Robustly stable pole-placement based adaptive control of continuous linear systems with multiestimation

Abstract

This paper deals with the pole-placement type robust adaptive control of continuous linear systems in the presence of bounded noise and a common class of unmodeled dynamics with the use of multiple estimation schemes working in parallel. The multiestimation scheme consisting of the above set of various single estimation schemes is a tool used to minimize the plant identification error by building an estimate which is a convex combination of the estimates at all time. The weighting functions of the individual estimates are provided at each time by a suboptimization scheme for a quadratic loss function of a possibly filtered tracking error and/or control input. The robust stability of the overall adaptive scheme is ensured by an adaptation relative dead zone which takes into account the contribution of the unmodeled dynamics and bounded noise. The basic results are derived for two different estimation strategies which have either a shared regressor with the plant or individual regressors for the input contribution and its relevant time-derivatives. In this second case, the plant input is obtained through a similar convex combination rule as the one used for the estimators in the first approach. An extension of the basic strategies is also pointed out including a combined use of the suboptimization scheme with a supervisor of past measures for the on-line calculation of the estimator weights in the convex combination.