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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.

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