Free Energy Principle Based State and Input Observer Design for Linear Systems with Colored Noise

The free energy principle from neuroscience provides a biologically plausible solution to the brain's inference mechanism. This paper reformulates this theory to design a brain-inspired state and input estimator for a linear time-invariant state space system with colored noise. This reformulation for linear systems bridges the gap between the neuroscientific theory and control theory, therefore opening up the possibility of evaluating it under the hood of standard control approaches. Through rigorous simulations under colored noises, the observer is shown to outperform Kalman Filter and Unknown Input Observer with minimal error in state and input estimation. It is tested against a wide range of scenarios and the proof of concept is demonstrated by applying it on a real system.