Iterative learning control requires initial repositioning, while the time functions to be learned should be of periodicity in repetitive control. However, there are cases in practice where the time-varying unknowns are not periodic but repetitive, and repetitive learning control is applicable with avoidance of initial repositioning. In this paper, repetitive learning control designs are presented for a broader class of nonlinear systems over finite intervals. The Freeman formula is modified and used for stabilization of the nominal nonlinear time-varying system undertaken. The global stability of the learning system and asymptotic convergence of the tracking error are established through analysis of both partially and fully saturated learning algorithms, respectively. The repetitive learning control method is theoretically shown to be effective in dealing with time-varying parametric uncertainties.
CitationSun M X, Wang D W, Chen P N. Repetitive learning control of nonlinear systems over finite intervals.
The note considers the problem of local stabilization of nonlinear systems by dynamic output feedback. A new concept, namely, local uniform observability of feedback control law, is introduced. The main result is that if a nonlinear system is th-order approximately stabilizable by a locally uniformly observable state feedback, then it is stabilizable by dynamic output feedback. Based on the approximate stability, a constructive method for designing dynamic compensators is presented. The design of the dynamic compensators is beyond the separation principle and can handle systems whose linearization might be uncontrollable and/or unobservable. An example of nonminimum phase nonlinear systems is presented to illustrate the utility of the results.Index Terms-Dynamic output feedback, local uniform observability, nonlinear systems, nonminimum phase systems, stabilization.
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