Optimality of nonlinear design techniques: A converse HJB approach

The issue of optimality in nonlinear controller design is confronted by using the converse HJB approach to classify dynamics under which certain design schemes are optimal. In particular, the techniques of Jacobian linearization, pseudo-Jacobian linearization, and feedback linearization are analyzed. Finally, the conditions for optimality are applied to the 2-D nonlinear oscillator, where simple, nontrivial examples are produced in which the various design techniques are optimal.