On the Gradient Projection Method for Optimal Control Problems with Nonnegative $\mathcal{L}^2 $ Inputs
T. Tian, J. C. Dunn · SIAM Journal on Control and Optimization · 1994
Local convergence and active constraint identification theorems are proved for gradient-projection iterates in the cone of nonnegative $\mathcal{L}^2 $ functions on [0,1]. The theorems are based on recently established infinite-dimensional extensions of the Kuhn–Tucker sufficient conditions and are directly applicable to a large class of continuous-time optimal control problems with smooth nonconvex nonquadratic objective functions and Hamiltonians that are quadratic in the control input u.