Optimization of higher-order systems and extensions of minimum principle

In previous years, using tools of linear and nonlinear systems theory, it has been shown that a large number of dynamic systems can be written in canonical forms. These canonical forms are alternatives to state-space forms and can be represented by higher-order differential equations. For planning and control purposes, these canonical forms provide a number of advantages when compared to their corresponding first-order forms. We address the question of optimization of dynamic systems described by higher-order differential equations. The minimum principle for higher-order systems is derived directly from their higher-order forms. The results are illustrated by an example