Nonlinear Optimal Control Theory

Chapter 8

Examples

8.1 Introduction

In this chapter we illustr ate the use of results presented in the preceding

chapters to determine optimal controls and optimal trajectories.

8.2 The Rocket Car

A car, which we take to be a point mass, is pr opelled 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, whe re u is the thrust force constrained

to satisfy −1 ≤ u ≤ 1. Initially the car is at a point x

0

with velocity y

0

. The

problem is to determine a thrust program u that brings the car to rest a t the

origin in minimum time.

If we consider the state of the system to