Abstract:
In this article, a robust output feedback reference quantum trajectory tracking control design is proposed through the simultaneous continuous weak measurement of noncommuting observables. Using the robust H∞ uncertainties-tolerant observer-based reference quantum trajectory tracking control (UTOBRQTTC) design strategy, the proposed method can robustly estimate the quantum trajectory and robustly track a sequence of any reference quantum states against undesired uncertainties and potential unavailable fault signals. Smoothed signal models are embedded into the augmented bilinear quantum system derived from the Lindblad master equation. With the regression of unavailable system and sensor fault signals by smoothed models, the proposed H∞ UTOBRQTTC design of the augmented bilinear quantum system can proactively compensate for the corruption of fault signals. Therefore, robust quantum trajectory estimation and reference quantum trajectory tracking can be achieved simultaneously via the proposed robust H∞ UTOBRQTTC design strategy. Furthermore, the nonlinear Hamilton–Jacobi inequality-constrained optimization problem of the optimal robust H∞ UTOBRQTTC design strategy can be treated as a linear matrix inequality (LMI)-constrained optimization problem by the upper bound of spectral radius of the augmented bilinear quantum system and the proposed two-step procedure, which can be efficiently solved with the help of the MATLAB LMI Toolbox. Finally, several simulation examples of two-level bilinear quantum systems represented by the Lindblad master equation are provided to demonstrate the estimation performance of quantum trajectory and fault signals and any arbitrary signal tracking performance for more practical applications of bilinear quantum systems.