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(t0,x0,y0) ∈ E0 = {( , x,<br />
y) / t ( 0, T ),<br />
y ∈( y , y ),<br />
x ∈[ d ( y) d ( y)<br />
]}<br />
t<br />
1 2<br />
1<br />
,<br />
2<br />
of all admitted commands (u(.), v(.)) : [0,T] → IR 2 +<br />
and the restrictions:<br />
∈ in class υ (t0,x0,y0)<br />
that verify the restrictions from (4)<br />
(9) (t,x(t), y(t)) ∈E0 ∀ t ∈(t0,T)<br />
In order to minimise the cost of producing the target weight within the set deadline,<br />
T>0 one must minimise functional C (.,.) defined by:<br />
(10) C(u(.), v(.)) = ( C u( t) C v( t)<br />
)<br />
t<br />
∫ 1<br />
+<br />
2<br />
dt.<br />
0<br />
where C1,C2 > 0 are the prices of the dietary protein and energy.<br />
The next step to be taken subsequently is to use the results and models from the<br />
literature to solve these problems of optimal control.<br />
References<br />
Burlacu Gh., R. Burlacu, I. Columbeanu, G. Alexandru <br />
proceselor de metabolism la monogastrice<br />
, 1987 -<br />
<br />
Român de Biometrie la Academia R.S.R. –<br />
1986 - Sufficient optimality condition for stratified optimal control<br />
problems, SIAM J Cont and Opt 24 (), 675-695.<br />
<br />
–<br />
Whittemore C.T. 1983 - Agricultural Systems, p 159-186.