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Global adaptive pole positioning. (English) Zbl 0553.93032
The adaptive pole placement scheme considered in this paper is the adaptive version of Wolovich’s frequency domain pole placement technique [see e.g. W. A. Wolovich, ibid. AC-26, 162-170 (1981; Zbl 0478.93031)]. The plant parameters are estimated by the identifier. Then a controller is implemented as if the parameter estimate were correct. In section 2, indirect adaptive pole placement is reviewed, with some observations. It is pointed out that the method is nonglobal and may not even stabilize the real plant. In section 3, minimum extensions of the nonglobal results are presented in order to obtain a global result. After providing two lemmas, a theorem concerning the convergence of the parameter estimate to the true values is presented. The conditions stated in the theorem are not yet global, but have advantage over the conditions in the theorem of section 2. In section 4, all assumptions required for a global result are listed. Then an algorithm for adaptive pole placement with global stability is given. The proof of global stability is given in sections 5 and 6.
Reviewer: K.Ichikawa

##### MSC:
 93B55 Pole and zero placement problems 93C05 Linear systems in control theory 93C40 Adaptive control/observation systems 93C99 Model systems in control theory
##### Keywords:
adaptive pole placement; algorithm; global stability
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