Abstract
This paper takes a class of first-order systems as an example to study the adaptive tracking control via binary-valued observations with fixed threshold. Using the statistical property of the system noise, a projection algorithm is proposed for parameter estimation. Then, the 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 and adaptive control law are shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergent 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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