ABSTRACT

This chapter attempts to relate the property of differential flatness with optimal trajectory generation. The modern literature on optimal control theory has focussed on optimization of cost functionals for dynamic systems governed by first-order ordinary differential equations. The optimality conditions and numerical procedures for such problems are available in well-known references ([6], [10], [11], [13], [14], [5]). However, in recent years, the authors of this book have attempted to use the underlying tools of calculus of variations for optimization of dynamic systems described by higher-order differential equations, motivated by problems which are differentially flat ([1], [2], [3], [4]). The results of calculus of variations for functional containing higher derivatives of functions is available in classical books on this subject ([9], [11]).