Though the theory of the maximum likelihood method for parameter estimation in dynamic systems is well developed, its application to complex systems has been limited by the unavailability of fast and reliable computational algorithms to maximize the likelihood function. Gradient-based algorithms have been mostly used for this purpose until now. A summary of such techniques was given by Gupta and Mehra (1974). Recent experience with algorithms which do not explicitly compute the gradients of the innovations or the likelihood function indicates that such algorithms offer potential benefits over gradient-based algorithms. This paper surveys direct search optimization methods and compares them to the algorithms requiring a direct computation of the gradients. An example problem is presented to show the class of problems for which such methods are likely to be useful.
{"title":"Direct search computational methods for maximum likelihood parameter estimation","authors":"N. Gupta","doi":"10.1109/CDC.1978.268064","DOIUrl":"https://doi.org/10.1109/CDC.1978.268064","url":null,"abstract":"Though the theory of the maximum likelihood method for parameter estimation in dynamic systems is well developed, its application to complex systems has been limited by the unavailability of fast and reliable computational algorithms to maximize the likelihood function. Gradient-based algorithms have been mostly used for this purpose until now. A summary of such techniques was given by Gupta and Mehra (1974). Recent experience with algorithms which do not explicitly compute the gradients of the innovations or the likelihood function indicates that such algorithms offer potential benefits over gradient-based algorithms. This paper surveys direct search optimization methods and compares them to the algorithms requiring a direct computation of the gradients. An example problem is presented to show the class of problems for which such methods are likely to be useful.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122111297","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 singular perturbation theory (SPT) approximation of optimal feedback control laws is presented and methods for on-line application of these approximations are discussed. It is shown that SPT control laws break down when the current state is near the terminal target state. The use of continuation methods to improve the accuracy of the SPT approximation and to obtain global solutions of Two-Point Boundary Value Problems (TPBVP) is also discussed. To illustrate the theoretical discussion we present the minimum-time control of a supersonic aircraft for a three-dimensional intercept problem.
{"title":"Application of singular perturbation techniques (SPT) and continuation methods for on-line aircraft trajectory optimization","authors":"R. Washburn, R. Mehra, S. Sajan","doi":"10.1109/CDC.1978.268078","DOIUrl":"https://doi.org/10.1109/CDC.1978.268078","url":null,"abstract":"The singular perturbation theory (SPT) approximation of optimal feedback control laws is presented and methods for on-line application of these approximations are discussed. It is shown that SPT control laws break down when the current state is near the terminal target state. The use of continuation methods to improve the accuracy of the SPT approximation and to obtain global solutions of Two-Point Boundary Value Problems (TPBVP) is also discussed. To illustrate the theoretical discussion we present the minimum-time control of a supersonic aircraft for a three-dimensional intercept problem.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116811022","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}
Control processes which can be modeled by certain linear hyperbolic, partial differential equations are considered with the purpose of identifying those which can be exactly controlled to a specified state in some finite time by control forces applied on the boundary of the region ¿ in which the process evolves. A class of processes for which such control is possible is determined in terms of asymptotic behavior of the fundamental solution of the modeling equation, and the optimal control time is shown to be no greater than the diameter of ¿.
{"title":"Exact boundary value controllability in hyperbolic problems","authors":"J. Lagnese","doi":"10.1109/CDC.1978.267936","DOIUrl":"https://doi.org/10.1109/CDC.1978.267936","url":null,"abstract":"Control processes which can be modeled by certain linear hyperbolic, partial differential equations are considered with the purpose of identifying those which can be exactly controlled to a specified state in some finite time by control forces applied on the boundary of the region ¿ in which the process evolves. A class of processes for which such control is possible is determined in terms of asymptotic behavior of the fundamental solution of the modeling equation, and the optimal control time is shown to be no greater than the diameter of ¿.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124061836","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 describes the algebra ß(¿0) of transfer functions of distributed systems; ß(¿0) generalizes the algebra of proper rational functions [see, e.g. 7,8]. The first theorem generalizes for the distributed case a result of Youla et al. [10]: any plant ¿ can be stabilized by pre-or post-compensation and the closed-loop natural frequencies can be preassigned in C¿ 0+, the domain of definition of ¿. The second theorem generalizes for the distributed case the known results of the lumped case [for a detailed review, see 10]: stabilization and asymptotically zero tracking-error can be achieved by a precompensator with elements in ß (¿0). Furthermore, the stabilization and tracking is robust.
