In this thesis optimal control problems subject to differential-algebraic equations (DAEs) with differential index 1 and 2 are discussed. Such equations occur for example as models of mechanical multi-body systems and electric circuits. Furthermore we obtain DAEs by space discretization of partial differential equations. After introduction and preliminaries a function space method for solving the optimal control problems is discussed in Chapter 3. The necessary optimality conditions for local minimizers are rewritten as a system of equations in Banach spaces. This system is solved by Newton's method. It turns out that the system of equations is not differentiable and a nonsmooth version of Newton's method is applied. The search direction in Newton's method is the solution of an index 2 DAE boundary value problem. Local and global convergence properties of the algorithm are discussed. The method is used to solve optimal control problems subject to the Navier-Stokes equations and the heat equation. The partial differential equations are discretized in space by finite differences and mixed finite element methods. In Chapter 4 the optimal control problems are discretized at first and a finite nonlinear program is obtained. The state equation is discretized by Euler's method and algebraic constraints are not considered. Convergence of the solution of the discretized problems against the solution of the continuous problem is investigated and proven for controls of bounded variation. The convergence order is 1/p for Lp-norms. The analytic convergence order is observed numerically for an example where the optimal control possesses infinitely many but countable jumps. In Chapter 5 the results of subproject 1 of the SyreNe BMBF project are presented. DAE models of electrical networks are coupled with semiconductors modeled by drift-diffusion equations. Space-discretization of the drift-diffusion equations yields a large nonlinear DAE system. Proper orthogonal decomposition is used to generate reduced order models. Finally an optimal control problem subject to the network equations is discussed. Using the reduced order models an efficient optimal control algorithm is defined.    «

In this thesis optimal control problems subject to differential-algebraic equations (DAEs) with differential index 1 and 2 are discussed. Such equations occur for example as models of mechanical multi-body systems and electric circuits. Furthermore we obtain DAEs by space discretization of partial differential equations. After introduction and preliminaries a function space method for solving the optimal control problems is discussed in Chapter 3. The necessary optimality conditions for local mi...    »