The problem of robust absolute stability for discrete-time interval Lurie systems containing an arbitrary number of monotonic sector-bounded memoryless time-invariant non-linearities is studied. This is accomplished via analysis of an interval matrix, and an algebraic sufficient condition with interval matrix inequality form is obtained for the discrete-time interval Lurie systems.
{"title":"The robust absolute stability of discrete-time interval Lurie system","authors":"Zuoxin Gan","doi":"10.1109/CDC.2001.981201","DOIUrl":"https://doi.org/10.1109/CDC.2001.981201","url":null,"abstract":"The problem of robust absolute stability for discrete-time interval Lurie systems containing an arbitrary number of monotonic sector-bounded memoryless time-invariant non-linearities is studied. This is accomplished via analysis of an interval matrix, and an algebraic sufficient condition with interval matrix inequality form is obtained for the discrete-time interval Lurie systems.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"57 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":"125806806","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 analyze the effect of functional feedback in an extremum seeking loop. Our study is motivated by a formation flight problem where the trailing aircraft experiences an outward rolling moment as the vortex effects of the leading aircraft come into play. Viewed as the extremized functional, this rolling moment feeds itself back to the lateral dynamics of the aircraft. In the initial half of the paper we impose restrictions on the curvature of the extremized functional and examine the effect under the assumption of a dynamic time-scale separation between the tracking loops of the linear dynamical system and the extremum seeking loop; in the latter half we remove both these assumptions and instead impose assumed functional forms on the extremized functional.
{"title":"Functional feedback in an extremum seeking loop","authors":"R. Banavar, D. Chichka, J. Speyer","doi":"10.1109/CDC.2001.981072","DOIUrl":"https://doi.org/10.1109/CDC.2001.981072","url":null,"abstract":"We analyze the effect of functional feedback in an extremum seeking loop. Our study is motivated by a formation flight problem where the trailing aircraft experiences an outward rolling moment as the vortex effects of the leading aircraft come into play. Viewed as the extremized functional, this rolling moment feeds itself back to the lateral dynamics of the aircraft. In the initial half of the paper we impose restrictions on the curvature of the extremized functional and examine the effect under the assumption of a dynamic time-scale separation between the tracking loops of the linear dynamical system and the extremum seeking loop; in the latter half we remove both these assumptions and instead impose assumed functional forms on the extremized functional.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"30 3 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":"126081957","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 investigates eigenstructure assignment in multivariable linear systems via output feedback. Three problems are proposed and are related to a type of generalized Sylvester matrix equations. By proposing a general complete parametric solution to this type of generalized Sylvester matrix equations based on singular value decompositions, a general complete parametric approach is then presented for the proposed eigenstructure assignment problems. General parametric expressions for both the closed-loop eigenvector matrices and the output feedback gain are established in terms of certain parameter vectors. These parameter vectors provide the design degrees of freedom and can be utilized to achieve some desired specifications. Based on the proposed results and the Matlab Optimization Toolbox, a Matlab file is created, which finds a solution that gives minimum closed-loop eigenvalue sensitivities for the problem of eigenstructure assignment via output feedback.
{"title":"Parametric eigenstructure assignment via output feedback based on singular value decompositions","authors":"G. Duan","doi":"10.1109/CDC.2001.980671","DOIUrl":"https://doi.org/10.1109/CDC.2001.980671","url":null,"abstract":"The paper investigates eigenstructure assignment in multivariable linear systems via output feedback. Three problems are proposed and are related to a type of generalized Sylvester matrix equations. By proposing a general complete parametric solution to this type of generalized Sylvester matrix equations based on singular value decompositions, a general complete parametric approach is then presented for the proposed eigenstructure assignment problems. General parametric expressions for both the closed-loop eigenvector matrices and the output feedback gain are established in terms of certain parameter vectors. These parameter vectors provide the design degrees of freedom and can be utilized to achieve some desired specifications. Based on the proposed results and the Matlab Optimization Toolbox, a Matlab file is created, which finds a solution that gives minimum closed-loop eigenvalue sensitivities for the problem of eigenstructure assignment via output feedback.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"42 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":"123337243","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 robust stabilization problem (RSP) of an interval plant family is considered. By representing the nominal plant with the normalized coprime factorization description, the RSP of interval plant family is converted to a particular H/sub /spl infin// control problem. An analytical formula for calculating the parametric stability radius /spl delta//sub max/ of the closed-loop system consisting of the interval plant family and the H/sub /spl infin// controller is given. Using /spl delta//sub max/, the stability margin /spl epsi//sub IP/, of the closed-loop system, described in terms of the H/sub /spl infin//-norm of the uncertain factors in the NCF description, is calculated. Numerical example shows that /spl epsi//sub IP/ is larger than the stability margin of the general unstructured uncertainties case.
