A new periodic recursive least-squares (PRLS) estimator is developed with data-weighting factors for a class of linear time-varying parametric systems where the uncertain parameters are periodic with a known periodicity. The periodical time-varying parameter can be regarded as a constant in the time interval of a periodicity. Then the proposed PRLS estimates the unknown time-varying parameter from period to period in batches. By using equivalent feedback principle, the feedback control law is constructed for the adaptive control. Another distinct feature of the proposed PRLS-based adaptive control is that the controller design and analysis are done via Lyapunov technology without any linear growth conditions imposed on the nonlinearities of the control plant. Simulation results further confirm the effectiveness of the presented approach.
"Data-Weighting Periodic RLS Based Adaptive Control Design and Analysis without Linear Growth Condition." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/191256