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dX1/dt = f(X1,X2, u1, p1)

dX2/dt = f(X1,X2, u2, p2)

where X1,X2 are state variables, u1,u2 are controls and p1,p2 are parameters. I would be interested in answer the question for what p1,p2 there is u2 = 0 for whole time. I’m looking for something like bifurcation theory/phase portrait from dynamical system which might be applied for optimal control problems.