{"title":"On structured singular values","authors":"J. Demmel","doi":"10.1109/CDC.1988.194711","DOIUrl":"https://doi.org/10.1109/CDC.1988.194711","url":null,"abstract":"The author shows how to estimate the norm of the smallest block-structured additive perturbation of a block 2*2 matrix that makes it singular. The estimates are accurate to within a factor of at most 3/sup 3/2/ (a factor of three for real matrices) and work for all possible block perturbation of a block 2*2 matrix and for a large class of matrix norms, including all p-norms and the Frobenius norm. Using an algorithm of W. Hager (1984) the author estimates bounds even for large matrices. He explicitly exhibits rank one or rank two perturbations which achieve his upper bounds. These explicit perturbations can be used as starting values for an optimization routine designed to compute the answer to higher accuracy than the present a priori estimates provide. These results extend to some block perturbations of 3*3 block matrices, although the upper and lower bounds may not always be close.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121199449","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":"Strong stochastic convexity and its applications in parametric optimization of queueing systems","authors":"J. Shanthikumar, D. Yao","doi":"10.1109/CDC.1988.194392","DOIUrl":"https://doi.org/10.1109/CDC.1988.194392","url":null,"abstract":"The authors establish the notion of strong stochastic convexity (SSCX), which implies stochastic convexity. They demonstrate that SSCX is a property exhibited by a wide range of random variables. They also show that SSCX is preserved under random mixture, random summation, and any increasing and convex operations that are applied to a set of independent random variables. Making use of the closure property of SSCX, the authors study GI/G/1 queues and tandem queues with general interarrival and service times and finite intermediate buffers. Applications of the SSCX property in the parametric optimization of such systems are also discussed.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115447896","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":"Asymptotic analysis of an assignment problem arising in a distributed communications protocol","authors":"B. Hajek","doi":"10.1109/CDC.1988.194566","DOIUrl":"https://doi.org/10.1109/CDC.1988.194566","url":null,"abstract":"Matchings for a random bipartite graph are considered. Each of the alpha M nodes on one side of the graph is directly connected to Q nodes chosen randomly and uniformly from among the M nodes on the other side of the graph. The size matchings found by two simple approximation algorithms, as well as the size of the maximum matching when Q=2, are asymptotically determined in the limit as Q tends to infinity with alpha fixed. The work is motivated by a distributed communications protocol for accessing a silent receiver. The theory of approximating slow Markov random walks by ordinary differential equations is used for the analysis.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125226341","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":"Structural convergence improvement schemes on adaptive control","authors":"H. Kang, G. Vachtsevanos, F. L. Lewis","doi":"10.1109/CDC.1988.194669","DOIUrl":"https://doi.org/10.1109/CDC.1988.194669","url":null,"abstract":"Convergent behavior of adaptive control with the synthesis of the feedback structure is studied. A refinement of the error model or a modification of the feedback block can improve the rate of convergence, taking the tradeoff between robustness and fast convergence into account. A typical error model for adaptive control systems is shown. Generalized adaptive systems, instability mechanisms, and robust design methods are presented. Results on designing the feedback structure by the Lyapunov method are given. A generalized design tool for adaptive control algorithms is introduced which improves the rate of convergence. Simulation examples are included.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116657808","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":"Optimal control of arrivals to a feedback queueing system","authors":"I. Christidou, I. Lambadaris, R. Mazumdar","doi":"10.1109/CDC.1988.194393","DOIUrl":"https://doi.org/10.1109/CDC.1988.194393","url":null,"abstract":"The performance analysis of ring type LANS has received much attention. The advantage of the ring type architecture is due to the fact that it is particularly suitable for the transport of real time traffic with guaranteed time delay performance. However, it can be shown that uncontrolled rings are unstable in the sense that the Markov chain that describes the behavior has adsorbing states which amount to deadlock. Thus, a natural question that arises is the control of ring type architectures. Motivated by this question, the authors consider a system of two coupled queues where a packet after being served in one queue can be fed into the other queue or leave the system. In addition there are external Poisson arrivals at each queue. These can in general be optimally controlled by applying a probabilistic rule minimizing an average discounted cost which is a linear function of the total amount of blocking as well as the number of packets in the system. It is shown that the optimal blocking mechanism is deterministic (bang-bang) and is characterized by two monotone switching curves in the state space associated with the system. The approach used relies on Markov decision theory and convexity arguments.