guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
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y<br />
2.4.11 Dynamic Programming <strong>and</strong> the Pontryagin Maximum Principle<br />
For the Bolza problem under consideration, the state system is given<br />
<strong>and</strong> the boundary conditions by<br />
ii = 4 cr, u)<br />
(2.4.148)<br />
x = x0 AT t =t, (2.4.149)<br />
7 C;r,,$)=O j .J=/,& pr r=+ (2.4.150)<br />
where t may or may not be specified. The control action u is to be selected<br />
so thatfan integral plus the function of the terminal state of the form<br />
G<br />
J ={ % (x,u)ort + +(X,9t,)= minimum<br />
0<br />
is a minimum. An application of the Pontryagin Max5mum Principle to this<br />
problem (Ref. 2.4.3) leads to the following requirements:<br />
(1) the control u is selected fromu so that at each instant the<br />
quantity H where<br />
(2.4.151)<br />
H = p’ f (x, u)- 7&t) = J; 3 5. (+.+ih%,U) (2.4.152)<br />
I<br />
is maximized.<br />
(2) the adjoint vector? satisfies the differential equations<br />
(2.4.153)