Numerical solution of the variational PDEs arising in optimal control theory
AUTOR(ES)
Costanza, Vicente, Troparevsky, Maria I., Rivadeneira, Pablo S.
FONTE
Computational & Applied Mathematics
DATA DE PUBLICAÇÃO
2012
RESUMO
An iterative method based on Picard's approach to ODEs' initial-value problems is proposed to solve first-order quasilinear PDEs with matrix-valued unknowns, in particular, the recently discovered variational PDEs for the missing boundary values in Hamilton equations of optimal control. As illustrations the iterative numerical solutions are checked against the analytical solutions to some examples arising from optimal control problems for nonlinear systems and regular Lagrangians in finite dimension, and against the numerical solution obtained through standard mathematical software. An application to the (n + 1)-dimensional variational PDEs associated with the n-dimensional finite-horizon time-variant linear-quadratic problem is discussed, due to the key role the LQR plays in two-degrees-of freedom control strategies for nonlinear systems with generalized costs. Mathematical subject classification: Primary: 35F30; Secondary: 93C10.
Documentos Relacionados
- Initial values for Riccati ODEs from variational PDEs
- Variational calculus (optimal control) applied to the optimization of the enzymatic synthesis of ampicillin
- A non-standard optimal control problem arising in an economics application
- A VARIATIONAL METHOD IN THE THEORY OF HARMONIC INTEGRALS*
- Lavrentiev-prox-regularization for optimal controlof PDEs with state constraints