Parabolic optimal control problems with a quintic B-spline dynamic model

A neural network scheme based on quintic B-spline functions of optimality systems arising from linear parabolic optimal control problems is discussed. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to the optimal solution of the original problem. Theoretical and experimental results show the advantages of B-spline functions and demonstrate that the suggested scheme is able to efficiently solve constrained optimal control problems. The resulting scheme also shows that robustness with respect to changes of the value of v, the weight of the cost of the control, is sufficiently small.