Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1429509
O. Mason, R. Shorten
In this paper, we present a number of results concerned with the stability of positive switched linear systems. In particular, we show that a recent conjecture concerning the existence of common quadratic Lyapunov functions (CQLFs) for positive LTI systems is true for second order systems, and establish a class of switched linear systems for which CQLF existence is equivalent to exponential stability under arbitrary switching. However, this conjecture is false for higher dimensional systems and we illustrate this fact with a counterexample. A number of stability criteria for positive switched linear systems based on common diagonal Lyapunov functions (CDLFs) are also presented, as well as a necessary and sufficient condition for a general pair of positive LTI systems to have a CDLF To the best of the authors' knowledge, this is the first time that a necessary and sufficient condition for CDLF existence for n-dimensional systems has appeared in the literature.
{"title":"Some results on the stability of positive switched linear systems","authors":"O. Mason, R. Shorten","doi":"10.1109/CDC.2004.1429509","DOIUrl":"https://doi.org/10.1109/CDC.2004.1429509","url":null,"abstract":"In this paper, we present a number of results concerned with the stability of positive switched linear systems. In particular, we show that a recent conjecture concerning the existence of common quadratic Lyapunov functions (CQLFs) for positive LTI systems is true for second order systems, and establish a class of switched linear systems for which CQLF existence is equivalent to exponential stability under arbitrary switching. However, this conjecture is false for higher dimensional systems and we illustrate this fact with a counterexample. A number of stability criteria for positive switched linear systems based on common diagonal Lyapunov functions (CDLFs) are also presented, as well as a necessary and sufficient condition for a general pair of positive LTI systems to have a CDLF To the best of the authors' knowledge, this is the first time that a necessary and sufficient condition for CDLF existence for n-dimensional systems has appeared in the literature.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116587298","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}
Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1430282
T. Kanade, O. Amidi, Qifa Ke
Autonomous control of small and micro air vehicles (SMAV) requires precise estimation of both vehicle state and its surrounding environment. Small cameras, which are available today at very low cost, are attractive sensors for SMAV. 3D vision by video and laser scanning has distinct advantages in that they provide positional information relative to objects and environments, in which the vehicle operates, that is critical to obstacle avoidance and mapping of the environment. This paper presents work on real-time 3D vision algorithms for recovering motion and structure from a video sequence, 3D terrain mapping from a laser range finder onboard a small autonomous helicopter, and sensor fusion of visual and GPS/INS sensors.
{"title":"Real-time and 3D vision for autonomous small and micro air vehicles","authors":"T. Kanade, O. Amidi, Qifa Ke","doi":"10.1109/CDC.2004.1430282","DOIUrl":"https://doi.org/10.1109/CDC.2004.1430282","url":null,"abstract":"Autonomous control of small and micro air vehicles (SMAV) requires precise estimation of both vehicle state and its surrounding environment. Small cameras, which are available today at very low cost, are attractive sensors for SMAV. 3D vision by video and laser scanning has distinct advantages in that they provide positional information relative to objects and environments, in which the vehicle operates, that is critical to obstacle avoidance and mapping of the environment. This paper presents work on real-time 3D vision algorithms for recovering motion and structure from a video sequence, 3D terrain mapping from a laser range finder onboard a small autonomous helicopter, and sensor fusion of visual and GPS/INS sensors.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114428070","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}
Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1428673
H. Yazarel, S. Prajna, George J. Pappas
Verification of continuous systems remains one of the main obstacles in the safety verification of hybrid systems. In this paper, by exploiting the structure of linear dynamical systems, we convert the exact safety verification of linear systems with certain eigen-structure as an emptiness problem for a semi-algebraic set. Sum of squares (SOS) decomposition is then employed to check emptiness of the set defined by polynomial equalities and inequalities which can be effectively computed by semidefinite programming.
