Adaptive control of singular nonlinear systems with convex/concave parametrization

This note is concerned with the model reference adaptive tracking problem of singular nonlinear systems with nonlinear parametrization where the nonlinearity in the parameters is convex or concave. Applying the standard coordinate transformation to the singular system to yield a reduced-order normal system, we convert the model reference adaptive tracking problem of singular system into the model reference adaptive tracking problem of normal system and obtain solvability conditions. The proposed controller ensures that the overall adaptive system has globally bounded solutions and achieves tracking to within a desired precision.