Adding a special boundary condition to an ODE

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Mario Trevino
Mario Trevino 2015-8-14
Hi everyone! Im solving an ODE using fmincon and a cost function. Im able to find the best parameters of the model and Im happy with that. However, I now need to make a slight change to the input model and include a new boundary condition which Im not sure how to implement. Let me explain: * Right now, the differential equation has two independent parameters to optimize, vgr Vprime= (x(1).*SSIM)+(x(2).*V), and both x(1) and x(2) are effectively bounded through values I define in fmincon. So far so good. However, I now need to add a new restriction, namely, for example, that the sum of these two components is bounded between 0 an 1, that is 0<=[(x(1).*SSIM)+(x(2).*V)]<= 1. Does this have an easy solution? Could somebody help me? Intuitively, I think that this restiction may lead to a multiplicity of posible solutions wich could invalidate the approach itself? any thoughts?

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