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.

Año de publicación:

2022

Keywords:

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

Fuente:

scopus