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Optimal control and real‐time optimization of mechanical multi‐body systems
Author(s) -
Gerdts M.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310067
Subject(s) - computer science , real time control system , control (management) , artificial intelligence
Abstract Numerical 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.