Pub Date : 1980-05-01DOI: 10.1080/00207178008961098
P. Dooren, G. Verghese, T. Kailath
In this short paper we show a number of properties of generalized state-space systems {sE-A,B,C,D} which can be constructed for any rational matrix R(s). The Kronecker structure of such systems is proven to yield information about the pole-zero structure (finite and infinite) and about the null space structure of R(s).
{"title":"Properties of the system matrix of a generalized state-space system","authors":"P. Dooren, G. Verghese, T. Kailath","doi":"10.1080/00207178008961098","DOIUrl":"https://doi.org/10.1080/00207178008961098","url":null,"abstract":"In this short paper we show a number of properties of generalized state-space systems {sE-A,B,C,D} which can be constructed for any rational matrix R(s). The Kronecker structure of such systems is proven to yield information about the pole-zero structure (finite and infinite) and about the null space structure of R(s).","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"446 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122597163","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 present a complete and novel solution to the well known buffer storage design problem in a serial production line. The key ingredient of the solution is the efficient calculation of the gradient vector of the throughput with respect to the various buffer sizes. Analytical and experimental results are presented.
{"title":"A gradient technique for general buffer storage design in a production line","authors":"Y. Ho, M. Eyler, T. Chien","doi":"10.1109/CDC.1978.268004","DOIUrl":"https://doi.org/10.1109/CDC.1978.268004","url":null,"abstract":"In this paper, we present a complete and novel solution to the well known buffer storage design problem in a serial production line. The key ingredient of the solution is the efficient calculation of the gradient vector of the throughput with respect to the various buffer sizes. Analytical and experimental results are presented.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"275 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1979-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134072245","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 asymptotic behavior of a Bayes optimal adaptive estimation scheme for a linear, discrete-time system with interrupted observations is investigated. The interrupted observation mechanism is expressed in terms of a stationary two-state Markov chain. The transition probability matrix is unknown and can take values only from a finite set.
{"title":"State estimation under uncertain observations with unknown statistics","authors":"Jitendra Tugnait, A. Haddad","doi":"10.1109/CDC.1978.268019","DOIUrl":"https://doi.org/10.1109/CDC.1978.268019","url":null,"abstract":"The asymptotic behavior of a Bayes optimal adaptive estimation scheme for a linear, discrete-time system with interrupted observations is investigated. The interrupted observation mechanism is expressed in terms of a stationary two-state Markov chain. The transition probability matrix is unknown and can take values only from a finite set.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1979-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125093183","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}
Two conditional gradient algorithms are considered for the problem min ¿F, with ¿ a bounded convex subset of a Banach space. Neither method requires line search; one method needs no Lipschitz constants. Convergence rate estimates are similar in the two cases, and depend critically on the continuity properties of a set valued operator T whose fixed points, ¿, are the extremals of F in ¿. The continuity properties of T at ¿ are determined by the way a(¿) = inf{¿= |y¿¿,||;y-¿||>¿} grows with increasing ¿. It is shown that for convex F and Lipschitz continuous F', the algorithms converge like o(1/n), geometrically, or in finitely many steps, according to whether a(¿)>0 for ¿>0, or a(¿)>A¿2 with A>0, or a(¿)>A¿ with A>0. These three abstract conditions are closely related to established notions of nonsingularity for an important class of optimal control problems with bounded control inputs. The first con-- dition is satisfied (in L1)when meas {t|s(t)=0} =0, where s(¿) is the switching function associated with the extremal control ¿(¿); the second condition is satisfied when s(¿) has finitely many zeros, all simple (typical of the bang-bang extremal); the third condition is satisfied when s(¿) is bounded away from zero. Strong or uniform convexity assumptions are not invoked in the main: convergence theorems. One of the theorems can be extended to a large subclass of quasiconvex functionals F.
