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Symbolic-Numeric Efficient Solution of Optimal Control Problems for Multibody Systems
| Citations: | 5 - 2 self |
BibTeX
@MISC{Bertolazzi_symbolic-numericefficient,
author = {Enrico Bertolazzi and Francesco Biral and Mauro and Da Lio},
title = {Symbolic-Numeric Efficient Solution of Optimal Control Problems for Multibody Systems},
year = {}
}
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Abstract
Abstract. This paper presents an efficient symbolic-numerical approach for generating and solving the Boundary Value Problem- Differential Algebraic Equation (BVP-DAE) originating from the variational form of the Optimal Control Problem (OCP). This paper presents the Method for the symbolic derivation, by means of symbolic manipulation software (Maple), of the equations of the OCP applied to a generic multibody system. The constrained problem is transformed into a non-constrained problem, by means of the Lagrange multipliers and penalty functions. From the first variation of the nonconstrained problem a BVP-DAE is obtained, and the finite difference discretization yields a non-linear systems. For the numerical solution of the non-linear system a damped Newton scheme is used. The sparse and structured jacobians is quickly inverted by exploiting the sparsity pattern in the solution strategy. The proposed method is implemented in an object oriented fashion, and coded in C++ language. Efficiency is ensured in core routines by using Lapack and Blas for linear algebra. 1.
Keyphrases
optimal control problem multibody system symbolic-numeric efficient solution non-linear system variational form penalty function first variation solution strategy numerical solution core routine generic multibody system constrained problem structured jacobians damped newton scheme efficient symbolic-numerical approach finite difference discretization symbolic manipulation software symbolic derivation linear algebra lagrange multiplier non-constrained problem sparsity pattern
