Summary.
The convergence rate is determined for Runge-Kutta discretizations of nonlinear control problems. The analysis utilizes a connection between the Kuhn-Tucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle. This connection can also be exploited in numerical solution techniques that require the gradient of the discrete cost function.
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Received January 11, 1999 / Revised version received October 11, 1999 / Published online July 12, 2000
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Hager, W. Runge-Kutta methods in optimal control and the transformed adjoint system. Numer. Math. 87, 247–282 (2000). https://doi.org/10.1007/s002110000178
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DOI: https://doi.org/10.1007/s002110000178