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ADAPTIVE TRACKING OF A CLASS OF FIRST-ORDER SYSTEMS WITH BINARY-VALUED OBSERVATIONS AND FIXED THRESHOLDS

Jin GUO , Ji-Feng ZHANG ,Yanlong ZHAO   

  1. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
  • Received:2011-11-16 Online:2012-12-25 Published:2012-12-20
  • Supported by:

    This research was supported by the National Natural Science Foundation of China under Grant Nos. 60934006,61174042, and 61120106011.

Jin GUO , Ji-Feng ZHANG ,Yanlong ZHAO. ADAPTIVE TRACKING OF A CLASS OF FIRST-ORDER SYSTEMS WITH BINARY-VALUED OBSERVATIONS AND FIXED THRESHOLDS[J]. Journal of Systems Science and Complexity, 2012, 25(6): 1041-1051.

This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A  ecursive projection algorithm is proposed for parameter estimation based on the statistical properties of the system noise. Then, an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectations of the innovation and output prediction with respect to the estimates, the closed-loop system is shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergence rate of the estimation error is also obtained. A numerical example is given to demonstrate the efficiency of the adaptive control law.
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