Adaptive robust control under unknown plant orders (Q1295061)

This paper introduces a robust indirect adaptive controller under additive and parametric disturbances. The plant is assumed to be describable by the equation \[ a(q^{-1})y(t)= q^{-k}b(q^{-1})u(t)+ d(t),\quad t\in\mathbb{N} \] with unknown initial conditions, where \(y(t)\), \(u(t)\) and \(d(t)\) are scalar output, control input and disturbance, \(k\) is an unknown time delay satisfying \(1\leq k\leq K\) where \(K>0\) is a priori known, and \(a(\cdot)\) and \(b(\cdot)\) are two polynomials with unknown bounded orders. It is also assumed that a robust linear controller of the plant can be defined for known parameters, model orders and time delay. The robust adaptive controller switches between model structures depending on an overall criterion of performance. It is not only proved that the adaptive control scheme is stable but also that its asymptotic performance can be set arbitrarily near to the performance achievable for a known plant. Finally, a simulation illustrates the performance of the scheme.