Optimal control of proper and nonproper descriptor systems

Abstract

In recent years, the analysis and synthesis of control systems in the descriptor form have been established. This general description of dynamical systems by differential/algebraic equations is important for many applications in mechanics and mechatronics, in electrical and electronic engineering, and in chemical engineering as well. The present contribution deals with the design of optimal control for such dynamic systems. This means that the calculus of variations and Pontryagin's maximum principle have to be generalized for descriptor systems. An important role in the applicability of usual design algorithms plays the properness of the systems. The distinction between proper and nonproper systems is necessary in determining descriptor systems which are exclusively governed by the control inputs or additionally by their higher-order time-derivatives. In case of nonproper systems, quite different optimal control problems appear. For both cases, necessary conditions for optimal control are presented.