Adaptive Constant-Force Trim Channel

1. Integration point: insert a low-dimensional trim head between a neural dynamics predictor and its MPC or model-based RL interface. Select $G$ from physically plausible persistent channels, such as vertical acceleration, horizontal force, or actuator torque offsets. Initially use a fixed selector and do not backpropagate through the trim estimator. 2. Pseudocode: compute neural prediction $\tilde{x}_{k+1}=\hat{F}_{\theta}(x_k,u_k)$; calculate $e_k=x_{k+1}-\tilde{x}_{k+1}-Gb_{k-1}$; compute $K_k$, $b_k$, and $P_k$ using the displayed equations; return $\tilde{x}_{k+1}+Gb_k$ to the planner; optionally reset or inflate $P_k$ when a regime-change detector fires. Add a penalty $\gamma\|b_k\|^2$ only when large biases are physically implausible. 3. Computed from the mechanism: the force-balance structure, innovation, RLS gain, and covariance. Estimated empirically: $G$, initial $P_0$, forgetting factor $\lambda$, and whether the trim should be constant or input-dependent. 4. First cheap experiment: train a neural Pendulum or CartPole model, inject a constant unknown force, and abruptly change its value halfway through evaluation. Compare neural-only, neural-plus-trained-global-bias, and neural-plus-RLS-trim models on one-step prediction and 20-step open-loop rollout. The predicted signature is geometric post-switch innovation reduction with recovery time proportional to $N_{\mathrm{eff}}\approx1/(1-\lambda)$. Fit the decay curve and require its time constant to agree with the RLS prediction within 20 percent. Lower $\lambda$ should adapt faster but produce a measurable higher stationary variance; accept the method only if it reduces post-switch bias by at least 50 percent without increasing pre-switch prediction variance by more than 20 percent.