In airborne Track-While-Scan systems, target parameters are updated via individual Kalman Filters. To insure numerical stability and accuracy, UD-Factorization techniques are used. A preset number of individual tracks is typically maintained in dense target environments. In real-time application the processing load is of concern. The UD-Factorization algorithm for measurement updates operates on each measurement individually when the error covariance matrix of the measurements is diagonal. In the inertial X-Y-Z TWS Kalman Filter for each track, this matrix is inherently non-diagonal and consequently needs to be operated upon. The proposed algorithm utilizes the lower triangular Cholesky square root technique to determine the normalized measurement vector and observation matrix, and yields an identity measurement error covariance matrix. To perform all the computations necessary requires considerable effort, and this paper delineates what is involved. The computationally cost-effective way to operate reduces to only a few subsidiary calculations above what would be necessary had the measurement error covariance matrix been diagonal to begin with. This algorithm is invoked prior to performing the Kalman Measurement Update equations.
{"title":"Use of Cholesky square roots amidst the UD-factorization implementation of Kalman filters in real-time airborne tracking systems","authors":"R. Yannone","doi":"10.1109/CDC.1984.272054","DOIUrl":"https://doi.org/10.1109/CDC.1984.272054","url":null,"abstract":"In airborne Track-While-Scan systems, target parameters are updated via individual Kalman Filters. To insure numerical stability and accuracy, UD-Factorization techniques are used. A preset number of individual tracks is typically maintained in dense target environments. In real-time application the processing load is of concern. The UD-Factorization algorithm for measurement updates operates on each measurement individually when the error covariance matrix of the measurements is diagonal. In the inertial X-Y-Z TWS Kalman Filter for each track, this matrix is inherently non-diagonal and consequently needs to be operated upon. The proposed algorithm utilizes the lower triangular Cholesky square root technique to determine the normalized measurement vector and observation matrix, and yields an identity measurement error covariance matrix. To perform all the computations necessary requires considerable effort, and this paper delineates what is involved. The computationally cost-effective way to operate reduces to only a few subsidiary calculations above what would be necessary had the measurement error covariance matrix been diagonal to begin with. This algorithm is invoked prior to performing the Kalman Measurement Update equations.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134391777","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 development of a model of an actual assembly line with emphasis on the factors determining the quality and yield of the product is described. The model can be generalized to describe assembly systems with converging/diverging structure. The paper stresses the need to look at the control of quality from a systems perspective rather than the traditional process orientation.
{"title":"Quality modeling and a quality control of a manufacturing system","authors":"J. Buzacott, D. Cheng","doi":"10.1109/CDC.1984.272323","DOIUrl":"https://doi.org/10.1109/CDC.1984.272323","url":null,"abstract":"The development of a model of an actual assembly line with emphasis on the factors determining the quality and yield of the product is described. The model can be generalized to describe assembly systems with converging/diverging structure. The paper stresses the need to look at the control of quality from a systems perspective rather than the traditional process orientation.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134564705","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 purpose of this paper is to show how the introduction of the concept of Shannon Information into Optimal Stochastic Control theory allows certain problems with partial observations to become tractable. In particular, adaptive control problems can be formulated sometimes as such problems; this leads to a class of adaptive regulators that extend the usual Linear Quadratic regulator. We start with a linear setting first.
{"title":"Entropy and dual control","authors":"O. Hijab","doi":"10.1109/CDC.1984.272249","DOIUrl":"https://doi.org/10.1109/CDC.1984.272249","url":null,"abstract":"The purpose of this paper is to show how the introduction of the concept of Shannon Information into Optimal Stochastic Control theory allows certain problems with partial observations to become tractable. In particular, adaptive control problems can be formulated sometimes as such problems; this leads to a class of adaptive regulators that extend the usual Linear Quadratic regulator. We start with a linear setting first.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114170340","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 least squares parameter identification technique is developed for a class of nonlinear deterministic systems modeled by polynomial input-output differential equations. The basis of the technique is Shinbrot's method of moment functionals using trigonometric modulating functions. Given the input-output data over sequential time intervals, the underlying computations utilize a Fast Fourier Transform algorithm on polynomials of the data without the need for estimating unknown initial conditions at the start of each finite time interval.
