The stability of two third-order population ecosystems is analyzed and system dependence on intrinsic rates of growth is demonstrated. A bounded, quasi-optimum feedback control law is derived to satisfy a quadratic cost function. The stabilizing effect of the law is studied both mathematically and via digital simulation.
{"title":"Analysis of a nonlinear population ecosystem","authors":"J. Pritchard, D. Anand","doi":"10.1109/CDC.1975.270597","DOIUrl":"https://doi.org/10.1109/CDC.1975.270597","url":null,"abstract":"The stability of two third-order population ecosystems is analyzed and system dependence on intrinsic rates of growth is demonstrated. A bounded, quasi-optimum feedback control law is derived to satisfy a quadratic cost function. The stabilizing effect of the law is studied both mathematically and via digital simulation.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"251 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115006893","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}
Simple mechanical linkages have not solved the many control problems associated with high performance aircraft maneuvering throughout a wide flight envelope. One procedure for retaining uniform handling qualities over such an envelope is to implement a digital adaptive controller. Towards such an implementation an explicit adaptive controller which makes direct use of online parameter identification, has been developed and applied to both linearized and nonlinear equations of motion for a typical fighter aircraft. This controller is composed of an online weighted least squares parameter identifier, a Kalman state filter, and a model following control law designed using single stage performance indices. Simulation experiments with realistic measurement noise indicate that the proposed adaptive system has the potential for on-board implementation.
{"title":"An implementable digital adaptive flight controller designed using stabilized single stage algorithms","authors":"H. Kaufman, G. Alag","doi":"10.1109/CDC.1975.270683","DOIUrl":"https://doi.org/10.1109/CDC.1975.270683","url":null,"abstract":"Simple mechanical linkages have not solved the many control problems associated with high performance aircraft maneuvering throughout a wide flight envelope. One procedure for retaining uniform handling qualities over such an envelope is to implement a digital adaptive controller. Towards such an implementation an explicit adaptive controller which makes direct use of online parameter identification, has been developed and applied to both linearized and nonlinear equations of motion for a typical fighter aircraft. This controller is composed of an online weighted least squares parameter identifier, a Kalman state filter, and a model following control law designed using single stage performance indices. Simulation experiments with realistic measurement noise indicate that the proposed adaptive system has the potential for on-board implementation.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125804453","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 synthesis procedure for dynamic compensators based on a differential operator representation is developed. The compensators satisfy the algebraic separation, principle and may qualify as 'control observers'. As such they show the same properties as a state observer in a control loop. However, this compensator approach is more general, in that it immediately allows zero placement to be taken into account. For single-input, multi-output systems, a simple and unified procedure, for the construction of minimal order compensators with and without arbitrary pole placement is established. This procedure then is generalized in a straightforward way to the construction of low order compensators for multi-input systems. The approach is particularly advantageous if a higher order (dynamic) state feedback control law is given. In this case, a total compensator of minimal order can be constructed.
{"title":"Compensators for state feedback control laws which satisfy the algebraic separation principle","authors":"G. Grubel","doi":"10.1109/CDC.1975.270619","DOIUrl":"https://doi.org/10.1109/CDC.1975.270619","url":null,"abstract":"A synthesis procedure for dynamic compensators based on a differential operator representation is developed. The compensators satisfy the algebraic separation, principle and may qualify as 'control observers'. As such they show the same properties as a state observer in a control loop. However, this compensator approach is more general, in that it immediately allows zero placement to be taken into account. For single-input, multi-output systems, a simple and unified procedure, for the construction of minimal order compensators with and without arbitrary pole placement is established. This procedure then is generalized in a straightforward way to the construction of low order compensators for multi-input systems. The approach is particularly advantageous if a higher order (dynamic) state feedback control law is given. In this case, a total compensator of minimal order can be constructed.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123784654","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, the fundamental nature of the "partitioned" algorithms is demonstrated by showing that the "partitioned" algorithms serve as the basis of a unifying approach to linear filtering and smoothing. Specifically, generalized "partitioned" filtering and smoothing algorithms are given in terms of forward and backward-time differentiations that are theoretically interesting, possibly computationally attractive, as well as provide a unification of the previous major approaches to filtering and smoothing and clear delineation of their inter-relationships. In particular, the generalized "partitioned" filtering algorithms are shown to contain as special cases both the Kalman-Bucy filter as well as the Chandrasekhar algorithms. Furthermore, the generalized "partitioned" algorithms lead to important generalizations of the Chandrasekhar algorithms [5-7, 18- 19], as well as of the previous "partitioned" algorithms of the author [15-19]. These generalizations pertain to arbitrary initial conditions and time-varying models. It is also shown [20-22] that the generalized "partitioned" algorithm may also be given in terms of an imbedded generalized Chandrasekhar algorithm with the consequent possible computational advantages. Similarly, the generalized "partitioned" smoothing algorithm is shown to contain as special cases the major algorithms for smoothing such as those of Mayne and Fraser [9-10], Kailath and Frost [12], and Meditch [11], as well as the related ones of Zachrisson [13], and Biswas and Mahalanobis [14]. Finally, backwards smoothing algorithms for arbitrary boundary conditions are also obtained as a special case of the "partitioned" smoothing algorithms.
