Adaptive estimation of time-varying parameters in linearly parametrized systems is considered. The estimation time is divided into small intervals; in each interval the time-varying parameter is approximated by a time polynomial with unknown coefficients. A condition for resetting of the parameter estimate at the beginning of each interval is derived; the condition guarantees that the estimate of the time-varying parameter is continuous and also allows for the coefficients of the polynomial to be different in various time intervals. A modified version of the least-squares algorithm is provided to estimate the time-varying parameters. Stability of the proposed algorithm is shown and discussed. Simulation results on an example are given to validate the proposed method.
The decentralized output feedback control problem for a class of large-scale interconnected nonlinear systems is considered. The nonlinear interconnection function of each subsystem is assumed to satisfy a quadratic constraint on the entire state of the large-scale system. A decentralized estimated state feedback controller and a decentralized observer are designed for each subsystem. Sufficient conditions, for each subsystem, under which the proposed controller and observer can achieve exponential stabilization of the overall large-scale system are developed. Simulation results on a numerical example are given to verify the proposed design.
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