A unified controllability/observability theory for some stochastic and deterministic partial differential equations

2010/03/30 by Zhang, Xu · 1 citation
#35Q93 (Secondary) #93B05 (Primary) #93B07 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1003.5819

Abstract

The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial analytic tool is a class of fundamental weighted identities for stochastic/deterministic partial differential operators, via which one can derive the desired global Carleman estimates. This method can also give a unified treatment of the stabilization, global unique continuation, and inverse problems for some stochastic/deterministic partial differential equations.

Cited by

• Memory-Type Null Controllability of Heat Equations with Delay Effects

Related

• A weighted identity for stochastic partial differential operators and its applications
• Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions
• Asymptotic strong Feller and weak observability inequality
• A Mini-Course on Stochastic Control
• Carleman estimate for semi-discrete stochastic parabolic operators in arbitrary dimension and applications to controllability