Abstract:  

In nonlinear control theory, input-output systems are interconnected in various ways to form more complex systems. If each component system is analytic, meaning it can be described in terms of a Chen-Fliess functional series expansion, then it can be represented uniquely by a formal power series over a noncommutative alphabet. System interconnections are then characterized in terms of algebraic operations on formal power series. In this talk, this methodology is applied to characterize the underlying combinatorial algebras of the basic system interconnections found in controls: the parallel, product, cascade and feedback connections. The feedback connection is perhaps the most interesting case as the underlying algebraic framework is that of a Faa di Bruno Hopf algebra. The antipode of this algebra provides a recursive algorithm for performing system inversion, which is a prerequisite for solving classical control problems such as output tracking and path planning.