Necessary optimality conditions for optimal control of the multistage differential-algebraic systems

In the article a new approach for optimal control of the multistage differential-algebraic systems was presented. A merit function based on Fletcher´s augmented Lagrangian was used. The necessary optimality conditions for the optimal control of multistage index-1 DAE systems were stated and locally optimal solution was obtained using the inexact Newton method. The only constraints for decision variables are lower and upper bounds. The piecewise-linear projection of the constraints on control variables and both differential and algebraic variables onto the feasible box were used. The numerical simulations on a catalyst mixing problem were executed in Matlab environment using Wroclaw Centre for Networking and Supercomputing.