Among the deterministic policies for the optimal control of stochastic systems the best one is of closed-loop type, because it presents the "dual effect" of control. The theoretical closed-loop solution structure is deduced from Bellman's principle but is very difficult to implement in the non-linear case. This communication presents a closed-loop solution by approximation of the minimum cost function by introduction of the gaussian sum method.
{"title":"Optimal control of non-linear stochastic systems by approximation of the optimal cost functional","authors":"G. Campion","doi":"10.1109/CDC.1978.268044","DOIUrl":"https://doi.org/10.1109/CDC.1978.268044","url":null,"abstract":"Among the deterministic policies for the optimal control of stochastic systems the best one is of closed-loop type, because it presents the \"dual effect\" of control. The theoretical closed-loop solution structure is deduced from Bellman's principle but is very difficult to implement in the non-linear case. This communication presents a closed-loop solution by approximation of the minimum cost function by introduction of the gaussian sum method.","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":"114129782","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 presents a new approach to the frequency-domain analysis of multiloop linear feed-back systems. The properties of the return difference equation are examined using the concepts of singular values, singular vectors and the spectral norm of a matrix. A number of new tools for multiloop systems are developed which are analogous to those for scalar Nyquist and Bode analysis. These provide a generalization of the scalar frequency-domain notions such as gain, bandwidth, stability margins and M-circles, and provide considerable insight into system robustness.
{"title":"Robustness of multiloop linear feedback systems","authors":"J. Doyle","doi":"10.1109/CDC.1978.267885","DOIUrl":"https://doi.org/10.1109/CDC.1978.267885","url":null,"abstract":"This paper presents a new approach to the frequency-domain analysis of multiloop linear feed-back systems. The properties of the return difference equation are examined using the concepts of singular values, singular vectors and the spectral norm of a matrix. A number of new tools for multiloop systems are developed which are analogous to those for scalar Nyquist and Bode analysis. These provide a generalization of the scalar frequency-domain notions such as gain, bandwidth, stability margins and M-circles, and provide considerable insight into system robustness.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"37 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":"123809423","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}
Modern statistical continuous-time nonlinear filtering theory has become so esoteric that its utility for practical applications is frequently questioned. This paper examines whether there may be an alternative rationale for arriving at a plausible nonlinear filter which could be more readily implemented in practice. This rationale dispenses with statistics entirely and approaches the problem as nonlinear least squares curve fitting. In order to do this we consider only a model which contains observation "noise" only, and no state "noise". The object is not so much to come up with a specific filter which solves a specific problem as to gain insight into the nature of the obstacles to computational ease which seem inherent in any formulation.
{"title":"Nonstatistical nonlinear filtering","authors":"R. Mortensen","doi":"10.1109/CDC.1978.267906","DOIUrl":"https://doi.org/10.1109/CDC.1978.267906","url":null,"abstract":"Modern statistical continuous-time nonlinear filtering theory has become so esoteric that its utility for practical applications is frequently questioned. This paper examines whether there may be an alternative rationale for arriving at a plausible nonlinear filter which could be more readily implemented in practice. This rationale dispenses with statistics entirely and approaches the problem as nonlinear least squares curve fitting. In order to do this we consider only a model which contains observation \"noise\" only, and no state \"noise\". The object is not so much to come up with a specific filter which solves a specific problem as to gain insight into the nature of the obstacles to computational ease which seem inherent in any formulation.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"31 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":"127114460","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}
Modern multivariate estimation theory has important potential applications in meteorological inverse problems involving weather assessment and prediction. This is especially true with the advent of sensitive satellite-borne passive spectrometers. which offer 24 hour global coverage. These applications include estimation of: (1) vertical temperature profiles, (2) cloud content, type, height and thickness, (3) atmospheric water vapor and liquid water columns, (4) surface parameters such as sea surface wind speed, sea ice, snow and soil, and (5) minor constituents such as O3. Typically, only a few noisy measurements are available and the problem is underdetermined. However, apriori information is available from climatology or forecast fields which can be combined with the data to yield filtered solutions. These problems are typically characterized by highly nonlinear measurements, necessitating approximate nonlinear filtering solutions. Several applications are presented. The extended Kalman filter (EKF) is utilized for recursive temperature profile retrievals using remote microwave soundings from a single scanning instrument. Horizontal and vertical spatio-temporal correlations are accounted for in the model. Numerical results indicate a 10-30% reduction in rms error when compared with standard regression techniques. Another application involves recovery of cloud and surface parameters from microwave data. The iterated extended Kalman filter(IEKF) is used to estimate cloud height, thickness and integrated liquid water, and surface wind speed. Analytical measurement models, which are highly nonlinear, are found using nonlinear regression in conjunction with sophisticated radiative transfer simulations. Numerical results are presented for the IEKF, EKF and regression solutions and these are compared with the Cramer-Rao bound. The IEKF offers the best inversion method of those tested.
