Optimal control and real‐time optimization of mechanical multi‐body systems

Abstract

AbstractNumerical methods for the solution and real‐time optimization of parametric optimal control problems for mechanical multi‐body systems are considered. The equations of motion are given as a differential‐algebraic equation (DAE) system of index 3 augmented by additional index 1 constraints. It turns out that the sensitivity analysis of parametric nonlinear programming problems is of central importance for the numerical solution of the optimal control problem by a direct shooting method and its real‐time optimization. On the one hand, a sensitivity analysis of the discretized optimal control problem provides a real‐time approximation of the optimal solution of a perturbed optimal control problem. On the other hand, a sensitivity analysis of the projection method used for consistent initialization yields consistent initial values of sensitivity matrices needed within the iterative solution process of the direct shooting method. Two examples conclude the article.