On the Stability of Nonautonomous Differential Equations $\dot x = [A + B(t)]x$, with Skew Symmetric Matrix $B(t)$

Morgan, Alexander P.; Narendra, Kumpati S.

doi:10.1137/0315013

Cited by 179 publications

(124 citation statements)

References 3 publications

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“…The above structure with skew-adjoint state dependent matrix is characteristic of adaptive systems [7]. The same matrix will be observed in the case of distributed adaptive consensus identifiers, in which the equivalent form will involve the same matrix as before and the contribution due to consensus enforcement.…”

Section: E(t) = a M E(t) + ( A(t) − A)x(t) + ( B(t) − B)u(t) = A M E(mentioning

confidence: 72%

Adaptive consensus estimation of multi-agent systems

Demetriou

Nestinger

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-This paper considers the effects of a penalty term in both the state and parameter estimates for multi-agent systems. It is assumed that the plant parameters are desired to be identified on-line and N agents are available to implement adaptive observers. Using an additive term which takes the form of a penalty on the mismatch between the state and parameter estimates, the proposed adaptive consensus estimation scheme ensures that both state and parameter estimates reach consensus. While the proposed adaptive consensus identifiers assume an all-to-all connectivity, the abstract framework that the adaptive identifiers are examined under, allows for any form of agent connectivity to be examined. As a measure of agreement of the estimates that is independent of the network topology, the deviation from the mean estimate for both the state and parameter estimates is defined and shown to converge to zero. Simulation studies of a second order system provide a verification of the proposed theoretical predictions.

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Section: E(t) = a M E(t) + ( A(t) − A)x(t) + ( B(t) − B)u(t) = A M E(mentioning

confidence: 72%

Adaptive consensus estimation of multi-agent systems

Demetriou

Nestinger

2011

IEEE Conference on Decision and Control and European Control Conference

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“…This choice of error model structure was the result an adaptive controller constructed in [15] for a linear system. At the time of the work by [16], boundedness of the regression vector for the linear adaptive control problem had not yet been proved. This problem was actively pursued and solved in the early 1980's when linear growth constraints were used to show that the corresponding regression vector, which is a linear function of the state, was indeed a bounded function of time [20], [19].…”

Section: Introductionmentioning

confidence: 99%

“…In the late 1970's in [16], the stability of an error model was analyzed for which the regression vector is a bounded function of time. This choice of error model structure was the result an adaptive controller constructed in [15] for a linear system.…”

Section: Introductionmentioning

confidence: 99%

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Friction compensation using adaptive non-linear control with persistent excitation

Misovec¹

1999

International Journal of Control

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“…Yet another approach requires the reference input to be persistently exciting of sufficient order. If no disturbances are present, this results in exponential stability of the overall adaptive system (Morgan and Narendra, 1977 [49]). …”

Section: Chapter 5 Design Considerationsmentioning

confidence: 99%

5. Adaptive control in the presence of disturbances

Ioannou¹,

Kokotović²

Adaptive Systems With Reduced Models

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PrefaceThe essence of adaptive control is to observe an unknown process, derive a hypothesis of how to control the process in order to obtain best performance and continuously update this hypothesis based on new information. In this thesis, I investigate ways to improve performance even as the information is corrupted by disturbances affecting the process.I would like to thank Professor D. Schröder for having introduced me to this exciting field of research and for having provided his continuous support and interest during the years of my doctoral work. His open-mindedness and vision was the incentive for me to pursue new ways of intelligent control for mechatronic systems.To my teacher and mentor, Professor K. S. Narendra, I express my profound gratitude for having accepted me as his graduate student even though I never officially enrolled at Yale.I thank him for having opened my eyes to the complex nature of research, for being such a brilliant thinker and such a dedicated teacher.The research reported in this doctoral thesis was made possible by Siemens AG, which generously provided me with an Ernst von Siemens-stipend over a period of three years. In AbstractThe emphasis of this thesis is on developing a theoretical framework for the practical design of adaptive systems. The state of the art in industrial adaptive control is to combine a parameter estimator with an (existing) linear control-loop. The success of the approach depends upon the knowledge of the physical parameters after completion of the estimation process. In the presence of disturbances, though, a correct estimation of the parameters is impossible. It is first shown how a system with unknown parameters can be controlled adaptively, without relying on parameter convergence. Following this, three classes of disturbances and the corresponding methods to reject them are developed: external disturbances, unmodelled dynamics and time-variations. In the latter case, a new algorithm based on multiple adaptive models is presented which was developed at Yale University during regular visits of the author at the Center for Systems Science. An experimental study of an adaptively controlled two-mass system concludes the thesis.

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On the Stability of Nonautonomous Differential Equations $\dot x = [A + B(t)]x$, with Skew Symmetric Matrix $B(t)$

Cited by 179 publications

References 3 publications

Adaptive consensus estimation of multi-agent systems

Adaptive consensus estimation of multi-agent systems

Friction compensation using adaptive non-linear control with persistent excitation

5. Adaptive control in the presence of disturbances

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