{"title":"Rates of convergence for conditional gradient algorithms near singular and nonsingular extremals","authors":"J. Dunn","doi":"10.1137/0317015","DOIUrl":"https://doi.org/10.1137/0317015","url":null,"abstract":"Two conditional gradient algorithms are considered for the problem min ¿F, with ¿ a bounded convex subset of a Banach space. Neither method requires line search; one method needs no Lipschitz constants. Convergence rate estimates are similar in the two cases, and depend critically on the continuity properties of a set valued operator T whose fixed points, ¿, are the extremals of F in ¿. The continuity properties of T at ¿ are determined by the way a(¿) = inf{¿= |y¿¿,||;y-¿||>¿} grows with increasing ¿. It is shown that for convex F and Lipschitz continuous F', the algorithms converge like o(1/n), geometrically, or in finitely many steps, according to whether a(¿)>0 for ¿>0, or a(¿)>A¿2 with A>0, or a(¿)>A¿ with A>0. These three abstract conditions are closely related to established notions of nonsingularity for an important class of optimal control problems with bounded control inputs. The first con-- dition is satisfied (in L1)when meas {t|s(t)=0} =0, where s(¿) is the switching function associated with the extremal control ¿(¿); the second condition is satisfied when s(¿) has finitely many zeros, all simple (typical of the bang-bang extremal); the third condition is satisfied when s(¿) is bounded away from zero. Strong or uniform convexity assumptions are not invoked in the main: convergence theorems. One of the theorems can be extended to a large subclass of quasiconvex functionals F.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1979-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122821006","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}
Let a semi-dynamical system, (A,B): (A,B) x=Ax + Bu x(0) = 0 be given on a Hilbert space X. When A is self-adjoint and semi-bounded with spectral measure E(¿) it is shown that controllability of the system (A,B) is equivalent to that of (f(A), B) where f(¿) is any semi-bounded, Borel measurable E(¿)-surjective function on-¿
在希尔伯特空间x上给出一个半动力系统(a,B):(a,B) x=Ax + Bu x(0) = 0，当a是自伴半有界且谱测度E(¿)时，证明了系统(a,B)的可控性等价于系统(f(a)， B)的可控性，其中f(¿)是在-¿
{"title":"Perturbation of controllable systems","authors":"R. O'Brien","doi":"10.1109/CDC.1978.267937","DOIUrl":"https://doi.org/10.1109/CDC.1978.267937","url":null,"abstract":"Let a semi-dynamical system, (A,B): (A,B) x=Ax + Bu x(0) = 0 be given on a Hilbert space X. When A is self-adjoint and semi-bounded with spectral measure E(¿) it is shown that controllability of the system (A,B) is equivalent to that of (f(A), B) where f(¿) is any semi-bounded, Borel measurable E(¿)-surjective function on-¿<t<+¿. In particular (A,B) is controllable if and only if (A¿, B) is controllable A¿=-(-A)¿. These results are then extended to the case where A generates a unlformly bounded C0 - semigroup on X and are applied to a system whose dynamics are governed by the singular integral operator generating the Poisson integral semigroup.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"721 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1979-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121127535","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}
Preliminary results for minimum message-delay routing in message-switched, store-and-forward, data-communication networks are presented using a minimum principle/queueing theory approach. The routing algorithm is a decentralized one which requires only local information. The results are illustrated via a special case, and extensions and problems for future research are discussed.
{"title":"A minimum principle/queueing theory approach to routing in message-switched networks","authors":"J. Meditch","doi":"10.1109/CDC.1978.267928","DOIUrl":"https://doi.org/10.1109/CDC.1978.267928","url":null,"abstract":"Preliminary results for minimum message-delay routing in message-switched, store-and-forward, data-communication networks are presented using a minimum principle/queueing theory approach. The routing algorithm is a decentralized one which requires only local information. The results are illustrated via a special case, and extensions and problems for future research are discussed.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125189134","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 decision model including perceptual noise or inconsistency is developed from expected value theory to evaluate driver stop and go decisions at signaled intersections. The model is applied to behavior in a car simulation and instrumented vehicle. Objective and subjective changes in driver decision making were measured with changes in blood alcohol concentration (BAC). Treatment levels averaged 0.00, 0.10 and 0.14 BAC for a total of 26 male subjects. Data were taken for drivers approaching signal lights at three timing configurations. The correlation between model predictions and behavior was highly significant. In contrast to previous research, analysis indicates that increased BAC results in increased perceptual inconsistency, which is the primary cause of increased risk taking at low probability of success signal lights.