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117060456","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":"On the control of magnetically levitated robot wrists","authors":"S. Salcudean","doi":"10.1109/CDC.1988.194293","DOIUrl":"https://doi.org/10.1109/CDC.1988.194293","url":null,"abstract":"The author deals with the problem of controlling six-degrees-of-freedom magnetically levitated robot wrists. This control problem is greatly simplified by the use of the Euler quaternion representation of rotation. It is shown that both the approximate and exact linearizations of the equations of motion are fully decoupled second-order systems, and therefore simple scalar PD/PID (proportional-derivative/proportional-integral-derivative) compensators can be used for their control. The author presents a novel nonlinear angular velocity or angular momentum observer and shows that it has global and eventually exponential convergence. The author presents simulation results and discusses some implementation issues and experimental results. The simulations, using the magic wrist parameters, showed that these controllers perform well.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117200321","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":"A randomized algorithm for simultaneous identification of linear systems","authors":"B. Ghosh, H. Schattler","doi":"10.1109/CDC.1988.194585","DOIUrl":"https://doi.org/10.1109/CDC.1988.194585","url":null,"abstract":"The authors propose, for the first time in system theory, a robust version of the well-known system identification problem. The problem, which they call the simultaneous identification problem, arises in trying to identify the parameters of a time-varying system. In the past, an identifier for a time-varying system was constructed by an immediate generalization of the ideas pertaining to a time invariant system. Unless the time variation of the plant is assumed to be slow, such an identification scheme would result in poor performance. As an alternative, a probabilistic randomized algorithm is presented, and its convergence is investigated.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117260433","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":"Linear quadratic Gaussian design for robust performance objectives","authors":"D. Looze, J. Freudenberg","doi":"10.1109/CDC.1988.194359","DOIUrl":"https://doi.org/10.1109/CDC.1988.194359","url":null,"abstract":"The authors describe a technique for selecting the weighting functions of the LQG/LTR (linear quadratic Gaussian/loop transfer function recovery) formal synthesis procedure to satisfy a robust performance objective. The objective of the feedback system design problem is to achieve a small structured singular value over all frequencies. Existing formal synthesis approaches are used to generate the compensator by selecting the design parameters of the formal synthesis techniques to achieve objectives specified in terms of the structured singular value. The authors consider a problem of tracking an exogenous reference signal (command-following) in the presence of an unstructured multiplicative modeling error at the plant input. For this problem, the characteristics of closed-loop systems which result in a small structured singular value have been identified and quantified. Two formal synthesis approaches for this problem are considered: H/sub 2/-optimization and H/sub infinity /-optimization.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120993340","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":"Tracking targets with unknown process noise variance using adaptive Kalman filtering","authors":"P. Gutman, M. Velger","doi":"10.1109/CDC.1988.194435","DOIUrl":"https://doi.org/10.1109/CDC.1988.194435","url":null,"abstract":"A simple algorithm is suggested to estimate, using a Kalman filter, the unknown process noise variance of an otherwise known linear plant. The process noise variance estimator is essentially dead beat, using the difference between the expected prediction error variance, computed in the Kalman filter, and the measured prediction error variance. The estimate is used to adapt the Kalman filter. The use of the adaptive filter is demonstrated in a simulated example in which a wildly manoeuvring target is tracked.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"25 9-10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121004322","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":"Controllability and observability in the state-feedback control of discrete-event systems","authors":"Yang Li, W. Wonham","doi":"10.1109/CDC.1988.194296","DOIUrl":"https://doi.org/10.1109/CDC.1988.194296","url":null,"abstract":"A discrete-event system (DES) is described by a state-transition model. By disabling and enabling controllable events according to a rule based on partial information about the current state of the system, a static state-feedback controller synthesizes a predicate specifying states reachable from the initial state in the controlled system. Concepts of controllable predicate and observable predicate are introduced. It is shown that a predicate can be synthesized by a static state-feedback controller utilizing only partial state information if and only if the predicate is both controllable and observable. Some general results are presented for a state-variable model of a controlled DES.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127097419","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}