Descriptor-Systems and Optimal Control

Many problems in mathematical modeling of lumped parameter systems lead to sets of mixed ordinary differential and algebraic equations. A natural generalization are so called descriptor systems or sets of implicit ordinary differential equations, which are linear in the derivatives. This contribution deals with variational problems for descriptor systems. Using the mathematical language of Pfaffian systems, we derive a canonical form of a descriptor system, which can be converted to an explicit control system in principle. Since the proposed approach does not use this transform explicitly, the Euler Lagrange and Hamilton Jacobi equations of the variational problem are derivable by pure algebraic manipulations. In addition, this approach leads to computer algebra based algorithms, which are needed to perform the required calculations efficiently.