在本文中，通过显示“分区”算法作为统一线性滤波和平滑方法的基础，证明了“分区”算法的基本性质。具体来说，广义的“分区”滤波和平滑算法是根据向前和向后时间微分给出的，这在理论上是有趣的，可能在计算上是有吸引力的，并且提供了先前主要滤波和平滑方法的统一，并清楚地描述了它们之间的相互关系。特别地，广义的“分区”滤波算法被证明包含卡尔曼-布西滤波和钱德拉塞卡算法作为特殊情况。此外，广义的“分区”算法对Chandrasekhar算法[5- 7,18 -19]以及作者之前的“分区”算法[15-19]进行了重要的推广。这些概括适用于任意初始条件和时变模型。研究还表明[20-22]，广义“分区”算法也可以用嵌入式广义钱德拉塞卡算法给出，由此可能具有计算优势。同样，广义的“分区”平滑算法作为特例包含了Mayne and Fraser[9-10]、Kailath and Frost[12]、Meditch[11]等主要的平滑算法，以及Zachrisson[13]、Biswas and Mahalanobis[14]等相关算法。最后，作为“分块”平滑算法的一种特例，给出了任意边界条件下的倒向平滑算法。
{"title":"A unifying approach to linear estimation via the partitioned algorithms, I: Continuous models","authors":"D. Lainiotis, K. Govindaraj","doi":"10.1109/CDC.1975.270586","DOIUrl":"https://doi.org/10.1109/CDC.1975.270586","url":null,"abstract":"In this paper, the fundamental nature of the \"partitioned\" algorithms is demonstrated by showing that the \"partitioned\" algorithms serve as the basis of a unifying approach to linear filtering and smoothing. Specifically, generalized \"partitioned\" filtering and smoothing algorithms are given in terms of forward and backward-time differentiations that are theoretically interesting, possibly computationally attractive, as well as provide a unification of the previous major approaches to filtering and smoothing and clear delineation of their inter-relationships. In particular, the generalized \"partitioned\" filtering algorithms are shown to contain as special cases both the Kalman-Bucy filter as well as the Chandrasekhar algorithms. Furthermore, the generalized \"partitioned\" algorithms lead to important generalizations of the Chandrasekhar algorithms [5-7, 18- 19], as well as of the previous \"partitioned\" algorithms of the author [15-19]. These generalizations pertain to arbitrary initial conditions and time-varying models. It is also shown [20-22] that the generalized \"partitioned\" algorithm may also be given in terms of an imbedded generalized Chandrasekhar algorithm with the consequent possible computational advantages. Similarly, the generalized \"partitioned\" smoothing algorithm is shown to contain as special cases the major algorithms for smoothing such as those of Mayne and Fraser [9-10], Kailath and Frost [12], and Meditch [11], as well as the related ones of Zachrisson [13], and Biswas and Mahalanobis [14]. Finally, backwards smoothing algorithms for arbitrary boundary conditions are also obtained as a special case of the \"partitioned\" smoothing algorithms.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"38 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126951104","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}
It is known that the minimum fuel control problem is equivalent to a minimum l1 norm problem with linear equality constraints. By applying the dual space theory of linear vector spaces, the minimum l1 norm can be found by maximizing a linear functional with a l¿ norm constraint. This maximization enables the application of a linear programming technique which is usually very efficient. The control sequence which achieves the minimum fuel cost is then found by applying the alignment property in the dual space.
