The Output Regulation and the Kalman Filter as the Signal Generator

In this work, the problem of following references and rejecting disturbances that are contaminated with noise and whose dynamics are too complex to have a mathematical model that describes the behavior of such signals is studied. In addition to exploiting the capabilities of the Kalman filter (KF) to clean the signals so that they can serve as external signals for the regulation theory, the construction of the generating system (exosystem) is proposed as a diagonal system by blocks, where each block is a Kalman filter that estimates each one of the corresponding reference/disturbance signals. The viability of the approach is verified by two examples, mimicking the problem of tracking a flying object moving freely in the 3D space by a quadrotor which is under the influence of the proposed controller when the displacements of the arbitrary flying object are measured by low-cost sensors.