability of "look-ahead" interconnected systems. Mesh stability is shown to be robust with respect to structural and singular perturbations. The theory is applied to an example in vehicle following.
{"title":"Mesh stability of look-ahead interconnected systems","authors":"P. Seiler, Karl Hedrick","doi":"10.1109/CDC.2001.980735","DOIUrl":"https://doi.org/10.1109/CDC.2001.980735","url":null,"abstract":"In this paper we define a notion of mesh stability for a class of interconnected nonlinear systems. Intuitively mesh stability is the property of damping disturbance propagation. We derive a set of sufficient conditions to assure mesh stability of \"look-ahead\" interconnected systems. Mesh stability is shown to be robust with respect to structural and singular perturbations. The theory is applied to an example in vehicle following.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"135 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":"132216127","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}
This paper considers an off-line reference management technique for systems with state and control constraints. The benefits of the approach are to guaranteeing the satisfaction of the specified constraints, that is the primary purpose of reference governors, and explicitly taking the performance improvement into account. The infinite number of constraints involved in the problem formulation are reduced into a finite number. The main idea is to restricting the state variable at the final instance of finite-time reference management to a certain invariant subset of the state space such that fulfilling constraints for the primal control system is equivalent to restricting the state dynamics to this set.
{"title":"A performance improving off-line reference management for systems with state and control constraints","authors":"K. Hirata, K. Kogiso","doi":"10.1109/CDC.2001.980939","DOIUrl":"https://doi.org/10.1109/CDC.2001.980939","url":null,"abstract":"This paper considers an off-line reference management technique for systems with state and control constraints. The benefits of the approach are to guaranteeing the satisfaction of the specified constraints, that is the primary purpose of reference governors, and explicitly taking the performance improvement into account. The infinite number of constraints involved in the problem formulation are reduced into a finite number. The main idea is to restricting the state variable at the final instance of finite-time reference management to a certain invariant subset of the state space such that fulfilling constraints for the primal control system is equivalent to restricting the state dynamics to this set.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"19 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":"132246163","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 propose an observer design using filtered measurements for single-output linear observable systems. The measurements are filtered using a low-pass filter with a specified cutoff frequency. Consequently, the observer is called low-pass filtered output observer. In this observer-filter scheme, both the filtered output and the raw output, together with the input, are fed to the observer in order to provide the state estimation.
{"title":"Observer design using low-pass filtered outputs","authors":"K. Busawon, Sean Danaher, P. Kaboré","doi":"10.1109/CDC.2001.980475","DOIUrl":"https://doi.org/10.1109/CDC.2001.980475","url":null,"abstract":"We propose an observer design using filtered measurements for single-output linear observable systems. The measurements are filtered using a low-pass filter with a specified cutoff frequency. Consequently, the observer is called low-pass filtered output observer. In this observer-filter scheme, both the filtered output and the raw output, together with the input, are fed to the observer in order to provide the state estimation.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"2 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":"132492888","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 provide new expressions for the asymptotic covariance of the estimated parameters (A, B, C, D) of a state space model obtained by some popular subspace identification method. The expressions, similar but simpler than the asymptotic covariance formulas which have so far been published in the literature, involve the inverses of the conditional covariance matrices /spl Sigma/(xx|u/sup +/), /spl Sigma/(u/sup +/u/sup +/|x) thus providing a direct link of possible ill-conditioning of the estimation problem with the asymptotic variance of the estimates. A study of ill-conditioning of subspace identification has been presented. The formulas can be applied to several subspace methods including N4SID, MOESP, CVA, etc.
{"title":"Asymptotic variances of subspace estimates","authors":"A. Chiuso, G. Picci","doi":"10.1109/CDC.2001.980485","DOIUrl":"https://doi.org/10.1109/CDC.2001.980485","url":null,"abstract":"We provide new expressions for the asymptotic covariance of the estimated parameters (A, B, C, D) of a state space model obtained by some popular subspace identification method. The expressions, similar but simpler than the asymptotic covariance formulas which have so far been published in the literature, involve the inverses of the conditional covariance matrices /spl Sigma/(xx|u/sup +/), /spl Sigma/(u/sup +/u/sup +/|x) thus providing a direct link of possible ill-conditioning of the estimation problem with the asymptotic variance of the estimates. A study of ill-conditioning of subspace identification has been presented. The formulas can be applied to several subspace methods including N4SID, MOESP, CVA, etc.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"12 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":"130213387","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 relay feedback and wavelet based method for the estimation of completely unknown processes for autotune purposes. From a single symmetrical relay feedback analysis a set of general expressions are presented for on-line process identification. Using these expressions the exact parameters of open loop stable and unstable first order plus time delay (FOPDT) and second order plus time delay (SOPDT) transfer function models may be obtained from simple measurements made on the limit cycle. However, noise in limit cycle output results in inaccurate estimate of the process model parameters. This paper proposes an effective mother wavelet for tracking the critical points of a noisy output signal. Further, using the wavelets based noise reduction it has been shown how accurate measurements can be made on the noisy limit cycle signal. Simulation studies illustrate the value of the proposed identification method.
