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differential equations - NDSolve for optimal control theory


For an optimal control problem, I need to solve a differential equation in which (a) the system is formulated according to a function and (b) initial/terminal conditions are discontinuous.


Here is an example of the code I would like to implement


fo[{u_, v_}] := If[u > v, {3 u - v^2, u^2}, {3 u - v^2, v^2}]


system = {{u'[t], v'[t]} == fo[{u[t], v[t]}], u[0] == 3, v[10] == 4}

NDSolve[system, {u[t],v[t]}, {t, 0, 0.3}]

Of course, there are more dimensions and function is more complicated. I have no idea if this is possible, and if so on how to proceed. Any suggestion is welcome.




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