Delay Feedback Active Inference based on Predicted States for Uncertain Systems with Input Delay

Active inference (AIF) as a comprehensive theory has been proven to be promising in state estimation and adaptive control of uncertain systems. However, the input delay in the controller was ignored in the normal framework. When taking input delay into consideration in the uncertain system, the optimal estimation state in the normal AIF differs greatly from the real state of the system due to the accumulation of the delay effect. Therefore, delay feedback active inference (DAIF) is proposed in this paper. Different from normal AIF, the predictive state based on the delay state becomes the expectation of the state in the generative model. Meanwhile, an epitaxial delayed feedback Proportional-Integral (PI) control is introduced to be the expectation of the preference controller. The variational free energy (VFE) is extended by adding a quadratic of control consumption. The model uncertainty and measurement uncertainty are approximated by the Gaussian distributions. It can be proven that the state estimation does not depend on the given target state in D-AIF. In the simulation experiment of the trajectory tracking of an unmanned aerial vehicle with input delay, the results show that delay feedback active inference control (D-AIFC) has smaller tracking error and perceptual accuracy and shows stronger robustness when dealing with sudden disturbance than active inference control (AIFC).