Predicate-Derived Residual Control

• Predicate-Derived Residual Control is a hybrid design that augments a nominal controller with bounded residual corrections activated and filtered by explicit predicates.
• It employs diverse predicate types—logical, geometric, variational—to filter candidate corrections, ensuring targeted improvement while preserving fallback safety.
• Empirical studies reveal significant gains in metrics like path tracking with trade-offs in other measures, underscoring auditable performance improvements and limitations.

Searching arXiv for the main paper and closely related residual-control formulations. Attempting arXiv lookup for specific IDs and keyword matches. Predicate-Derived Residual Control denotes a family of hybrid designs in which a nominal controller, planner, optimizer, or surrogate remains in place, while a residual correction is selected, activated, filtered, or regularized by predicates. In the fixed-wing UAV formulation that states the concept explicitly, a learned supervisor is placed above an unchanged actuator-facing autopilot; it selects bounded residuals on commanded airspeed, altitude, and heading, projects the modified references into an admissible envelope, ranks candidates by a no-op-relative Hamiltonian advantage, and filters them through control-Lyapunov- and control-barrier-inspired predicates with a guaranteed no-op fallback (Iscan et al., 31 May 2026). Closely related formulations derive residual behavior from inverse symbolic predicates in manipulation (Yildirim et al., 3 Jun 2026), relative safety predicates in mechatronic residual reinforcement learning (Staessens et al., 2021), decision-tree predicates in residual MPC (Zhao et al., 2023), variational test predicates in parametric PDE regression (Bachmayr et al., 2024), and projected-pressure feasibility predicates in stochastic constrained optimization (Liu et al., 5 Jun 2026).

1. Conceptual scope and recurring structure

Across the cited formulations, residual control is not a replacement of the nominal mechanism but an augmentation of it. The residual may act on command references, actuator inputs, symbolic inverse objectives, prediction models, loss functionals, or multiplier memories. The “predicate-derived” qualifier indicates that admissibility or prioritization is not left to an unconstrained learned score alone: it is shaped by explicit logical, geometric, variational, or inequality-derived conditions.

Taken together, the literature represented here suggests several recurrent predicate sources. Runtime inequality predicates appear as CLF/CBF-style gates and admissibility rules in UAV command supervision. Symbolic predicates appear as STRIPS-like operator effects and inverse restoration targets in inverse manipulation. Learned mode predicates appear through IOHMM hidden-state specialization in process control. Decision-tree predicates appear as random-forest splits that switch local residual models in autonomous driving. Variational predicates appear as test spaces and test norms whose induced dual norms certify error in parametric PDE surrogates. Constraint predicates appear as projected-pressure maps in stochastic constrained decision-making (Iscan et al., 31 May 2026).

Representative setting	Residual object	Predicate source
Fixed-wing UAV supervision (Iscan et al., 31 May 2026)	Command-reference residual on $r=[V_{a,c},h_c,\psi_c]$	CLF/CBF-inspired runtime predicates and admissibility rules
Inverse manipulation (Yildirim et al., 3 Jun 2026)	Residual inverse skill after symbolic prefix	Unresolved symbolic predicates from $I(o)=Pre\cup Del\cup \neg Add$
Autonomous driving MPC (Zhao et al., 2023)	Residual model added to nominal prediction	Random-forest decision predicates over non-control features
Parametric PDE regression (Bachmayr et al., 2024)	Residual loss controlling surrogate accuracy	Variational test spaces and norms
Stochastic constrained optimization (Liu et al., 5 Jun 2026)	Pressure-memory residual for multiplier tracking	Projected inequality predicates $c(x)\le 0$

This structure makes the residual auditable in a way that direct black-box replacement often is not. In the UAV setting, the supervisor adjusts only commanded references and leaves the autopilot to generate elevator, aileron, rudder, and throttle commands. In CRRL, the residual is constrained relative to the base controller’s output. In inverse manipulation, the residual policy is invoked only after a symbolic planner has satisfied as much of the inverse objective as possible (Iscan et al., 31 May 2026).

2. Fixed-wing UAV command supervision as a canonical instantiation

The most explicit control-theoretic instantiation appears in “Autopilot-Preserving Residual Q-Learning with HJB-Inspired Finite-Action Risk Filtering for Fixed-Wing UAV Command Supervision” (Iscan et al., 31 May 2026). The plant is a 12-state nonlinear rigid body with wind-relative aerodynamics and actuator dynamics,

$$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$

The learned supervisor acts only on the command vector $r=[V_{a,c},h_c,\psi_c]$ through a finite residual action set

$$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$

with examples $a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$, $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$, and $a_{\psi+}\mapsto [0,0,+3^\circ]$. The modified command is projected before it reaches the autopilot: $$\tilde r_k=\Pi_{\mathcal C}\big(r_k+\Delta r(a_k)\big),\quad \mathcal C=[20,140]~\mathrm{m/s}\times[0,450]~\mathrm{m}\times[-180^\circ,180^\circ).$$ The no-op action $I(o)=Pre\cup Del\cup \neg Add$0 has $I(o)=Pre\cup Del\cup \neg Add$1 and is always available.