{"title":"Applications of estimation theory to inverse problems in meteorology","authors":"D. Gustafson, W. Ledsham","doi":"10.1109/CDC.1978.267958","DOIUrl":"https://doi.org/10.1109/CDC.1978.267958","url":null,"abstract":"Modern multivariate estimation theory has important potential applications in meteorological inverse problems involving weather assessment and prediction. This is especially true with the advent of sensitive satellite-borne passive spectrometers. which offer 24 hour global coverage. These applications include estimation of: (1) vertical temperature profiles, (2) cloud content, type, height and thickness, (3) atmospheric water vapor and liquid water columns, (4) surface parameters such as sea surface wind speed, sea ice, snow and soil, and (5) minor constituents such as O3. Typically, only a few noisy measurements are available and the problem is underdetermined. However, apriori information is available from climatology or forecast fields which can be combined with the data to yield filtered solutions. These problems are typically characterized by highly nonlinear measurements, necessitating approximate nonlinear filtering solutions. Several applications are presented. The extended Kalman filter (EKF) is utilized for recursive temperature profile retrievals using remote microwave soundings from a single scanning instrument. Horizontal and vertical spatio-temporal correlations are accounted for in the model. Numerical results indicate a 10-30% reduction in rms error when compared with standard regression techniques. Another application involves recovery of cloud and surface parameters from microwave data. The iterated extended Kalman filter(IEKF) is used to estimate cloud height, thickness and integrated liquid water, and surface wind speed. Analytical measurement models, which are highly nonlinear, are found using nonlinear regression in conjunction with sophisticated radiative transfer simulations. Numerical results are presented for the IEKF, EKF and regression solutions and these are compared with the Cramer-Rao bound. The IEKF offers the best inversion method of those tested.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"59 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":"133029592","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 Adaptive Line Enhancer (ALE) was first described by Widrow et al, as a practical on-line technique for separating the coherent components from the incoherent components of an input signal. Subsequent work has shown this same adaptive filtering structure to be applicable to maximum entropy spectral estimation, predictive deconvolution, and narrowband interference rejection, as well as other applications which have historically used matrix inversion and Levinson's algorithm techniques. While an often cited advantage of adaptive filtering is its tolerance of slowly time-varying input statistics, the existing analyses of the ALE have concentrated on the stationary case. This paper extends these results, applying the theory to the case of inputs containing sinusoids whose frequencies slowly vary in time. This is approached by developing a time-varying eigenvalue-eigenvector description of the expected filter impulse response vector which holds for any slowly nonstationary input. These results are then used to predict the expected impulse response vector for the ALE input of stationary white noise plus a sinusoid with linearly swept frequency. The response of the ALE for this particular input signal provides useful benchmarks for dealing with more complex forms of frequency modulation.
{"title":"Response of the adaptive line enhancer to chirped sinusoids","authors":"J. Treichler","doi":"10.1109/CDC.1978.268141","DOIUrl":"https://doi.org/10.1109/CDC.1978.268141","url":null,"abstract":"The Adaptive Line Enhancer (ALE) was first described by Widrow et al, as a practical on-line technique for separating the coherent components from the incoherent components of an input signal. Subsequent work has shown this same adaptive filtering structure to be applicable to maximum entropy spectral estimation, predictive deconvolution, and narrowband interference rejection, as well as other applications which have historically used matrix inversion and Levinson's algorithm techniques. While an often cited advantage of adaptive filtering is its tolerance of slowly time-varying input statistics, the existing analyses of the ALE have concentrated on the stationary case. This paper extends these results, applying the theory to the case of inputs containing sinusoids whose frequencies slowly vary in time. This is approached by developing a time-varying eigenvalue-eigenvector description of the expected filter impulse response vector which holds for any slowly nonstationary input. These results are then used to predict the expected impulse response vector for the ALE input of stationary white noise plus a sinusoid with linearly swept frequency. The response of the ALE for this particular input signal provides useful benchmarks for dealing with more complex forms of frequency modulation.","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":"130206873","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 describes the results of a study to investigate the value of applying sophisticated controls to solar heating systems. A residential solar heating system utilizing a heat pump operating in the series-storage mode is considered and optimal control theory is used to derive a control strategy. The basic question addressed is how much of an improvement in efficiency can be gained, relative to a conventionally designed controller, if an unrestricted control strategy is applied in an optimal fashion. The efficiency comparison is made on the basis of the amount of auxiliary energy required to attain an acceptable level of room temperature regulation. The second-order model for the system is derived using basic energy balance techniques and 4 control inputs are employed overall. The optimal control inputs are determined using Pontryagin's Maximum Principle which requires solution of a two-point boundary value problem. This is solved numerically using an iterative technique.