{"title":"Parameter identification for a class of polynomial differential systems","authors":"A. Pearson, F. Lee","doi":"10.1109/CDC.1984.272374","DOIUrl":"https://doi.org/10.1109/CDC.1984.272374","url":null,"abstract":"A least squares parameter identification technique is developed for a class of nonlinear deterministic systems modeled by polynomial input-output differential equations. The basis of the technique is Shinbrot's method of moment functionals using trigonometric modulating functions. Given the input-output data over sequential time intervals, the underlying computations utilize a Fast Fourier Transform algorithm on polynomials of the data without the need for estimating unknown initial conditions at the start of each finite time interval.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114186860","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 parametric hierarchical control approach is used to compute decentralized gains for a two time-scale large scale system of interconnected singularly perturbed systems. In the neighborhood of (local) optimal coordination parameter values the supremal problem preserves the open-loop two time-scale structure. This observation motivates a singular perturbation type of approximate solution of the supremal problem. An illustrative numerical example is given.
{"title":"Parameterized hierarchical control of interconnected singularly perturbed systems","authors":"D. Looze, David H. Gahutu","doi":"10.1109/CDC.1984.272147","DOIUrl":"https://doi.org/10.1109/CDC.1984.272147","url":null,"abstract":"A parametric hierarchical control approach is used to compute decentralized gains for a two time-scale large scale system of interconnected singularly perturbed systems. In the neighborhood of (local) optimal coordination parameter values the supremal problem preserves the open-loop two time-scale structure. This observation motivates a singular perturbation type of approximate solution of the supremal problem. An illustrative numerical example is given.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"7 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117046200","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 methodology of [1] is extended to design problems in which servomechanism controllers are sought for obtaining asymptotically exact error regulation for a class of design signals and "good" error regulation for applied signals which may be unknown or random in nature. Application is made in examples to band-limited random reference and disturbance signals.
{"title":"The design of servomechanism controllers for exact and approximate error regulation","authors":"B. Scherzinger, E. Davison","doi":"10.1109/CDC.1984.272210","DOIUrl":"https://doi.org/10.1109/CDC.1984.272210","url":null,"abstract":"The methodology of [1] is extended to design problems in which servomechanism controllers are sought for obtaining asymptotically exact error regulation for a class of design signals and \"good\" error regulation for applied signals which may be unknown or random in nature. Application is made in examples to band-limited random reference and disturbance signals.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"221 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115837830","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}
Efficient and numerically well-conditioned scoring algorithms are presented for the maximum-likelihood estimation of initial means and covariances from an ensemble of tests when the initial condition is not observable per test. These algorithms take account also of the possibility that the estimated initial covariance may be singular. A sufficient statistic is used to reduce the computational burden and singular-value-decomposition and square root techniques are used to increase the numerical accuracy of the algorithm.
{"title":"Efficient estimation of initial-condition parameters for partially observable initial conditions","authors":"M. Shuster, D. Porter","doi":"10.1109/CDC.1984.272225","DOIUrl":"https://doi.org/10.1109/CDC.1984.272225","url":null,"abstract":"Efficient and numerically well-conditioned scoring algorithms are presented for the maximum-likelihood estimation of initial means and covariances from an ensemble of tests when the initial condition is not observable per test. These algorithms take account also of the possibility that the estimated initial covariance may be singular. A sufficient statistic is used to reduce the computational burden and singular-value-decomposition and square root techniques are used to increase the numerical accuracy of the algorithm.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116133690","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 examine the Markovian properties of three important random fields: Lévy's Brownian motion, free Euclidean field, and Wiener process. In so doing, we advance the proposition that appropriate candidates for Markov fields are stochastic differential forms and their Markovian property is characterized by being "one derivative" removed from white noise.
{"title":"Markovian random fields","authors":"E. Wong","doi":"10.1109/CDC.1984.272296","DOIUrl":"https://doi.org/10.1109/CDC.1984.272296","url":null,"abstract":"In this paper we examine the Markovian properties of three important random fields: Lévy's Brownian motion, free Euclidean field, and Wiener process. In so doing, we advance the proposition that appropriate candidates for Markov fields are stochastic differential forms and their Markovian property is characterized by being \"one derivative\" removed from white noise.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123133516","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 popular approach to adaptive control consists of I.) estimating the parameters of the system at each time instant and II.) applying a control input at each time instant which is optimal with respect to a specified cost criterion if the estimated parameters are indeed the true values. The natural question for such a scheme is whether the control law based on the estimated parameters will converge asymptotically to the optimal control law with regard to the specified cost criterion for the true parameter values. In other words, will the adaptive control law self-tune to the optimal control law? Much attention has recently been paid to the problem of controlling an unknown ARMAX system where the specified cost criterion is the variance of the output process and recently it has been shown that an adaptive control law, as above, does self-tune to the minimum variance control law, see (1). Our main contention here is that the self-tuning result for a minimum variance cost criterion rests on self-tuning to an optimal control law will not generally occur for general cost criteria. The particular case of a quadratic cost criterion penalizing not only the variance of the output but also the variance of the input is analyzed by Ljung's O.D.E.'s to demonstrate this. One special situation in which self-tuning can be expected is when the ARMAX system has a large enough delay.
