Stability and optimization of the golden-section adaptive control

The stability of the characteristic model-based golden-section adaptive control is discussed and the relationship between the controller parameters l₁, l₂ and the closed-loop dynamic performance is analyzed. It is shown that l₁, l₂ are closely related to the parameters bounds in the characteristic model. For the typical case of a second order linear system with a pair of stable eigenvalues, it is proved that l₂ ≈ 0.618 corresponds to the smallest spectral radius in the worst case. By describing the slowly time-varying property in an explicit inequality form, a bridge is built between the instantaneous stability and the time-varying stability. A numerical example is given to show the advantage of the golden-section adaptive controller over that of the classical model reference adaptive control law.