Some results on nonlinear optimal control

This thesis consists of two individual mathematical papers which have been developed in the course of the author’s thesis work. They deal with certain aspects of optimal control of systems in which the system equations are nonlinear, the cost integrand is non- quadratic, or both.

The first paper deals an extension from the linear-quadratic case to systems as just described of the so called Newton-Kleinman method. Here we carry out this extension theoretically and prove that the associated sequence of stabilizing feedback controls converges uniformly to the optimal control.

In the second chapter of this work we generalize the existence and uniqueness theory for the nonlinear-nonquadratic optimal control problem from the critical point and periodic cases studied earlier by Lukes and Zhang, respectively, to the case where the invariant target set is a compact submanifold of the state space.