{"title":"Sophisticated solar heating controllers: Are they cost effective","authors":"R. Blodgett, J. Nebus, W. Trimmer, T. Taylor","doi":"10.1109/CDC.1978.267920","DOIUrl":"https://doi.org/10.1109/CDC.1978.267920","url":null,"abstract":"This paper describes the results of a study to investigate the value of applying sophisticated controls to solar heating systems. A residential solar heating system utilizing a heat pump operating in the series-storage mode is considered and optimal control theory is used to derive a control strategy. The basic question addressed is how much of an improvement in efficiency can be gained, relative to a conventionally designed controller, if an unrestricted control strategy is applied in an optimal fashion. The efficiency comparison is made on the basis of the amount of auxiliary energy required to attain an acceptable level of room temperature regulation. The second-order model for the system is derived using basic energy balance techniques and 4 control inputs are employed overall. The optimal control inputs are determined using Pontryagin's Maximum Principle which requires solution of a two-point boundary value problem. This is solved numerically using an iterative technique.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"134 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":"134040891","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 presents the results of a preliminary analysis designed to predict the properties of an adaptive noise-cancelling filter which is implemented using a lattice structure. Previous work in this area has been restricted to adaptive filters implemented using tapped-delay-lines. The comparison given shows that the lattice form has a time constant of convergence which is independent of the eigenvalue spread of the input data. Further, misadjustment values are shown to depend upon both filter length and the normalized adaptive step size.
{"title":"Convergence properties of an adaptive noise cancelling lattice structure","authors":"L. Griffiths, R. Medaugh","doi":"10.1109/CDC.1978.268139","DOIUrl":"https://doi.org/10.1109/CDC.1978.268139","url":null,"abstract":"This paper presents the results of a preliminary analysis designed to predict the properties of an adaptive noise-cancelling filter which is implemented using a lattice structure. Previous work in this area has been restricted to adaptive filters implemented using tapped-delay-lines. The comparison given shows that the lattice form has a time constant of convergence which is independent of the eigenvalue spread of the input data. Further, misadjustment values are shown to depend upon both filter length and the normalized adaptive step size.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"7 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":"122355176","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. Willsky, P. Houpt, S. Gershwin, Andrew Kurkjian, C. Greene, E. Chow
{"title":"Detection of incidents on freeways","authors":"A. Willsky, P. Houpt, S. Gershwin, Andrew Kurkjian, C. Greene, E. Chow","doi":"10.1109/CDC.1978.268088","DOIUrl":"https://doi.org/10.1109/CDC.1978.268088","url":null,"abstract":"","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"122 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":"127965543","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 missile-aircraft pursuit-evasion problem is formulated by a three-dimensional linearized kinematic model. The formulation is valid both for the optimal control (against a known adversary strategy) and the zero sum differential game versions. Assuming perfect information the linearized kinematic model yields for both versions a solution which can be implemented in real-time for airborne application. The avoidance of a known pursuer by an evader who has no state information is solved by a stochastically optimal periodical maneuver. Other examples of imperfect information are briefly discussed.
{"title":"Recent advances in optimal pursuit and evasion","authors":"J. Shinar, S. Gutman","doi":"10.1109/CDC.1978.268074","DOIUrl":"https://doi.org/10.1109/CDC.1978.268074","url":null,"abstract":"The missile-aircraft pursuit-evasion problem is formulated by a three-dimensional linearized kinematic model. The formulation is valid both for the optimal control (against a known adversary strategy) and the zero sum differential game versions. Assuming perfect information the linearized kinematic model yields for both versions a solution which can be implemented in real-time for airborne application. The avoidance of a known pursuer by an evader who has no state information is solved by a stochastically optimal periodical maneuver. Other examples of imperfect information are briefly discussed.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"94 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":"129089717","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}
Several control schemes have been proposed in the past for optimal control of congested intersections but they have not been applied in real life situations partly because of the complex instrumentation required for their application and partly because they do not combine all control objectives at such intersections. Open and closed loop control policies minimizing total intersection delays subject to queue size constraints have also been proposed by the authors. All control policies, however, have the disadvantage that they are based on simple traffic models describing the effective size of the queues rather than the queue lengths. In this paper a new model is presented describing the queue dynamics at signalized intersections as a function of the demands, the intersection characteristics and the control decisions. A control policy combining the results of this model and control principles previously developed by the authors is also proposed.
{"title":"Real time control of critical intersections based on queue dynamics","authors":"G. Stephanopoulos, P. Michalopoulos","doi":"10.1109/CDC.1978.268085","DOIUrl":"https://doi.org/10.1109/CDC.1978.268085","url":null,"abstract":"Several control schemes have been proposed in the past for optimal control of congested intersections but they have not been applied in real life situations partly because of the complex instrumentation required for their application and partly because they do not combine all control objectives at such intersections. Open and closed loop control policies minimizing total intersection delays subject to queue size constraints have also been proposed by the authors. All control policies, however, have the disadvantage that they are based on simple traffic models describing the effective size of the queues rather than the queue lengths. In this paper a new model is presented describing the queue dynamics at signalized intersections as a function of the demands, the intersection characteristics and the control decisions. A control policy combining the results of this model and control principles previously developed by the authors is also proposed.","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":"129310504","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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