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Interconnections Of Nonlinear Systems Driven By L₂-Itô Stochastic Processes, Luis A. Duffaut Espinosa

Electrical & Computer Engineering Theses & Dissertations

Fliess operators have been an object of study in connection with nonlinear systems acting on deterministic inputs since the early 1970's. They describe a broad class of nonlinear input-output maps using a type of functional series expansion, but in most applications, a system's inputs have noise components. In such circumstances, new mathematical machinery is needed to properly describe the input-output map via the Chen-Fliess algebraic formalism. In this dissertation, a class of L₂-Itô stochastic processes is introduced specifically for this purpose. Then, an extension of the Fliess operator theory is presented and sufficient conditions are given under which …

Generating Series For Interconnected Nonlinear Systems And The Formal Laplace-Borel Transform, Yaqin Li

Electrical & Computer Engineering Theses & Dissertations

Formal power series methods provide effective tools for nonlinear system analysis. For a broad range of analytic nonlinear systems, their input-output mapping can be described by a Fliess operator associated with a formal power series. In this dissertation, the inter connection of two Fliess operators is characterized by the generating series of the composite system. In addition, the formal Laplace-Borel transform of a Fliess operator is defined and its fundamental properties are presented. The formal Laplace-Borel transform produces an elegant description of system interconnections in a purely algebraic context.

Specifically, four basic interconnections of Fliess operators are addressed: the parallel, …