A new approach to nonlinear descriptor systems with variable rank of Jacobians

It is well known that it is difficult to analytically/numerically solve the optimal control problems in a descriptor form and there is little research in the case where the rank of Jacobians is not constant. In this paper we propose a numerical approach to optimal control problems with nonlinear descriptor systems where the rank of Jacobians varies. First, we transform the descriptor-based control problem into the standard control problem with state/control constraints. Focusing on the multiplier method, we present an algorithm for the numerical solutions of the constrained optimal control problems by means of a function space approach. Finally, some numerical examples are given to show the effectiveness of our approach in comparison with the penalty function approach.