Time Optimal Control of Mechanical Systems

Abstract

We treat the problem of time-optimal control of dynamical systems with the help of differential geometry.

If the problem of time-optimal control is to be solved, a system of first-order differential equations, the so-called adjoint system, has to be integrated. In most cases this cannot be done, neither analytically nor numerically. To reduce the complexity of the adjoint system we suggest to reduce its dimension by using First Integrals. In order to find those we formulate our problem in the language of differential geometry and apply the tools of the theory of dynamical systems.

We state a rule for obtaining First Integrals for several classes of systems. Our procedure and the results we gained with it, mean a step towards optimal control of nonlinear systems.