Runge–Kutta Based Procedure for the Optimal Control of Differential-Algebraic Equations

A new approach for optimization of control problems defined by fully implicit differential-algebraic equations is described in the paper. The main feature of the approach is that system equations are substituted by discrete-time implicit equations resulting from the integration of the system equations by an implicit Runge–Kutta method. The optimization variables are parameters of piecewise constant approximations to control functions; thus, the control problem is reduced to the control space only. The method copes efficiently with problems defined by large-scale differential-algebraic equations.