Revisiting Certainty Equivalence: The Structural Coupling Between Estimation and Control in Underactuated Nonlinear Systems

What the math gives to ML

The paper identifies a concrete failure mode of certainty-equivalent feedback: estimation error does not merely add noise to a nonlinear controller, but enters tracking dynamics through state-dependent higher-order residuals and an innovation-driven coupling loop. Its transferable asset is the explicit decomposition into nominal feedback dynamics, innovation coupling, and structural residual, together with an innovation-compensation control term. This suggests augmenting a learned partially observed policy with estimator innovation as a separate control input rather than forcing the policy to infer all corrections implicitly from its latent state. A practical implementation is a residual innovation-compensated policy with uncertainty-dependent gain scheduling, evaluated against recurrent policies and standard belief-state controllers.