On the principle of smooth fit for some convex optimal control problems

Proceedings of the 8th International Symposium on Mechatronics and its Applications (ISMA12)¹, Sharjah, UAE. The purpose of this work is to show that the principle of smooth fit can fail even for convex problems. Using the dynamic programming approach which involves using differential equation methods, we get the value function for a convex optimal control problem. Then this value function turns out to be a convex viscosity solution of the dynamic programming equation, not C² along the free boundary, and hence not a classical solution of the above mentioned equation.