Abstract
It is well known that classical Runge-Kutta approximations for dynamical systems do not converge with high order when the control is not smooth with respect to time. We consider here a generalization of RK schemes for linear systems which preserves its order with measurable controls, and obtain as consequence a result of high-order approximation for the reachable set.
Zusammenfassung
Es ist bekannt, daß klassische Runge-Kutta-Approximationen für dynamische Systeme nicht mit höherer Ordnung konvergieren, falls die Kontrolle nicht glatt bezüglich der Zeit ist. Wir betrachten hier eine Verallgemeinerung von RK-Schemata für lineare Systeme, bei der für meßbare Kontrollen die Konvergenzordnung erhalten bleibt, und erhalten als Konsequenz eine Approximation der erreichbaren Menge von hoher Ordnung.
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Ferretti, R. High-order approximations of linear control systems via Runge-Kutta schemes. Computing 58, 351–364 (1997). https://doi.org/10.1007/BF02684347
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DOI: https://doi.org/10.1007/BF02684347