Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics
Compact conditions for the prediction and stability analysis of period-doubling bifurcations are obtained by the harmonic balance method. The implications of the results to control design are illustrated through the development of a design procedure for control design which can delay a given period-doubling bifurcation as well as meet stability objectives. This paper is organized as follows. Section 1 consists of an introduction. In Section 2 the class of systems investigated in the paper is specified and known harmonic balance results for this class are presented in a compact form. In Section 3, harmonic balance results are obtained for the prediction and stability analysis of period-doubling bifurcations. In Section 4 a control problem is defined and a design procedure for its solutions is outlined. Section 5 contains a detailed example illustrating the results; in this example, a controller is given that can delay or eliminate the period-doubling cascade to chaotic motion. Finally, concluding remarks are collected in Section 6.
scientific article; zbMATH DE number 946987
scientific article