Revisiting Certainty Equivalence: The Structural Coupling Between Estimation and Control in Underactuated Nonlinear Systems
For control engineers working on underactuated nonlinear systems, this work provides a practical alternative to classical CE-based designs that mitigates performance degradation during aggressive maneuvers.
The paper revisits the certainty equivalence principle for nonlinear systems, showing that estimated states create coupling between estimation and tracking dynamics. It proposes an estimation-aware control paradigm that improves tracking bandwidth by 39% and stability margins by up to 55% in quadrotor simulations at speeds up to 57.6 km/h.
The certainty equivalence (CE) principle underpins a wide range of control architectures by enabling the separation of estimation and control design. While this property holds for linear systems, its validity in nonlinear settings remains limited and often implicitly assumed. This paper revisits CE from a nonlinear perspective, showing that estimated states induce an intrinsic coupling between estimation and tracking dynamics. By analyzing the closed-loop system in tracking-error coordinates, we demonstrate that nonlinear state dependence gives rise to higher-order interaction terms during aggressive transients. Motivated by this limitation, we propose an estimation-aware (EA) control paradigm that incorporates estimation quality into the feedback law to isolate estimation-induced loops. The formulation remains filtering-agnostic while preserving general applicability to smooth, underactuated nonlinear systems. We derive analytical conditions guaranteeing bounded tracking under uncertainty, validating the framework under high-fidelity quadrotor flight simulation along complex 3D trajectories at speeds up to 57.6 km/h. Frequency-domain evaluations demonstrate that the EA law extends tracking bandwidth by 39% and improves stability margins by up to 55%, effectively mitigating severe cross-couplings to offer a robust alternative to classical CE-based designs.