In this chapter we illustrate the use of results presented in the preceding chapters to determine optimal controls and optimal trajectories.
A car, which we take to be a point mass, is propelled by rocket thrusts along a linear track endowed with coordinates. Units are assumed to be normalized so that the equation of motion is x¨ = u, where u is the thrust force constrained to satisfy −1 ≤ u ≤ 1. Initially the car is at a point x0 with velocity y0. The problem is to determine a thrust program u that brings the car to rest at the origin in minimum time.