Finite-dimensional VS-MRAC of distributed parameter systems with boundary inputs

Abstract

A design method is proposed for actual finite-dimensional VS-MRAC (variable structure model reference adaptive control) of asymptotically stable distributed systems with bounded disturbances, boundary inputs and arbitrary relative degree. Ideal finite-dimensional VS-MRAC is first stated and then actual finite-dimensional VS-M RAC is stated by using the results. The main results obtained in this paper are as follows. First, in the case of the ideal finite-dimensional VS-MRAC, each ideal sliding mode is always attained in a finite time, independently of the reference input and in spite of the presence of unmodelled dynamics and disturbances. The output error converges exponentially to zero, and it is assured that all signals in the closed-loop system are ultimately uniformly bounded. Next, in the case of the actual finite-dimensional VS-MRAC, each equivalent control is approximated by each average control, and the absolute value of the output error can be made asymptotically arbitrarily small, independently of the reference input and in spite of the presence of unmodelled dynamics and disturbances. Furthermore, it is assured that all signals in the closed-loop system are ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by using a numerical example

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MOTOFUMI SASAKI

Tel.: +(81) 764 41 1271; Fax: +(81) 764 41 8432

TOSHIHIRO IWAKI

Tel.: +(81) 764 41 1271; Fax: +(81) 764 41 8432