Runge-Kutta discretizations of optimal control problems (Q2722586)

This paper provides a survey of results for the error associated with Runge-Kutta discretizations. Discretizations are required to obtain numerical solutions of infinite dimensional problems such as those appearing in nonlinear optical controller designs. First the results concerning the unconstrained control problem are reviewed, which, under appropriate regularity assumptions, can be extended to constrained problems. The error estimates for the first-order Euler discretization of control-constrained, state-constrained and mixed control and state-constrained problems are discussed. Finally the convergence rates for Runge-Kutta discretizations/approximations in control problems are presented and commented upon.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00036].