Multiplier methods for nonlinear optimal control
SIAM Journal on Numerical Analysis
Lipschitzian stability in nonlinear control and optimization
SIAM Journal on Control and Optimization
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Second-Order Runge--Kutta Approximations in Control Constrained Optimal Control
SIAM Journal on Numerical Analysis
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We consider an optimal control problem with control constraints satisfying conditions of smoothness and coercivity. By applying two Runge-Kutta schemes: one to the differential equation and a different one to the adjoint differential equation that is related to the maximum principle for optimal control, we show that the error of approximation taken with respect to the mesh spacing is of second order. This extends previous results where the same scheme was applied to the prime and to the adjoint equation. This extends previously known results where the same discretization scheme is applied to the primal and to the adjoint equation.