{"title":"Robust stabilization of interval plant family using H/sub /spl infin//-optimization technique","authors":"Dahua Xie, Kan Li, Qing-he Wu","doi":"10.1109/CDC.2001.981198","DOIUrl":"https://doi.org/10.1109/CDC.2001.981198","url":null,"abstract":"The robust stabilization problem (RSP) of an interval plant family is considered. By representing the nominal plant with the normalized coprime factorization description, the RSP of interval plant family is converted to a particular H/sub /spl infin// control problem. An analytical formula for calculating the parametric stability radius /spl delta//sub max/ of the closed-loop system consisting of the interval plant family and the H/sub /spl infin// controller is given. Using /spl delta//sub max/, the stability margin /spl epsi//sub IP/, of the closed-loop system, described in terms of the H/sub /spl infin//-norm of the uncertain factors in the NCF description, is calculated. Numerical example shows that /spl epsi//sub IP/ is larger than the stability margin of the general unstructured uncertainties case.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"185 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":"123452938","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 problem of optimally defining and controlling the behaviour of a single machine processing a certain number of jobs and modelled as a discrete event dynamic system is addressed. The number of jobs, their sizes, and their service sequence are fixed, whereas their timing is the matter of the optimisation problem. The objective function to be optimised is a weighted sum of the inventory cost of the quadratic deviations from the due-dates of jobs and their completion times, and the quadratic deviations between the unitary processing times of jobs and those specified by the regular system functioning. An optimisation problem with quadratic cost function and nonlinear constraints is stated and formalised as a multi-stage optimal control problem. The control problem is solved by a procedure making use of dynamic programming techniques; the optimal closed-loop control laws at each stage are thus obtained.
{"title":"Single machine scheduling with fixed lot-sizes and variable processing times","authors":"A. D. Febbraro, R. Minciardi, S. Sacone","doi":"10.1109/CDC.2001.980612","DOIUrl":"https://doi.org/10.1109/CDC.2001.980612","url":null,"abstract":"The problem of optimally defining and controlling the behaviour of a single machine processing a certain number of jobs and modelled as a discrete event dynamic system is addressed. The number of jobs, their sizes, and their service sequence are fixed, whereas their timing is the matter of the optimisation problem. The objective function to be optimised is a weighted sum of the inventory cost of the quadratic deviations from the due-dates of jobs and their completion times, and the quadratic deviations between the unitary processing times of jobs and those specified by the regular system functioning. An optimisation problem with quadratic cost function and nonlinear constraints is stated and formalised as a multi-stage optimal control problem. The control problem is solved by a procedure making use of dynamic programming techniques; the optimal closed-loop control laws at each stage are thus obtained.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"106 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":"123560865","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 a tool to analyze the effect of error recovery systems on closed-loop flight control systems. In particular, the paper develops closed-loop models and analyzes the mean-square stability effect of error recovery rollback, reset, and cold restart systems in digital control systems. The error recovery mechanisms are triggered by transient or intermittent faults which could be caused, for example, by high intensity electromagnetic radiation. The tool is illustrated by analyzing a stabilizing controller for the longitudinal dynamics of the AFTI/F-16 aircraft. This example compares different recovery methodologies by determining the minimum interarrival spacing between upsets which maintains closed-loop mean-square stability.
{"title":"Stability analysis of upset recovery methods for electromagnetic interference","authors":"O. González, W. Gray, A. Tejada, S. Patilkulkarni","doi":"10.1109/CDC.2001.980829","DOIUrl":"https://doi.org/10.1109/CDC.2001.980829","url":null,"abstract":"Presents a tool to analyze the effect of error recovery systems on closed-loop flight control systems. In particular, the paper develops closed-loop models and analyzes the mean-square stability effect of error recovery rollback, reset, and cold restart systems in digital control systems. The error recovery mechanisms are triggered by transient or intermittent faults which could be caused, for example, by high intensity electromagnetic radiation. The tool is illustrated by analyzing a stabilizing controller for the longitudinal dynamics of the AFTI/F-16 aircraft. This example compares different recovery methodologies by determining the minimum interarrival spacing between upsets which maintains closed-loop mean-square stability.","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":"125311854","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}
Establishes results for the robust absolute stability of a class of nonlinear continuous-time systems with time-varying matrix uncertainties of polyhedral type and multiple time-varying sector nonlinearities. By using the variational method and the Lyapunov second method, criteria for robust absolute stability are obtained in different forms for the given class of systems. Specifically, the parametric classes of Lyapunov functions are determined which define the necessary and sufficient conditions of robust absolute stability. The piecewise linear Lyapunov functions of the infinity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations.
