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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.

Nonlinear boundary control of coupled Burgers' equations

Kobayashi T., Oya M.

Control and Cybernetics

2003

Vol. 32, no 2

245-258

This paper is concerned with adaptive stabilization of two coupled viscous Burgers' equations by nonlinear boundary controllers. Under the existence of bounded deterministic disturbances, the adaptive controllers are constructed by the concept of high-gain nonlinear output feedback and the estimation mechanism of the unknown parameters. In the controlled system the global stability and the convergence of the system states to zero will be guaranteed. It is shown that the theory can be generalized to the systems with higher-order nonlinearity.