Conjugate gradient algorithm for optimal control problems with parameters

The basic conjugate gradient method for unconstrained optimal control problems was proposed by Lasdon et al. in [1]. The penalty function approach to the solution of inequality constrained optimal control problems has been considered in [2] and the clipping-off technique that solves optimal control problems with magnitude constraint on the control inputs is described in [3, 4]. The proposed algorithm is more simple and easier to apply than an alternative sequential conjugate-gradientrestoration algorithm of [5]. On the other hand, the algorithm of [5] need not to use penalty function to deal with optimal control problems with terminal constraints. Also the robust conjugate-gradient algorithm in [6] can compute optimal controls, however without parameter optimization.