Learning identification and control of a class of discrete periodic systems

In this paper, periodic learning control is presented for deterministic periodic auto-regressive exogenous systems. The control problem is approached in a certainty equivalence framework, of which a periodic learning identification algorithm is formed to estimate the periodic time-varying parameters, and the only prior knowledge is the periodicity. The learning algorithm updates the estimates periodically, tailored for the purpose of periodic parameters estimation. The main properties of the algorithm are explored for establishing the stability and global convergence of the proposed control scheme. With the aid of the key technical lemma, the asymptotical convergence of the tracking error is guaranteed as the number of periods approaches infinity, while the input and output signals of the discrete periodic systems remain bounded. The effectiveness of the proposed method is verified through numerical simulation.