A transformation for necessary optimality conditions for systems with polynomial nonlinearities

This work shows a new formulation means to obtain the optimal control for systems having polynomial nonlinearities by using functional analytic methods. The polynomic system is reduced to a quadratic form by introducing a set of pseudostate variables and the structure of the system is characterized by a set of matrices. A new set of optimizing equations is obtained and the necessary and sufficient conditions are met by the positive definiteness requirement on the system matrix.