Gray, W. Steven (Old Dominion Univ.), Wang, Yuan (Florida Atlantic Univ.)

Noncausal Fliess Operators and Their Shuffle Algebra

Scheduled for presentation during the Regular Session "Nonlinear Control III" (FrP10), Friday, July 28, 2006, 15:45−16:10, Room 103

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 25, 2024

Abstract

Fliess operators as a class of nonlinear operators have been well studied in several respects. They have a well developed realization theory and convenient representations in terms of infinite products of exponential Lie series. Their interconnection as subsystems has been studied, as has their connection to rational systems. They find applications in such diverse areas as discretization methods for controls systems, optimal control, neural network analysis, and the numerical solution of stochastic differential equations. One issue concerning Fliess operators, however, that has received little attention is their possible generalization to the noncausal case. Examples of such operators appear implicitly in the literature addressing Hilbert adjoints of casual nonlinear operators and system inversion for the purpose of output tracking. But a general, systematic treatment of the subject has not appeared. In this paper, a noncausal extension of a Fliess operator is developed with the primary focus being on local convergence, continuity, and the associated shuffle algebra. The latter is a prerequisite for the development of a realization theory and for characterizing system interconnections.