Convergence analysis for reduced-order adaptive controller design of uncertain SISO linear systems with noisy output measurements

نویسندگان

  • Qingrong Zhao
  • Zigang Pan
  • Emmanuel Fernandez
چکیده

'Convergence analysis for reduced-order adaptive controller design of uncertain SISO linear systems with noisy output measurements', International This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. We consider in this article a class of uncertain SISO linear systems that are subject to system and measurement noises. Reduced-order adaptive controller designs have been proposed before for such systems by the authors and stability analysis of the closed-loop systems has been established. Here we analyse, further, the robustness properties for these reduced-order adaptive control systems by providing detailed convergence analysis results for the key closed-loop signals and parameter estimates. We rigorously prove that, whenever the exogenous disturbance input is of finite energy and bounded, and the reference trajectory and its derivatives up to rth order are bounded, r being the relative degree of the transfer function of the true system, a set of signals, including the tracking error, the estimation error between the system output and its estimate, the projection signal, are of finite energy and converge to zero; and the system states and their estimates exhibit asymptotic behaviours with certain formats. With an additional persistency of excitation condition, it is also proved that the estimate and the worst-case estimate of the state vector asymptotically track the actual state vector; and the estimate and the worst-case estimate of the unknown parameter vector converge to the true value. A numerical example is given to illustrate the theoretical findings. 1. Introduction Adaptive control has been an important research topic in control theory since the 1970s. For any type of adaptive controller, proving closed-loop stability is paramount. Moreover, for a complete robustness study, disturbance attenuation and convergence analysis for closed-loop system signals and parameters are key issues to study, besides closed-loop stability. In view of the approach adopted to …

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عنوان ژورنال:
  • Int. J. Control

دوره 82  شماره 

صفحات  -

تاریخ انتشار 2009