Nonlinear Adaptive Control for Systems with Unknown Degrees and Uncertain Relative Degrees

Abstract

This paper presents a design method of adaptive controllers for nonlinear systems with unknown degrees and with uncertain relative degrees. Contrary to the previous researches of adaptive control where the degrees and relative degrees of the controlled objects are assumed to be known exactly, the degrees are assumed to be completely unknown and the relative degrees partly unknown in the present paper. To be exact, the relative degrees are assumed to be r, r+1, or r+2 with known r. It is shown that a single adaptive scheme can deal with such uncertainty of relative degrees and unknown degrees, and that the resulting adaptive systems are asymptotically stable. Several simulation studies also show the effectiveness of the proposed method.