{"title":"Necessary and sufficient conditions for robust absolute stability of time-varying nonlinear continuous-time systems","authors":"A. Molchanov, Derong Liu","doi":"10.1109/CDC.2001.980066","DOIUrl":"https://doi.org/10.1109/CDC.2001.980066","url":null,"abstract":"Establishes results for the robust absolute stability of a class of nonlinear continuous-time systems with time-varying matrix uncertainties of polyhedral type and multiple time-varying sector nonlinearities. By using the variational method and the Lyapunov second method, criteria for robust absolute stability are obtained in different forms for the given class of systems. Specifically, the parametric classes of Lyapunov functions are determined which define the necessary and sufficient conditions of robust absolute stability. The piecewise linear Lyapunov functions of the infinity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"9 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":"125550391","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}
Addresses an approach to guidance algorithm design based on the concept of information sets (IS). As an example of guidance problem/spl Gamma/ a model of defense scenario against a reentering ballistic missile is considered. In this scenario/spl Gamma/ a maneuverable decelerating target is to be destroyed by a hit-to-kill interceptor fitted with an IR array seeker and lateral impulse thrusters. The key element of the proposed approach is a description of the "interceptor-target" system state by means of IS. The results of Monte Carlo tests of the developed algorithm are presented.
{"title":"Advanced guidance law design based on the information-set concept","authors":"D. Emeliyanov, E. Rubinovich, B. Miller","doi":"10.1109/CDC.2001.980178","DOIUrl":"https://doi.org/10.1109/CDC.2001.980178","url":null,"abstract":"Addresses an approach to guidance algorithm design based on the concept of information sets (IS). As an example of guidance problem/spl Gamma/ a model of defense scenario against a reentering ballistic missile is considered. In this scenario/spl Gamma/ a maneuverable decelerating target is to be destroyed by a hit-to-kill interceptor fitted with an IR array seeker and lateral impulse thrusters. The key element of the proposed approach is a description of the \"interceptor-target\" system state by means of IS. The results of Monte Carlo tests of the developed algorithm are presented.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"53 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":"126642838","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}
Wavelet theory provides a new type of function expansion and and has found many applications in signal processing. The discrete wavelet transform of a signal x(t) in L/sup 2/(R) is usually computed by the so-called pyramid algorithm. It however requires a proper initialization, i.e., expansion coefficients with respect to the basis of one of the desirable approximation subspaces. An interesting question is how we can obtain such coefficients when only sampled values of x(t) are available. The paper provides a design method for a digital filter that optimally gives such coefficients assuming certain a priori knowledge on the frequency characteristic of the target functions. We then extend the result to the case of non-orthogonal wavelets. Examples show the effectiveness of the proposed method.
{"title":"Optimal wavelet expansion via sampled-data control theory","authors":"K. Kashima, Y. Yamamoto, M. Nagahara","doi":"10.1109/CDC.2001.980964","DOIUrl":"https://doi.org/10.1109/CDC.2001.980964","url":null,"abstract":"Wavelet theory provides a new type of function expansion and and has found many applications in signal processing. The discrete wavelet transform of a signal x(t) in L/sup 2/(R) is usually computed by the so-called pyramid algorithm. It however requires a proper initialization, i.e., expansion coefficients with respect to the basis of one of the desirable approximation subspaces. An interesting question is how we can obtain such coefficients when only sampled values of x(t) are available. The paper provides a design method for a digital filter that optimally gives such coefficients assuming certain a priori knowledge on the frequency characteristic of the target functions. We then extend the result to the case of non-orthogonal wavelets. Examples show the effectiveness of the proposed method.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"15 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":"126852202","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 adaptive fuzzy control, approximation accuracy of the designed fuzzy system plays a key role in the overall system performance. Up to now, a linear parameterization method has been used to derive suitable adaptive laws, even in the adaptation of premise-part membership functions. However, the premise-part adaptation schemes with linear parameterization have some fundamental limitation due to the inadequacy of the gradient algorithm for general nonlinearly parameterized functions. In the paper, a new adaptive fuzzy control method with adaptation both of the premise-part and consequence-part membership functions is presented. The proposed adaptive fuzzy control scheme does not suffer from the problems appearing in conventional premise-part adaptation by using a nongradient strategy. The global stability as well as performance enhancement is given via simulations and application results of vehicle speed control.
{"title":"Premise-part adaptation laws for adaptive fuzzy control and its application to vehicle speed control","authors":"G. D. Lee, Sung Wan Kim, T. Park","doi":"10.1109/CDC.2001.980632","DOIUrl":"https://doi.org/10.1109/CDC.2001.980632","url":null,"abstract":"In adaptive fuzzy control, approximation accuracy of the designed fuzzy system plays a key role in the overall system performance. Up to now, a linear parameterization method has been used to derive suitable adaptive laws, even in the adaptation of premise-part membership functions. However, the premise-part adaptation schemes with linear parameterization have some fundamental limitation due to the inadequacy of the gradient algorithm for general nonlinearly parameterized functions. In the paper, a new adaptive fuzzy control method with adaptation both of the premise-part and consequence-part membership functions is presented. The proposed adaptive fuzzy control scheme does not suffer from the problems appearing in conventional premise-part adaptation by using a nongradient strategy. The global stability as well as performance enhancement is given via simulations and application results of vehicle speed control.","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":"115030912","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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