Optimal control with actuator/sensor noise strengths related to feedback and Kalman gain

The linear quadratic Gaussian (LQG) method gives optimal results only when the noise covariance matrices of the actuators and sensors do not depend on feedback and Kalman gain matrices. However, in practical systems the strengths of the actuator and sensor noise generally depend on their capacities and the magnitudes of their signals, while the signal magnitudes and the required capacities depend on the feedback and Kalman gain matrices. Therefore, the covariance matrices of the actuator and sensor noises will actually depend on the feedback and Kalman gain matrices. This fact will make the LQG non-optimal or make the LQG system unstable. The authors investigate the problems of optimal control under the assumption that the noise covariance matrices of the actuators and sensors are functions of the capacities and the signal magnitude of the actuators and sensors, and thus are functions of the feedback and Kalman gain matrices. Under that assumption, the noise covariance matrices of the actuators and sensors are known before the feedback and Kalman gain matrices are designed. The new method will determine the optimal feedback and Kalman gain matrices and the required capacities of the actuators and sensors