The Lagrange relaxation method in optimal control problems
A normal Bolza optimal control problem is under consideration, i.e., it is assumed that in the Lagrange minimum principle the multiplier corresponding to the functional is nontrivial. The formula for variation of the functional is derived and a gradient-like minimization algorithm is proposed. Each iteration is accompanied with a correction procedure intended to improve control performance in the case when the dimension of the control exceeds the dimension of the state space. The argument is more heuristic than rigorous. However, it is claimed that the proposed algorithm helps to improve considerably performance of the energy saving control for a walking robot model.
scientific article; zbMATH DE number 652098