Two-Dimensional Optimal Control Problem

This Demonstration depicts the solution of a two-dimensional optimal control problem both in phase space and physical space. The controlled object is a material point steered by acceleration with no external forces present. The problem is to steer such an object to the origin with zero velocity in minimal time. The problem was originally solved by Russian academician L. S. Pontryagin by using the maximum principle. The optimal control is a relay function with one switching point. You can choose the initial state of the point with the 2D slider.

Notation:

—initial point in phase space

—the final point in phase space

—the optimal acceleration before switching

—the optimal acceleration after switching

—the switching point

—the duration of the motion

—the switching time

—the running time