Optimization of Chen-Fliess series and Output Reachability of Nonlinear Systems
Perez Avellaneda, Ivan
Perez Avellaneda, Ivan
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Abstract
The optimization of Chen-Fliess series allows the computation of reachable sets of nonlinear affine control systems. This provides an input-output approach to reachability analysis. Here, the framework of differential languages is explained to allow a description of higher-order derivatives of Chen-Fliess series. This is achieved by defining the derivative operation of a word in a monoid that coincides with the Gˆateaux derivative of a Chen-Fliess series. In this context, the Hessian of a Chen-Fliess series, its second-order Taylor approximation, and the second-order optimization condition are provided. Then the Newton-Raphson algorithm is adapted to Chen-Fliess series optimization to compute reachable sets.
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Date
2023-01-01