Optimization equations To employ the standard methods of optimal control theory to our problem, it is necessary to recast our equations into a set of simultaneous first order equations — the so-called problem of Mayer. But, when p0(p,r) from equation (4) is substituted into equation (5), we obtain a double integral which is difficult to deal with. A simple way out is to discretize w0(p,r) so that the integral becomes a finite sum. To do so, we divide the interval 0 < p < Ro into equally spaced intervals The total power, Wn, collected by the receiver represents one of the constraints and we want to express this in terms of they( variables. From equation (8), we have In terms of u, equation (6) for the power transmitted up to radius r becomes
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