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Second-order Runge-Kutta approximations in control constrained optimal control. (English) Zbl 0968.49022

Summary: We analyze second-order Runge-Kutta approximations to a nonlinear optimal control problem with control constraints. If the optimal control has a derivative of bounded variation and a coercivity condition holds, we show that for a special class of Runge-Kutta schemes, the error in the discrete approximating control is \(O(h^2)\) where \(h\) is the mesh spacing.

MSC:

49M25 Discrete approximations in optimal control
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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