{"title":"S.O.S. for safety","authors":"H. Yazarel, S. Prajna, George J. Pappas","doi":"10.1109/CDC.2004.1428673","DOIUrl":"https://doi.org/10.1109/CDC.2004.1428673","url":null,"abstract":"Verification of continuous systems remains one of the main obstacles in the safety verification of hybrid systems. In this paper, by exploiting the structure of linear dynamical systems, we convert the exact safety verification of linear systems with certain eigen-structure as an emptiness problem for a semi-algebraic set. Sum of squares (SOS) decomposition is then employed to check emptiness of the set defined by polynomial equalities and inequalities which can be effectively computed by semidefinite programming.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116323584","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}
Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1429313
Wei Wu, A. Arapostathis, Ratnesh Kumar
This paper continues the study of safety control for Markov chains, a notion we introduced in our recent work. In our past work we have restricted our attention to Markov stationary controls, and derived necessary and sufficient conditions for safety enforcement in this class of policies. As opposed to optimal control of Markov chains under complete observations, where optimality is normally achieved in the class of stationary policies, enforcement of safety can benefit from the consideration of non-stationary policies. In this work we show that in meeting the safety control objective, it suffices to consider a class of non-stationary policies which are induced from the class of stationary policies of an augmented chain. Also, given a controlled Markov chain and a safety specification (describing bounds within which the probability distribution must always lie), we present an algorithm for computing the maximal set of safe initial distributions-the initial distributions from where it is possible to control the chain so that the safety specification is always satisfied.
{"title":"On non-stationary policies and maximal invariant safe sets of controlled Markov chains","authors":"Wei Wu, A. Arapostathis, Ratnesh Kumar","doi":"10.1109/CDC.2004.1429313","DOIUrl":"https://doi.org/10.1109/CDC.2004.1429313","url":null,"abstract":"This paper continues the study of safety control for Markov chains, a notion we introduced in our recent work. In our past work we have restricted our attention to Markov stationary controls, and derived necessary and sufficient conditions for safety enforcement in this class of policies. As opposed to optimal control of Markov chains under complete observations, where optimality is normally achieved in the class of stationary policies, enforcement of safety can benefit from the consideration of non-stationary policies. In this work we show that in meeting the safety control objective, it suffices to consider a class of non-stationary policies which are induced from the class of stationary policies of an augmented chain. Also, given a controlled Markov chain and a safety specification (describing bounds within which the probability distribution must always lie), we present an algorithm for computing the maximal set of safe initial distributions-the initial distributions from where it is possible to control the chain so that the safety specification is always satisfied.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125095314","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}
Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1429392
K. Johnson, L. Pao, M. Balas, V. Kulkarni, L. Fingersh
Variable speed wind turbines are designed to follow wind speed variations in low winds in order to maximize aerodynamic efficiency. Unfortunately, uncertainty in the aerodynamic parameters may lead to sub-optimal power capture in variable speed turbines. Adaptive generator torque control is one method of eliminating this sub-optimality; however, before adaptive control can become widely used in the wind industry, it must be proven to be safe. This paper analyzes the stability of an adaptive torque control law and the gain adaptation law in use on the Controls Advanced Research Turbine (CART) at the National Renewable Energy Laboratory's National Wind Technology Center.
{"title":"Stability analysis of an adaptive torque controller for variable speed wind turbines","authors":"K. Johnson, L. Pao, M. Balas, V. Kulkarni, L. Fingersh","doi":"10.1109/CDC.2004.1429392","DOIUrl":"https://doi.org/10.1109/CDC.2004.1429392","url":null,"abstract":"Variable speed wind turbines are designed to follow wind speed variations in low winds in order to maximize aerodynamic efficiency. Unfortunately, uncertainty in the aerodynamic parameters may lead to sub-optimal power capture in variable speed turbines. Adaptive generator torque control is one method of eliminating this sub-optimality; however, before adaptive control can become widely used in the wind industry, it must be proven to be safe. This paper analyzes the stability of an adaptive torque control law and the gain adaptation law in use on the Controls Advanced Research Turbine (CART) at the National Renewable Energy Laboratory's National Wind Technology Center.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"379 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122869198","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}
Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1428636
Nai One Lai, C. Edwards, S. Spurgeon
This paper presents a novel approach to the problem of discrete time output feedback sliding mode control design. The method described applies to uncertain systems (with matched uncertainties), which are not necessarily minimum phase or relative degree one. A new sliding surface is proposed, which is associated with the equivalent control of the output feedback sliding mode controller. The practicality of the results in this paper is demonstrated through the implementation of the controller on a small dc motor test rig.
