Test of ACW-gradient optimisation algorithm in computation of an optimal control policy for achieving acceptable nitrate concentration of greenhouse lettuce

The adjustable control-variation weight (ACW)-gradient method proposed by Weinreb [Optimal Control with Multiple Bounded Inputs, Department of Electrical Engineering, Stanford University, Stanford, 1985, p. 148] is put to the test in finding optimal control laws for an optimisation problem with bounds on the inputs and terminal state constraints, presented by Ioslovich and Seginer [Acceptable nitrate concentraion of greenhouse lettuce: an optimal control policy for temperature, plant spacing and nitrate supply, in: Proceedings of the Agricontrol 2000, Wageningen, The Netherlands, IFAC, Wageningen University and Research Centre, Royal Dutch Institute of Engineers, 2000]. By making certain assumptions they derived properties of the solution in an analytic way. Here, it is shown that the numerical ACW-gradient algorithm is capable of finding solutions without making additional assumptions.