The local solvability of a Hamilton-Jacobi-Bellman PDE around a nonhyperbolic critical point

Authors
Citation
Aj. Krener, The local solvability of a Hamilton-Jacobi-Bellman PDE around a nonhyperbolic critical point, SIAM J CON, 39(5), 2001, pp. 1461-1484
Citations number
23
Categorie Soggetti
Mathematics,"Engineering Mathematics
Journal title
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN journal
03630129 → ACNP
Volume
39
Issue
5
Year of publication
2001
Pages
1461 - 1484
Database
ISI
SICI code
0363-0129(20010305)39:5<1461:TLSOAH>2.0.ZU;2-1
Abstract
We show the existence of a local solution to a Hamilton-Jacobi-Bellman (HJB ) PDE around a critical point where the corresponding Hamiltonian ODE is no t hyperbolic, i.e., it has eigenvalues on the imaginary axis. Such problems arise in nonlinear regulation, disturbance rejection, gain scheduling, and linear parameter varying control. The proof is based on an extension of th e center manifold theorem due to Aulbach, Flockerzi, and Knobloch. The meth od is easily extended to the Hamilton-Jacobi-Isaacs (HJI) PDE. Software is available on the web to compute local approximtate solutions of HJB and HJI PDEs.