New general guidance method in constrained optimal control, part 1: numerical method
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
Stable parallel algorithms for two-point boundary value problems
SIAM Journal on Scientific and Statistical Computing
Optimal control of the industrial robot Manutec r3
Computational optimal control
Variational calculus and optimal control (2nd ed.): optimization with elementary convexity
Variational calculus and optimal control (2nd ed.): optimization with elementary convexity
Numerical solution of constrained optimal control problems with parameters
Applied Mathematics and Computation
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Mathematics and Computers in Simulation - IMACS sponsored special issue on method of lines
Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge
Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
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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 nonconstrained 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 nonlinear systems. For the numerical solution of the nonlinear 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.