Finite-Iteration Learning Control for Nonlinear Systems With Parameter Uncertainties

For any given target trajectory, asymptotic tracking error convergence can be achieved as the number of iterations tends to infinity by applying existing iterative learning control strategies. In this study, we propose two finite-iteration learning control (FILC) strategies for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i>th-order nonlinear systems with parameter uncertainties to make the tracking error converge to zero in a finite number of iterations. In each strategy, an iterative learning estimation law and a control law are designed individually. Using these two strategies, both unknown parameter estimation and target trajectory tracking are achieved simultaneously in finite iterations. A recursion-based biaxial nonlinear convergence analysis method is proposed to establish strict proofs for the finite-iteration convergence. In addition, the necessary number of iterations for zero-error tracking performance is derived through a detailed analysis of the evolutionary dynamics at different time points. Thus, a comprehensive design and analysis framework is established for FILC. Illustrative simulation examples are presented to verify the theoretical results.