Initial values for Riccati ODEs from variational PDEs

VICENTE COSTANZA; PABLO S. RIVADENEIRA

COMPUTATIONAL AND APPLIED MATHEMATICS

Scielo Brasil

Lugar: Rio de Janeiro; Año: 2011 vol. 30 p. 331 - 347

1807-0302

The recently discovered variational PDEs (partial differential equations) for fin-ding missingboundary conditions in Hamilton equations of optimal control are applied tothe extended-space transformation of time-variant linear-quadratic regulator (LQR) problems. Theseproblems become autonomous but with nonlinear dynamics and costs. Thenu-me-ri-cal 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-degrees-of freedomcontrol strategies for nonlinear systems with generalized costs.