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Adaptive stabilization of infinite-dimensional undamped second order systems without velocity feedback

Kobayashi T., Oya M.

Archives of Control Sciences

2004

Vol. 14, no. 1

73-84

In this paper adaptive stabilization of infinite-dimensional undamped second order systems is considered in the case where the input and output operators are collocated. the systems may have an infinite number of poles, and zeros on the imaginary axis. In the case where only position feedback is available, a parallel compensator is effective. The stabilizer is constructed by an adaptive p-controller for the augmented system which consists of the controlled system and a parallel compensator. The asymptotic stsbility of the closed-loop system is proved by LaSalle's invariance pronciple under compactness of the resolvent.

Low gain adaptive stabilization of undamped second order systems

Kobayashi T.

Archives of Control Sciences

2001

Vol. 11, no. 1/2

63-75

In this paper low-gain adaptive stabilization of undamped second order systems is considered in the case of collocated input and output operators. The systems have poles and zeros on the imaginary axis. In the case where velocity feedback is available, the adaptive stabilizer is constructed by an adaptive low-gain PD-controller (proportional plus derivative controller). In the case where only position feedback is available, the adaptive stabilizer is constructed by a low-gain adaptive P-controller for the augmented system which consists of the controlled system and a parallel compensator. Numerical examples are given to illustrate the effectiveness of the proposed controllers

Some remarks on adaptive stabilization of infinite-dimensional second order systems

Kobayashi T.

Archives of Control Sciences

2000

Vol. 10, no. 1/2

5-16

In this paper adaptive stabilization of infinite-dimensional undamped second order systems is considered in the case of the input and output operators being collocated. The advantage of the adaptive law is that good control performance can be automatically achieved even in the presence of various types of uncertainties. The adaptive stabilizer is constructed by the concept of high-gain output feedback. An energy-like function and a multiplier function are introduced and adaptive stabilization of the linear second order systems is analyzed. It is shown that the theory of adaptive stabilization can be also applied to some nonlinear systems.