Necessary optimality conditions for two-step descriptor systems

Abstract

This paper is concerned with an optimal control problem for general two-step descriptor systems. Based on the nonsmooth analysis and variational techniques, we establish the first-order necessary optimality conditions. Then, due to the expression of the general solution for linear descriptor systems, which is established by virtue of the Drazin inverse, we derived the generalized second-order necessary conditions for the first time. Also, for unfixed switching point case, we give some discussions.

Keywords

• steps descriptor systems
• nonsmooth analysis
• necessary optimality conditions
• variational techniques