In this chapter, we introduce the concept of Lagrange multipliers. We show how the Lagrange Multiplier Rule and the John Multiplier Theorem help us handle the equality and inequality constraints in optimal control problems.
Consider the simplest optimal control problem, in which we wish to find the control function u that optimizes
 |
(3.4) |
subject to the differential equation constraint
 |
(3.5) |
with the initial condition
| (3.6) |
At the optimum, it is necessary ...
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