{"title":"A decision model applied to alcohol effects on driver signal light behavior","authors":"S. Schwartz, R. Allen","doi":"10.1109/CDC.1978.268136","DOIUrl":"https://doi.org/10.1109/CDC.1978.268136","url":null,"abstract":"A decision model including perceptual noise or inconsistency is developed from expected value theory to evaluate driver stop and go decisions at signaled intersections. The model is applied to behavior in a car simulation and instrumented vehicle. Objective and subjective changes in driver decision making were measured with changes in blood alcohol concentration (BAC). Treatment levels averaged 0.00, 0.10 and 0.14 BAC for a total of 26 male subjects. Data were taken for drivers approaching signal lights at three timing configurations. The correlation between model predictions and behavior was highly significant. In contrast to previous research, analysis indicates that increased BAC results in increased perceptual inconsistency, which is the primary cause of increased risk taking at low probability of success signal lights.","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":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134159148","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 present a procedure for the spectral factorization of multidimensional spectral density functions. Properties of the multidimensional cepstrum are developed and used as a basis for the procedure. In analogy with Wiener's one-dimensional factorization, the resulting factors are stable and realizable (i.e., recursible). A numerical algorithm for performing the factorization is described, along with its use in obtaining unilateral representations of multidimensional random fields.
{"title":"Multidimensional spectral factorization","authors":"D. Goodman, M. Ekstrom","doi":"10.1109/CDC.1978.268011","DOIUrl":"https://doi.org/10.1109/CDC.1978.268011","url":null,"abstract":"In this paper, we present a procedure for the spectral factorization of multidimensional spectral density functions. Properties of the multidimensional cepstrum are developed and used as a basis for the procedure. In analogy with Wiener's one-dimensional factorization, the resulting factors are stable and realizable (i.e., recursible). A numerical algorithm for performing the factorization is described, along with its use in obtaining unilateral representations of multidimensional random fields.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126530795","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 considered is to optimally control the nonlinear system: x = a1(x) + A1(x)z + B1(x)u, x(0) = xo (1a) µz = a2(x) + A2(x)z + B2(x)u, z(0) = zo (1b) with respect to the performance index J=¿0 ¿[p(x) + s'(x)z + z'Q(x)z + u'R(x)u]dt (2) where µ > 0 is the small singular perturbation parameter, x, z are n-, m- dimensional states, respectively, and u is an r-dimensional control.
考虑的问题是最优控制非线性系统:x = a1(x) + a1(x) z + B1(x)u, x(0) = xo (1a)µz = a2(x) + a2(x) z + B2(x)u, z(0) = zo (1b)，相对于性能指标J=¿0¿[p(x) + s'(x)z + z' q (x)z + u' r (x)u]dt(2)，其中µ> 0是小奇异扰动参数，x, z分别是n维，m维状态，u是r维控制。
{"title":"Near-optimal feedback stabilization of a class of nonlinear singularly perturbed systems","authors":"J. Chow, P. Kokotovic","doi":"10.1109/CDC.1978.267942","DOIUrl":"https://doi.org/10.1109/CDC.1978.267942","url":null,"abstract":"The problem considered is to optimally control the nonlinear system: x = a1(x) + A1(x)z + B1(x)u, x(0) = xo (1a) µz = a2(x) + A2(x)z + B2(x)u, z(0) = zo (1b) with respect to the performance index J=¿0 ¿[p(x) + s'(x)z + z'Q(x)z + u'R(x)u]dt (2) where µ > 0 is the small singular perturbation parameter, x, z are n-, m- dimensional states, respectively, and u is an r-dimensional control.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125371468","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 spacecraft attitude dynamics and control problem is introduced as a broad class of nonlinear systems. Some of the basic properties of these systems are described from a system theory point of view. Various system theory concepts and research topics which have applicability to this class of systems are identified and briefly described. The subject of multibody dynamics is presented in a vector space setting and related to system theory concepts.
{"title":"System theory aspects of multi-body dynamics","authors":"W. Jerkovsky","doi":"10.1109/CDC.1978.267949","DOIUrl":"https://doi.org/10.1109/CDC.1978.267949","url":null,"abstract":"The spacecraft attitude dynamics and control problem is introduced as a broad class of nonlinear systems. Some of the basic properties of these systems are described from a system theory point of view. Various system theory concepts and research topics which have applicability to this class of systems are identified and briefly described. The subject of multibody dynamics is presented in a vector space setting and related to system theory concepts.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"216 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130439150","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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