Discounted cost linear quadratic Gaussian control for descriptor systems

Abstract

We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterise the feasibility of this problem using a linear matrix inequality. In particular, conditions for existence and uniqueness of optimal controls are derived, which are weaker compared to the standard approaches in the literature. We further show that also for the stochastic problem, the optimal control is given in terms of the stabilising solution of the Lur'e equation, which generalises the algebraic Riccati equation. We conclude our paper by examining an application of our theory to fluid dynamics problems.

Keywords:

• Descriptor systems
• linear quadratic Gaussian control
• Kalman–Yakubovich–Popov inequality
• dissipation inequality
• Navier–Stokes equation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

L.-M. Pfurtscheller was supported by a scholarship of the Vizerektorat für Forschung, University of Innsbruck and by a scholarship of the German Academic Exchange Service (DAAD).