In this paper, we derive the discrete linear-exponential-quadratic-Gaussian (LEQG) controller which can take both the system and measurement noise covariances into consideration. Comparing with the traditional linear-quadratic-Gaussian (LQG) design, the LEQG has the wilder design freedom. The proposed discrete LEQG control scheme is then applied to the study of reliable control which can tolerate abnormal operation within some pre-specified set of actuators. This is achieved by suitable modification of the algebraic Riccati equation for the design of the controller. The bounds of gain margins for the feedback control gains of reliable stabilization are also derived. The stability of the overall system is preserved despite the abnormal operation of actuators within a pre-specified subset in the bounds of gain margins.
- Algebraic Riccati equation
- Discrete linear-exponential-quadratic-Gaussian control
- Kalman filter
- Reliable control