Optimization of Chen-Fliess series and Output Reachability of Nonlinear Systems
Conference Year
2023
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.
Primary Faculty Mentor Name
Luis Duffaut Espinosa
Status
Graduate
Student College
College of Engineering and Mathematical Sciences
Program/Major
Electrical Engineering
Primary Research Category
Engineering and Math Science
Optimization of Chen-Fliess series and Output Reachability of Nonlinear Systems
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.