{"title":"Will self-tuning occur for general cost criteria?","authors":"P. Kumar","doi":"10.1109/CDC.1984.272251","DOIUrl":"https://doi.org/10.1109/CDC.1984.272251","url":null,"abstract":"A popular approach to adaptive control consists of I.) estimating the parameters of the system at each time instant and II.) applying a control input at each time instant which is optimal with respect to a specified cost criterion if the estimated parameters are indeed the true values. The natural question for such a scheme is whether the control law based on the estimated parameters will converge asymptotically to the optimal control law with regard to the specified cost criterion for the true parameter values. In other words, will the adaptive control law self-tune to the optimal control law? Much attention has recently been paid to the problem of controlling an unknown ARMAX system where the specified cost criterion is the variance of the output process and recently it has been shown that an adaptive control law, as above, does self-tune to the minimum variance control law, see (1). Our main contention here is that the self-tuning result for a minimum variance cost criterion rests on self-tuning to an optimal control law will not generally occur for general cost criteria. The particular case of a quadratic cost criterion penalizing not only the variance of the output but also the variance of the input is analyzed by Ljung's O.D.E.'s to demonstrate this. One special situation in which self-tuning can be expected is when the ARMAX system has a large enough delay.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"123 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123285955","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 a recent study, the robustness of a tail controlled homing missile constant gain autopilot to changes in the aerodynamic stability derivative M¿ was examined. The constant gains were determined from nominal values of the aerodynamic control derivative, M¿, and the stability derivative. The stability derivative was then varied in the positive direction until damping degraded to unacceptable levels and in the negative direction until the system time constant became too slow to achieve a successful intercept against a maneuvering target. Therefore the range of M¿'s realized represented an allowable uncertainty in M¿. In this paper it is shown that the robustness to variations in M¿ of an autopilot designed about a nominal M¿ and M¿ is strongly dependent on M¿ and less dependent on the nominal value of M¿. If M¿ and M¿ values are known accurately and gains can be calculated at each value, then a variable gain flight control system can be designed. It is shown that the range of M¿ values which a variable gain flight control system can tolerate is much larger than the range of M¿ values which a fixed gain flight control system can handle. The effect of the open loop crossover frequency ¿CR and the actuator bandwidth on the allowable region of M¿ for both a constant gain and a variable gain flight control system is also discussed. This expansion on the previous study will become more important as improvements in computer technologies such as larger throughput and memory capability allow the autopilot to become more sophisticated.
{"title":"Homing missile autopilot response sensitivity to stability derivative variations","authors":"F. Nesline, M. Nesline","doi":"10.1109/CDC.1984.272187","DOIUrl":"https://doi.org/10.1109/CDC.1984.272187","url":null,"abstract":"In a recent study, the robustness of a tail controlled homing missile constant gain autopilot to changes in the aerodynamic stability derivative M¿ was examined. The constant gains were determined from nominal values of the aerodynamic control derivative, M¿, and the stability derivative. The stability derivative was then varied in the positive direction until damping degraded to unacceptable levels and in the negative direction until the system time constant became too slow to achieve a successful intercept against a maneuvering target. Therefore the range of M¿'s realized represented an allowable uncertainty in M¿. In this paper it is shown that the robustness to variations in M¿ of an autopilot designed about a nominal M¿ and M¿ is strongly dependent on M¿ and less dependent on the nominal value of M¿. If M¿ and M¿ values are known accurately and gains can be calculated at each value, then a variable gain flight control system can be designed. It is shown that the range of M¿ values which a variable gain flight control system can tolerate is much larger than the range of M¿ values which a fixed gain flight control system can handle. The effect of the open loop crossover frequency ¿CR and the actuator bandwidth on the allowable region of M¿ for both a constant gain and a variable gain flight control system is also discussed. This expansion on the previous study will become more important as improvements in computer technologies such as larger throughput and memory capability allow the autopilot to become more sophisticated.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124863731","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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