Finite Horizon $H^\infty$ Control for a Class of Linear Quantum Measurement Delayed Systems: A Dynamic Game Approach

Abstract

In this paper, a finite horizon $H^\infty$ control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of delayed measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, the finite horizon $H^\infty$ control problem for the class of linear quantum systems under consideration is solved for the case of delayed measurements by solving the finite horizon $H^\infty$ control problem for an equivalent stochastic $H^\infty$ control problem following a dynamic game approach.