{"title":"On the minimum fuel control problem for discrete systems","authors":"Chaw-Bing Chang","doi":"10.1109/CDC.1975.270606","DOIUrl":"https://doi.org/10.1109/CDC.1975.270606","url":null,"abstract":"It is known that the minimum fuel control problem is equivalent to a minimum l1 norm problem with linear equality constraints. By applying the dual space theory of linear vector spaces, the minimum l1 norm can be found by maximizing a linear functional with a l¿ norm constraint. This maximization enables the application of a linear programming technique which is usually very efficient. The control sequence which achieves the minimum fuel cost is then found by applying the alignment property in the dual space.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126957436","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}
{"title":"Stochastic aspects of biological systems and measurements","authors":"T. Johnson","doi":"10.1109/CDC.1975.270751","DOIUrl":"https://doi.org/10.1109/CDC.1975.270751","url":null,"abstract":"","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115026620","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}
{"title":"The relationship between traffic characteristics and control system effectiveness","authors":"P. Tarnoff","doi":"10.1109/CDC.1975.270591","DOIUrl":"https://doi.org/10.1109/CDC.1975.270591","url":null,"abstract":"","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129028672","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 theme of this essay is simple: what economic equilibrium is in a particular market (structure) depends on what individuals and firms know and how they react in disequilibrium processes to information imperfectly available in that market. Three simplified cases are used to demonstrate this point. The cases technically are shown to be related to the kinds of analyses common in System Theory. From this it is argued that as economists move away from general equilibrium models under certainty with analysis by static equilibrium systems of simultaneous equations, the concepts and methods of systems science will become more important to the economist.
{"title":"Process and information in economic models of markets","authors":"Clement G. Krouse","doi":"10.1109/CDC.1975.270637","DOIUrl":"https://doi.org/10.1109/CDC.1975.270637","url":null,"abstract":"The theme of this essay is simple: what economic equilibrium is in a particular market (structure) depends on what individuals and firms know and how they react in disequilibrium processes to information imperfectly available in that market. Three simplified cases are used to demonstrate this point. The cases technically are shown to be related to the kinds of analyses common in System Theory. From this it is argued that as economists move away from general equilibrium models under certainty with analysis by static equilibrium systems of simultaneous equations, the concepts and methods of systems science will become more important to the economist.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121488817","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}
Optimal control of singularly perturbed systems with free terminal time is considered. A reduction in system order is achieved by perturbing a small scalar parameter in the system equations. Using the solution of this reduced order problem, an asymptotic series approximation method is presented for obtaining the solution to the complete problem. A backward sweep approach on the reduced model is used in determining the asymptotic series terms. Numerical results on an example show the applicability of the method.
{"title":"Asymptotic series solution of singularly perturbed free time optimal control problems","authors":"P. Reddy","doi":"10.1109/CDC.1975.270644","DOIUrl":"https://doi.org/10.1109/CDC.1975.270644","url":null,"abstract":"Optimal control of singularly perturbed systems with free terminal time is considered. A reduction in system order is achieved by perturbing a small scalar parameter in the system equations. Using the solution of this reduced order problem, an asymptotic series approximation method is presented for obtaining the solution to the complete problem. A backward sweep approach on the reduced model is used in determining the asymptotic series terms. Numerical results on an example show the applicability of the method.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121593894","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 control of a class of stochastic systems with a norm invariant property is considered. The average value of the terminal norm is constrained to be zero. A fixed configuration controller is used to minimize a performance measure which penalizes both excessive control energy and variance of the terminal value of the norm.
{"title":"Fixed configuration control of stochastic norm invariant systems","authors":"C. Sims","doi":"10.1109/CDC.1975.270673","DOIUrl":"https://doi.org/10.1109/CDC.1975.270673","url":null,"abstract":"The control of a class of stochastic systems with a norm invariant property is considered. The average value of the terminal norm is constrained to be zero. A fixed configuration controller is used to minimize a performance measure which penalizes both excessive control energy and variance of the terminal value of the norm.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124034774","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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