On Deterministic and Stochastic Linear Quadratic Control Problems

Conference paper
Part of the Trends in Mathematics book series (TM)

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.

Keywords

LQR LQG Stochastic control RDEs SRDEs 

Mathematics Subject Classification (2010)

34H05 95B40 49J55 15A24 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Traffic and Transport EngineeringUniversity of BelgradeBelgradeSerbia
  2. 2.Department of MathematicsUniversity of InnsbruckInnsbruckAustria

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