On deterministic and stochastic linear quadratic control problems

Abstract:

The numerical treatment of linear quadratic regulator (LQR), linear quadratic Gaussian (LQG) design and stochastic control problems of certain type require solving Riccati equations. In the finite time horizon case, the Riccati differential equation (RDE) arises. We show that within a Galerkin projection framework the solutions of the finite-dimensional RDEs converge in the strong operator topology to the solutions of the infinite-dimensional RDEs. A discussion about LQG design in the context of receding horizon control for nonlinear problems as well as a brief discussion about stochastic control is also addressed. Numerical experiments validate the proposed convergence result.

Año de publicación:

2015

Keywords:

• LQG
• Stochastic Control
• SRDEs
• LQR
• RDEs

Fuente:

scopus