In this paper, we consider adaptive stabilization and an adaptive regulator design for collocated distributed-parameter systems in the case of the input and output operators being unbounded. Adaptive stabilization is realized by the concept of high-gain output feedback. The adaptive regulator is constructed via the concept of high-gain output feedback, using a mechanism to estimate the unknown parameters of the bounded disturbances. The state of the controlled system is shown to converge to zero.
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Toshihiro Kobayashi (1999) studied this question.