Iterative learning identification algorithms with quantifiable rate of learning for a class of discrete time-varying systems

For a class of discrete repetitive operation of the time-varying systems over finite intervals, two kinds of iterative learning identification algorithms are presented in this paper to estimate time-varying parameters, which reach any given accuracy within limited number of iterations. The mathematical relationships between iterative numbers and estimating errors of time-varying parameter are presented, by virtue of the iterative learning identification algorithms in this paper. As a result, the convergence speed is quantified and quickened. And consequently, after arbitrary iteration, both estimating errors of parameter and tracking errors can be calculated quantitatively. In addition, the parameter estimation error converges to zero, with designed iterative numbers, in an exponential form along the iterative axis based on the two identification algorithms proposed in the paper. Theoretical proof is given and numerical simulation results demonstrate that the proposed learning algorithms are effective and valid.