{"title":"Discrete output feedback sliding mode based tracking control","authors":"Nai One Lai, C. Edwards, S. Spurgeon","doi":"10.1109/CDC.2004.1428636","DOIUrl":"https://doi.org/10.1109/CDC.2004.1428636","url":null,"abstract":"This paper presents a novel approach to the problem of discrete time output feedback sliding mode control design. The method described applies to uncertain systems (with matched uncertainties), which are not necessarily minimum phase or relative degree one. A new sliding surface is proposed, which is associated with the equivalent control of the output feedback sliding mode controller. The practicality of the results in this paper is demonstrated through the implementation of the controller on a small dc motor test rig.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123523188","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}
Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1429446
K. Zheng, Aik Lee, J. Bentsman, P. Krein
Two-degrees-of-freedom (2DOF) controller design is viewed as a standard technique capable of simultaneously addressing the performance objectives of the main operating modes - tracking and disturbance rejection - of an induction motor control system. However, in a typical industrial reduced cost controller implementation, the open-loop prefilter performance in the 2DOF topology could be severely degraded by the controller uncertainty, i.e., the mismatch between the dynamics of the analytical controller representation and its realization in software/hardware. This problem is addressed in the present work by a multi-objective hybrid control strategy. The latter consists in employing in each mode the corresponding optimally tuned One-degree-of-freedom (1DOF) design robust with respect to both the plant and the controller uncertainty, and organizing a rapid and smooth switching, or transfer, between the mode-specific controllers to provide sequencing of the operating modes, as necessary. Simulation results show that the technique proposed yields the fast switching robust controllers that provide the desired performance under rather significant controller uncertainty across the entire induction motor operating sequence, thereby offering an alternative, minimally affected by the reduced cost controller implementation, to a 2DOF design.
{"title":"High performance robust linear controller synthesis for an induction motor using a multi-objective hybrid control strategy","authors":"K. Zheng, Aik Lee, J. Bentsman, P. Krein","doi":"10.1109/CDC.2004.1429446","DOIUrl":"https://doi.org/10.1109/CDC.2004.1429446","url":null,"abstract":"Two-degrees-of-freedom (2DOF) controller design is viewed as a standard technique capable of simultaneously addressing the performance objectives of the main operating modes - tracking and disturbance rejection - of an induction motor control system. However, in a typical industrial reduced cost controller implementation, the open-loop prefilter performance in the 2DOF topology could be severely degraded by the controller uncertainty, i.e., the mismatch between the dynamics of the analytical controller representation and its realization in software/hardware. This problem is addressed in the present work by a multi-objective hybrid control strategy. The latter consists in employing in each mode the corresponding optimally tuned One-degree-of-freedom (1DOF) design robust with respect to both the plant and the controller uncertainty, and organizing a rapid and smooth switching, or transfer, between the mode-specific controllers to provide sequencing of the operating modes, as necessary. Simulation results show that the technique proposed yields the fast switching robust controllers that provide the desired performance under rather significant controller uncertainty across the entire induction motor operating sequence, thereby offering an alternative, minimally affected by the reduced cost controller implementation, to a 2DOF design.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130338186","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}
Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1428978
J. L. Mancilla-Aguilar, R. García, Eduardo Sontag, Y. Wang
This work provides representations of switched systems described by controlled differential inclusions, in terms of perturbed control systems whose dynamics are given by differential equations, and whose inputs consist of the original controls together with disturbances that evolve in compact sets. Several applications dealing with properties of stability with respect to inputs and of detectability, and their characterizations in terms of Lyapunov functions, are derived as consequences of the representation theorem for such switched systems, and more generally, for systems with switching signals governed by digraphs.
