Chapter 4
Optimal Control Theory
4.1 Formulation of general optimal control problem
We consider a control system described in vector form as

x= f(x;u) (4.1)
where
x = (x1;:::;xn)T ; u = (u1;:::um)T (4.2)
f(x;u) = (f1(x;u);:::fn(x;u))T: (4.3)
 The initial points x0 2 X0 and x1 2 X1; where X0 and X1 are manifolds in Rn:
 The class
represents the set of all admissible controls and
u 2
= fu : u is bounded and piecewise continuous; u(t) 2
;
Rmg (4.4)
where
is compact and convex.
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