Prediction-centred active inference with stability guarantees for nonlinear delayed feedback

Abstract State reconstruction and delay compensation are central to nonlinear feedback in which commands are delayed and measurements arrive intermittently. Conventional active inference (AIF) centres the hidden-state prior on the reference, while predictor feedback takes its state from a fixed-gain observer outside the control objective, so the estimate either inherits the tracking error or ignores the reliability of the evidence. Predictor-feedback delay-aware active inference (PF-DAIF) removes this coupling. In its factorized generative model, an input-history predictor centres the state prior, time-aligned measurements with bounded adaptive precision form the sensory likelihood, and the reference enters only a projected action evaluated at a forecast of the arrival state. The stationary belief error becomes a matrix-weighted convex combination of the predictor and sensing residuals, independent of the reference, and the inference dynamics contract the belief, keep the precision bounded and dissipate the free energy. An augmented model of the sampled loop yields an exact spectral stability test for fixed delay, linear matrix inequalities for mean-square stability under switching delay and packet loss, and a common Lyapunov condition over the precision range, while a local Razumikhin-type condition covers the nonlinear plant. Simulations of a delayed linear benchmark and an underactuated quadrotor with time-varying delay, packet loss, gusts and sensor bias compare PF-DAIF with target-centred AIF and a Smith-predictor PID controller. The forecast action preserves stability over delay ranges in which present-state feedback develops a growing oscillation, the estimation error stays well below that of AIF and is insensitive to reference shifts, and the tracking accuracy matches Smith-predictor control at moderate delays.