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Nonlinear control-affine systems described by ordinary differential equationswith bounded measurable input functions are considered. The problem of theexistence of periodic trajectories to these systems is formulated in the senseof Carath\'eodory solutions. It is shown that, under the dominant linearizationassumption, the periodic boundary value problem admits a unique solution forany admissible control. This solution can be obtained as the limit of theproposed simple iterative scheme and Newton-type method. Under additionaltechnical assumptions, sufficient contraction conditions of the correspondinggenerating operators are derived analytically. The proposed iterative approachis applied for the computation of periodic solutions of a realistic chemicalreaction model with discontinuous control inputs.

Iterative approximations of periodic trajectories for nonlinear systems with discontinuous inputs