Mathematical Control Theory

Passivity based stabilization of nonlinear differential repetitive processes with application to iterative learning control

M. A. Emel'yanov

Arzamas Polytechnical Institute of R.E. Alekseev Nizhny Novgorod State Technical University

Abstract: Repetitive processes propagate information in two independent directions. They arise in the modeling of industrial systems such as metal rolling and can be used as a setting for control law design. The latter area has seen experimental verification for designs based on linear dynamic models. This paper addresses stabilization and disturbance attenuation for differential nonlinear repetitive processes where vector Lyapunov functions are used to characterize a physically relevant stability property and the disturbance attenuation is expressed in terms of an H? norm. An extension to processes with failures modeled by a finite state Markov chain is also developed and applied to iterative learning control design in the presence of model uncertainty and information channel failures. An illustrative example is also given.

Keywords: repetitive process, nonlinear 2D-systems, differential nonlinear repetitive processes, passivity, stability, iterative learning control.

UDC: 62.50
BBK: B161.84я43

Received: January 31, 2015
Published: May 31, 2016

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