Iterative Approximations of Periodic Trajectories for Nonlinear Systems With Discontinuous Inputs
Year: 2025
Type: article
Abstract: Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of Carathéodory solutions. It is shown that, under the dominant linearization assumption, the considered class of boundary value problems admits a unique solution for any admissible control. These solutions can be obtained as the limit of the proposed simple iterative scheme and, in the case of periodic boundary conditions, via the developed Newton-type schemes. Under additional technical assumptions, sufficient contraction conditions of the corresponding generating operators are derived analytically. The proposed iterative approach is applied to compute periodic solutions of a realistic chemical reaction model with discontinuous control inputs.
Source: IEEE Control Systems Letters
Authors: Alexander Zuyev, Peter Benner
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4411269920