首页|Iterative Approximations of Periodic Trajectories for Nonlinear Systems With Discontinuous Inputs

Iterative Approximations of Periodic Trajectories for Nonlinear Systems With Discontinuous Inputs

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Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of a broad class of 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.

VectorsBoundary conditionsIterative methodsChemical reactionsNonlinear control systemsMathematical modelsConvergenceTrajectoryOrdinary differential equationsOptimization

Alexander Zuyev、Peter Benner

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Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany|National Academy of Sciences of Ukraine, Institute of Applied Mathematics and Mechanics, Sloviansk, Ukraine

Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

2025

10.1109/LCSYS.2025.3579409

IEEE Control Systems Letters

IEEE Control Systems Letters

ISSN：
年,卷(期)：2025.9(1)
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