Robust Optimal Control of Biobjective Linear–Quadratic System With Noisy Observation
Guangchen Wang, Zhuangzhuang Xing
Abstract
This note is dedicated to a kind of partially observable linear–quadratic control problem with model uncertainty, where the coefficients of cost functional are uncertain representing different market conditions. By virtue of backward separation technique, stochastic maximum principle, as well as filtering method, a feedback form of candidate optimal control is designed. Moreover, through some delicate analysis, the existence of maximal reference probability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bar{\lambda }^*$</tex-math></inline-formula> is certified. A considerable innovation of this note is the characterization of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bar{\lambda }^*$</tex-math></inline-formula> by computation of the optimal cost. Finally, a numerical simulation is presented to authenticate our theoretical results.