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Abstract : |
Abstract. The Fliess series of nonlinear control theory is closely related to shuffle algebras considered by algebraic combinatorists. An infinite product expansion of this series underlies several path planning algorithms, and is the basis for polynomial realizations of nilpotent control systems. This product expansion is based on explicit knowledge of the dual bases to Poincar'e Birkhoff Witt bases built on Hall sets. We demonstrate that a chronological algebra, a structure more fundamental than shuffle algebras underlies the product expansion. Moreover, it is very closely related to the structure of general Hall sets. Keywords. Nonlinear control, chronological algebra, Chen-Fliess series let 1, |