本文描述了分布式系统传递函数的代数ß(¿0);ß(¿0)推广了固有有理函数的代数[参见，例如7,8]。第一个定理推广了Youla et al.[10]在分布式情况下的结果:任何对象都可以通过预补偿或后补偿来稳定，并且闭环固有频率可以在C¿0+中预分配，C¿0+是C¿0+的定义域。第二个定理推广了分布情况下集总情况的已知结果[详细回顾，见10]:稳定性和渐近零跟踪误差可以通过具有ß(¿0)元素的预补偿器来实现。此外，该系统具有鲁棒性。
{"title":"Stabilization, tracking and disturbance rejection in linear multivariable distributed systems","authors":"F. Callier, C. Desoer","doi":"10.1109/CDC.1978.267981","DOIUrl":"https://doi.org/10.1109/CDC.1978.267981","url":null,"abstract":"The paper describes the algebra ß(¿0) of transfer functions of distributed systems; ß(¿0) generalizes the algebra of proper rational functions [see, e.g. 7,8]. The first theorem generalizes for the distributed case a result of Youla et al. [10]: any plant ¿ can be stabilized by pre-or post-compensation and the closed-loop natural frequencies can be preassigned in C¿ 0+, the domain of definition of ¿. The second theorem generalizes for the distributed case the known results of the lumped case [for a detailed review, see 10]: stabilization and asymptotically zero tracking-error can be achieved by a precompensator with elements in ß (¿0). Furthermore, the stabilization and tracking is robust.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126124648","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 regulator problem is considered in the context of linear time-invariant multivariable systems. The exogeneous signal, the disturbance and/or reference signal, is assumed to be generated by a model (the exomodel) with unknown initial conditions. Unlike in previous treatments, the exomodel parameters are not assumed known. A two-stage adaptive control scheme is presented, the first stage being an identifier of the exomodel and the second stage a time-varying robust regulator containing an internal model of the exomodel which is tuned on-line by the first stage.
{"title":"Adaptive robust regulation of linear multivariable systems: Tracking signals generated by models with unknown parameters","authors":"B. Francis, M. Vidyasagar","doi":"10.1109/CDC.1978.268101","DOIUrl":"https://doi.org/10.1109/CDC.1978.268101","url":null,"abstract":"The regulator problem is considered in the context of linear time-invariant multivariable systems. The exogeneous signal, the disturbance and/or reference signal, is assumed to be generated by a model (the exomodel) with unknown initial conditions. Unlike in previous treatments, the exomodel parameters are not assumed known. A two-stage adaptive control scheme is presented, the first stage being an identifier of the exomodel and the second stage a time-varying robust regulator containing an internal model of the exomodel which is tuned on-line by the first stage.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124805907","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 new procedure for investigating the global observability of classes of nonlinear differential equations is proposed. The method makes use of given qualitative properties of the flow. It is shown that for Morse-Smale flows, local observability criteria can be tied together, resulting in a global observability criterion.
{"title":"Global observability for nonlinear autonomous differential equations","authors":"D. Aeyels, D. Elliott","doi":"10.1109/CDC.1978.268092","DOIUrl":"https://doi.org/10.1109/CDC.1978.268092","url":null,"abstract":"A new procedure for investigating the global observability of classes of nonlinear differential equations is proposed. The method makes use of given qualitative properties of the flow. It is shown that for Morse-Smale flows, local observability criteria can be tied together, resulting in a global observability criterion.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125020726","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}
Many of the problems and limitations previously encountered in designing adaptive controllers might now be accomodated due to the existance of powerful LSI logic. Thus, new research directions can be defined related to the development of both estimation algorithms and control update procedures.
