Sequential unconstrained approach for solving index one constrained differential-algebraic optimal control problems

A constrained index-one differential algebraic optimal control problem is presented. The algebraic constraint is assumed to have an index one property. With the help of implicit function theorem, the reduced constrained optimal control problem in the state-space is then obtained. The main goal of this work is to solve the present problem by using an unconstrained sequential minimization approach. The necessary mathematical requirements, conditions and proofs are developed. Based on the obtained results, computational algorithm to solve this problem approximately is developed. Numerical illustrations of constrained differential algebraic optimal control problems are implemented. Due to the numerical results and their comparisons, an efficient approximate method is obtained.