Variational PDEs and the Time-Variant LQR problem

VICENTE COSTANZA; PABLO S. RIVADENEIRA

Rosario

Congreso; RPIC 2009 - XIII Reunión de Trabajo para el procesamiento de la Información y Control; 2009

Universidad de Rosario - RPIC

The recently discovered variational PDEs for finding missingboundary conditions in Hamilton equations of optimal control are applied tothe extended-space transformation of time-variant LQR problems. Theseproblems become autonomous but with nonlinear dynamics and costs. Thenumerical solutions to the PDEs are checked against the analytical solutionsto the original LQR problem. This is the first validation of the PDEs inthe literature for a nonlinear context. It is also found that the initialvalue of the Riccati matrix can be obtained from the spatial derivative ofthe Hamiltonian flow, which satisfies the variational equation. This lastresult has practical implications when implementing two-degree-of freedomcontrol strategies for nonlinear systems with generalized costs.