{"title":"Representation of switched systems by perturbed control systems","authors":"J. L. Mancilla-Aguilar, R. García, Eduardo Sontag, Y. Wang","doi":"10.1109/CDC.2004.1428978","DOIUrl":"https://doi.org/10.1109/CDC.2004.1428978","url":null,"abstract":"This work provides representations of switched systems described by controlled differential inclusions, in terms of perturbed control systems whose dynamics are given by differential equations, and whose inputs consist of the original controls together with disturbances that evolve in compact sets. Several applications dealing with properties of stability with respect to inputs and of detectability, and their characterizations in terms of Lyapunov functions, are derived as consequences of the representation theorem for such switched systems, and more generally, for systems with switching signals governed by digraphs.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"651 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132022837","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}
Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1429499
N. Chopra, M. Spong
Bilateral teleoperators, designed within the passivity framework using concepts of scattering and two-port network theory, provide robust stability against constant delay in the network and velocity tracking, but cannot guarantee position tracking in general. In this paper we fundamentally extend the passivity based traditional architecture to guarantee position and force tracking in the face of offset of initial conditions, environmental contacts and packet losses in the network. We propose a novel coordination architecture which uses state feedback to define a new passive output for the master and slave robots containing both position and velocity information. A passive coordination control is also developed, which uses the new outputs to kinematically lock the master and slave robots. For effective extension to practical applications, an adaptive version of the scheme is also developed. Simulation results are presented which demonstrate the effectiveness of the proposed architecture.
{"title":"Adaptive coordination control of bilateral teleoperators with time delay","authors":"N. Chopra, M. Spong","doi":"10.1109/CDC.2004.1429499","DOIUrl":"https://doi.org/10.1109/CDC.2004.1429499","url":null,"abstract":"Bilateral teleoperators, designed within the passivity framework using concepts of scattering and two-port network theory, provide robust stability against constant delay in the network and velocity tracking, but cannot guarantee position tracking in general. In this paper we fundamentally extend the passivity based traditional architecture to guarantee position and force tracking in the face of offset of initial conditions, environmental contacts and packet losses in the network. We propose a novel coordination architecture which uses state feedback to define a new passive output for the master and slave robots containing both position and velocity information. A passive coordination control is also developed, which uses the new outputs to kinematically lock the master and slave robots. For effective extension to practical applications, an adaptive version of the scheme is also developed. Simulation results are presented which demonstrate the effectiveness of the proposed architecture.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130583977","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}
Pub Date : 2004-11-19DOI: 10.1088/0305-4470/37/46/004
J. Rogge, D. Aeyels
In this paper we discuss the behavior of a finite group of phase oscillators unidirectionally coupled in a ring. The dynamics is described by the Kuramoto model. In the case of identical oscillators, all phase locking solutions are obtained explicitly, together with their stability properties. For nonidentical oscillators it is proven that there exist phase locking solutions for sufficiently strong coupling. An algorithm for obtaining all phase locking solutions is given. These solutions can be subdivided into classes, the stability properties of each of which are established separately. The stability results are extended to interconnections belonging to a class of odd functions. Finally, a connection with the field of active antenna arrays is made, generalizing some results earlier obtained in this field.
{"title":"Stability of phase locking in a ring of unidirectionally coupled oscillators","authors":"J. Rogge, D. Aeyels","doi":"10.1088/0305-4470/37/46/004","DOIUrl":"https://doi.org/10.1088/0305-4470/37/46/004","url":null,"abstract":"In this paper we discuss the behavior of a finite group of phase oscillators unidirectionally coupled in a ring. The dynamics is described by the Kuramoto model. In the case of identical oscillators, all phase locking solutions are obtained explicitly, together with their stability properties. For nonidentical oscillators it is proven that there exist phase locking solutions for sufficiently strong coupling. An algorithm for obtaining all phase locking solutions is given. These solutions can be subdivided into classes, the stability properties of each of which are established separately. The stability results are extended to interconnections belonging to a class of odd functions. Finally, a connection with the field of active antenna arrays is made, generalizing some results earlier obtained in this field.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124845546","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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