{"title":"Relay feedback and wavelet based estimation of plant model parameters","authors":"S. Majhi, J. S. Sahmbi, D. Atherton","doi":"10.1109/CDC.2001.980336","DOIUrl":"https://doi.org/10.1109/CDC.2001.980336","url":null,"abstract":"The paper presents a relay feedback and wavelet based method for the estimation of completely unknown processes for autotune purposes. From a single symmetrical relay feedback analysis a set of general expressions are presented for on-line process identification. Using these expressions the exact parameters of open loop stable and unstable first order plus time delay (FOPDT) and second order plus time delay (SOPDT) transfer function models may be obtained from simple measurements made on the limit cycle. However, noise in limit cycle output results in inaccurate estimate of the process model parameters. This paper proposes an effective mother wavelet for tracking the critical points of a noisy output signal. Further, using the wavelets based noise reduction it has been shown how accurate measurements can be made on the noisy limit cycle signal. Simulation studies illustrate the value of the proposed identification method.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"19 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":"130229000","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}
Motivated by aircraft control system design, the paper presents tests for the stability and performance of a set of affine parameter-dependent linear systems. Based on these tests, the tracking controller design method via output feedback is provided. These tests and design method are based on the notion of affine quadratic stability/performance where the fixed Lyapunov function is replaced by an affine parameter-dependent Lyapunov function. Sufficient conditions to test and realize the stability/performance of this class of systems are given in terms of solvability of linear matrix inequalities (LMIs). These tests and design methods are less conservative than existing methods.
{"title":"Output-feedback tracking control of a set of affine parameter-dependent systems","authors":"F. Liao, Jianliang Wang, Guanghong Yang","doi":"10.1109/CDC.2001.980983","DOIUrl":"https://doi.org/10.1109/CDC.2001.980983","url":null,"abstract":"Motivated by aircraft control system design, the paper presents tests for the stability and performance of a set of affine parameter-dependent linear systems. Based on these tests, the tracking controller design method via output feedback is provided. These tests and design method are based on the notion of affine quadratic stability/performance where the fixed Lyapunov function is replaced by an affine parameter-dependent Lyapunov function. Sufficient conditions to test and realize the stability/performance of this class of systems are given in terms of solvability of linear matrix inequalities (LMIs). These tests and design methods are less conservative than existing methods.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"78 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":"134243633","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}
Feedback is ubiquitous and is a basic concept in the area of control, where it is used primarily for reducing internal or external uncertainties, or both. In this paper, we study the capability of feedback in dealing with both internal and external uncertainties for a class of pth-order nonlinear autoregressive control systems. The size of the uncertainty is described by the Lipschitz constant (L) of the uncertain nonlinear function under consideration. It is shown that, if p and L satisfy the following relationship: L+ 1/2 /spl ges//sup (1+p)//spl radic/(pL)(1+1/p), where pL>1, then there exists no globally stabilizing feedback for the corresponding class of uncertain systems, and we thus find a quantitative limit to the capability of the feedback mechanism in dealing with structural uncertainties.
{"title":"A limit to the capability of feedback","authors":"Yanxia Zhang, Lei Guo","doi":"10.1109/CDC.2001.981206","DOIUrl":"https://doi.org/10.1109/CDC.2001.981206","url":null,"abstract":"Feedback is ubiquitous and is a basic concept in the area of control, where it is used primarily for reducing internal or external uncertainties, or both. In this paper, we study the capability of feedback in dealing with both internal and external uncertainties for a class of pth-order nonlinear autoregressive control systems. The size of the uncertainty is described by the Lipschitz constant (L) of the uncertain nonlinear function under consideration. It is shown that, if p and L satisfy the following relationship: L+ 1/2 /spl ges//sup (1+p)//spl radic/(pL)(1+1/p), where pL>1, then there exists no globally stabilizing feedback for the corresponding class of uncertain systems, and we thus find a quantitative limit to the capability of the feedback mechanism in dealing with structural uncertainties.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"18 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":"131716546","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 objective of the work is twofold. A first part is devoted to the problem of tracking trajectories of feedforward systems. A family of the time-varying state feedbacks which globally uniformly asymptotically and locally exponentially stabilize trajectories which are not necessarily periodic functions of the time is exhibited. Strict Lyapunov functions are constructed. In a second part, the problem of tracking a trajectory of the practical system called cart-pendulum system is solved.
{"title":"Tracking trajectories of feedforward systems: application to the cart-pendulum system","authors":"F. Mazenc, S. Bowong","doi":"10.1109/CDC.2001.980146","DOIUrl":"https://doi.org/10.1109/CDC.2001.980146","url":null,"abstract":"The objective of the work is twofold. A first part is devoted to the problem of tracking trajectories of feedforward systems. A family of the time-varying state feedbacks which globally uniformly asymptotically and locally exponentially stabilize trajectories which are not necessarily periodic functions of the time is exhibited. Strict Lyapunov functions are constructed. In a second part, the problem of tracking a trajectory of the practical system called cart-pendulum system is solved.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"27 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":"131723044","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}
M. Zhong, S. Ding, B. Tang, Ping Zhang, T. Jeinsch
Deals with the design of a fault detection filter for discrete-time systems with both model uncertainty and disturbances. We propose an approach to the solution, which consists of two steps: (a) selection of a stable weighting function matrix, optimized in the sense of the maximum sensitivity from the faults to residual signal; (b) formulation of the design of fault detection filters as a model-matching problem and solving the optimization problem using the LMI technique. The achieved results are illustrated by a numerical example.
{"title":"An LMI approach to robust fault detection filter design for discrete-time systems with model uncertainty","authors":"M. Zhong, S. Ding, B. Tang, Ping Zhang, T. Jeinsch","doi":"10.1109/CDC.2001.980421","DOIUrl":"https://doi.org/10.1109/CDC.2001.980421","url":null,"abstract":"Deals with the design of a fault detection filter for discrete-time systems with both model uncertainty and disturbances. We propose an approach to the solution, which consists of two steps: (a) selection of a stable weighting function matrix, optimized in the sense of the maximum sensitivity from the faults to residual signal; (b) formulation of the design of fault detection filters as a model-matching problem and solving the optimization problem using the LMI technique. The achieved results are illustrated by a numerical example.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"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":"131005004","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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