The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Second order discrete approximations to strongly convex differential inclusions
Systems & Control Letters
Second-order discrete approximation to linear differential inclusions
SIAM Journal on Numerical Analysis
Primal-dual interior-point methods
Primal-dual interior-point methods
Second-Order Runge--Kutta Approximations in Control Constrained Optimal Control
SIAM Journal on Numerical Analysis
Selection strategies for set-valued runge-kutta methods
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Selection strategies for set-valued runge-kutta methods
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
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A numerical method for the approximation of reachable sets of linear control systems is discussed. The method is based on the formulation of suitable optimal control problems with varying objective function, whose discretization by Runge-Kutta methods leads to finite-dimensional convex optimization problems. It turns out that the order of approximation for the reachable set depends on the particular choice of the Runge-Kutta method in combination with the selection strategy used for control approximation. For an inappropriate combination, the expected order of convergence cannot be achieved in general. The method is illustrated by two test examples using different Runge-Kutta methods and selection strategies, in which the run times are analysed, the order of convergence is estimated numerically and compared with theoretical results in similar areas.