Online optimisation of the free parameters in discrete adaptive control systems

A method is proposed for improving the adaptation transients in discrete-time adaptive systems. The method is based upon the well known fact that usually some of the parameters entering the adaptation gain can be freely chosen within certain bounds while maintaining the stability of the whole system. The philosophy of the method is to interpret these parameters as additional inputs to the adaptive control systems to be computed online in order to minimise a quadratic criterion of the tracking error. As an intermediate step, an equivalent time-varying and near-linear system, which is an approximate model for the whole system, is derived in order to compute a bang-bang (or eventually linear) mode suboptimal control. The resulting control is finally translated into modifications of the parameters entering the adaptation gain updating equation.