On the asymptotic properties of the LQG feedforward self-tuner

Abstract

In this paper, we investigate the stability and convergence of the indirect adaptive LQG feedforward controller, designed in order to precompensate the effect of the measurable disturbances, for a general S1SO non-minimum-phase stable plant. We study the equilibrium set of the associated ODE and obtain a necessary condition and some sufficient conditions on the parameters of the original plant structure, such that the limit set contains only the true parameter vector. As shown by some examples, the limit set, in general, contains points which do not correspond to the true parameter vector nor yield an optimal controller design. Simulation results show that in certain cases, when no extra excitation is present, the parameter estimates can indeed converge to such limit points, meaning that the adaptive system is not self-tuning. Finally, the global stability and convergence of the adaptive controller, based on the stochastic gradient algorithm, are established and it is shown that if the exogenous input is of sufficient order of excitation, the system is self-tuning.