An analysis of time optimal control problem for one dimensional rotating arm using a path parameter

It is known that time optimal solutions for dynamical systems that are linear in control input become bang-bang type except singular solutions. It is, however, still a difficult problem to obtain a complete optimal solution for general nonlinear dynamical systems. The present paper proposes a method to analyze a time optimal control problem of a class of nonlinear system. It is called path parameter method. Especially for the problem that a spatial path is prescribed, the method is effective. As an application of the path parameter method, a time optimal control problem for the system of one dimensional rotating arm is analyzed by the method. Although the system is a nonlinear one, time optimal solutions can be obtained easily by the method. Furthermore, a global structure of the optimal solutions and minimum inputs for arbitrary boundary conditions are presented by this analysis