{"title":"Adaptive control systems, classification, problems, and suggestions","authors":"H. Kaufman","doi":"10.1109/CDC.1978.268147","DOIUrl":"https://doi.org/10.1109/CDC.1978.268147","url":null,"abstract":"Many of the problems and limitations previously encountered in designing adaptive controllers might now be accomodated due to the existance of powerful LSI logic. Thus, new research directions can be defined related to the development of both estimation algorithms and control update procedures.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129438347","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 stochastic algorithm, familiar from adaptive estimation, is introduced and its homogeneous part is shown to be exponentially convergent for a wide class of inputs, which need not be stationary. The implications of this convergence rate for the nonhomogeneous algorithm in practical situations are qualitatively examined and a possible approach to improving performance in use is suggested.
{"title":"Exponentially convergent behaviour of simple stochastic adaptive estimation algorithms","authors":"R. Bitmead, B. O. Anderson","doi":"10.1109/CDC.1978.267996","DOIUrl":"https://doi.org/10.1109/CDC.1978.267996","url":null,"abstract":"A stochastic algorithm, familiar from adaptive estimation, is introduced and its homogeneous part is shown to be exponentially convergent for a wide class of inputs, which need not be stationary. The implications of this convergence rate for the nonhomogeneous algorithm in practical situations are qualitatively examined and a possible approach to improving performance in use is suggested.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129465481","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 tracking and ultimate identification of closely spaced objects is an area of interest to many surveillance systems. Much effort in recent years has been concentrated on the more "front-end" problem of optimizing the initial detection. However, the sorting and processing of crossing tracks and parallel tracks is a problem regardless of signal to noise ratio. In this paper, the application of a pattern recognition approach is investigated. A simulated track scenario is developed and the approach evaluated using the scenario. Examples of performance and results of the simulation study are given.
{"title":"On the detection of target trajectories in a multi target environment","authors":"M. Smith, E. Winter","doi":"10.1109/CDC.1978.268123","DOIUrl":"https://doi.org/10.1109/CDC.1978.268123","url":null,"abstract":"The tracking and ultimate identification of closely spaced objects is an area of interest to many surveillance systems. Much effort in recent years has been concentrated on the more \"front-end\" problem of optimizing the initial detection. However, the sorting and processing of crossing tracks and parallel tracks is a problem regardless of signal to noise ratio. In this paper, the application of a pattern recognition approach is investigated. A simulated track scenario is developed and the approach evaluated using the scenario. Examples of performance and results of the simulation study are given.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"43 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129712376","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 discrete-time, Least-Mean-Squares (LMS) algorithm is often proposed for application to adaptive antenna arrays. In analyzing the mean-square error performance of LMS, however, previous results in the open literature have generally employed approximations which are valid only in the limit for very slow adaptation in an essentially stationary environment. In this paper we apply an exact mean-square error analysis for the application of discrete-time LMS to narrow-band adaptive arrays. The results provide considerable insight into the transient response of LMS under conditions of rapid adaptation, which is of importance in many practical applications.
{"title":"New results on convergence of the discrete-time LMS algorithm applied to narrowband adaptive arrays","authors":"K. Senne, L. Horowitz","doi":"10.1109/CDC.1978.268118","DOIUrl":"https://doi.org/10.1109/CDC.1978.268118","url":null,"abstract":"The discrete-time, Least-Mean-Squares (LMS) algorithm is often proposed for application to adaptive antenna arrays. In analyzing the mean-square error performance of LMS, however, previous results in the open literature have generally employed approximations which are valid only in the limit for very slow adaptation in an essentially stationary environment. In this paper we apply an exact mean-square error analysis for the application of discrete-time LMS to narrow-band adaptive arrays. The results provide considerable insight into the transient response of LMS under conditions of rapid adaptation, which is of importance in many practical applications.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129791497","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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