The architectural point is that the autopilot remains unchanged and actuator-facing. Representative loops include a heading-to-roll and roll PID, a pitch PID, and throttle airspeed regulation in altitude-hold, all with saturation; a longitudinal state machine selects takeoff, climb, descend, and altitude-hold modes; actuators are clipped, rate-limited, and lagged (Iscan et al., 31 May 2026). This preserves the nominal low-level handling of saturation and rate limits while permitting high-level adaptation under wind, gusts, and turbulence.

Residual choice is prioritized by an HJB-inspired critic. The feature vector is

$I(o)=Pre\cup Del\cup \neg Add$2

and the value proxy blends a quadratic term with a small-grid value iteration: $I(o)=Pre\cup Del\cup \neg Add$3 with $I(o)=Pre\cup Del\cup \neg Add$4, $I(o)=Pre\cup Del\cup \neg Add$5 diagonal, and $I(o)=Pre\cup Del\cup \neg Add$6 mapping to a grid with 1296 cells. Candidates are ranked by the no-op-relative Hamiltonian advantage

$I(o)=Pre\cup Del\cup \neg Add$7

so that negative $I(o)=Pre\cup Del\cup \neg Add$8 indicates improvement over the no-op under the critic (Iscan et al., 31 May 2026).

Predicate-derived filtering is then applied through a finite-action shield. The hard block disallows heading residuals under large reference error and disturbance: $I(o)=Pre\cup Del\cup \neg Add$9 A CLF-style gate limits value growth,

$c(x)\le 0$0

and a CBF-style gate restricts altitude-increase or high-risk actions through $c(x)\le 0$1. The filtered set is

$c(x)\le 0$2

which guarantees the no-op fallback (Iscan et al., 31 May 2026).

The per-step flow is correspondingly explicit: compute tracking and risk features; delegate to tabular Q under specified severe-disturbance conditions; build $c(x)\le 0$3; evaluate $c(x)\le 0$4, $c(x)\le 0$5, $c(x)\le 0$6, and $c(x)\le 0$7; apply CLF/CBF gates; select $c(x)\le 0$8; project the command; run actuator and plant update; compute reward and update the Q-table. The autopilot sample time is $c(x)\le 0$9 s, the plant is integrated by RK4 with five substeps, $$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$0, candidate evaluation per step is $$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$1, and the value-iteration grid is cached at runtime (Iscan et al., 31 May 2026).

Empirically, in a shared 12-state runtime over 20 scenarios, mean RMS path-tracking error was 338.617 m for the baseline autopilot, 88.809 m for tabular-Q residual, and 44.809 m for HJB residual, corresponding to reductions of 86.77% versus baseline and 49.54% versus Q-learning. Altitude RMS was 114.137 m, 65.819 m, and 64.710 m; airspeed RMS was 10.546 m/s, 15.086 m/s, and 15.191 m/s; control-activity index was 5.665, 6.524, and 6.346; safety-violation fraction was 0.004802, 0.003090, and 0.003332; and max $$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$2 was 7.414, 6.844, and 6.800. The baseline won every scenario on airspeed RMS, while the HJB residual won 15 scenarios on path RMS and 18 on altitude RMS, so no method dominated every metric (Iscan et al., 31 May 2026).

3. Predicate construction across control, planning, and modeling

Beyond UAV command supervision, the same design logic recurs with different predicate semantics. In inverse manipulation, operators extracted from demonstrations have the STRIPS-like form $$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$3, and the inverse target is

$$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$4

After a BFS-based symbolic planner executes a prefix $$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$5, predicates with $$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$6 become fences and unresolved predicates become the active set for residual RL. The reward

$$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$7

therefore drives only the unresolved inverse predicates while penalizing violations of the already restored ones. On ManiSkill3 PushCube, the symbolic prefix uses scripted pick and place to satisfy three of four inverse predicates, and a residual SAC policy refines the remaining $$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$8 predicate (Yildirim et al., 3 Jun 2026).

In process control, the specialized deep residual policy controller uses an IOHMM-derived gating variable. The hybrid law is

$$x=\begin{bmatrix} p_n & p_e & p_d & u & v & w & \phi & \theta & \psi & p & q & r \end{bmatrix}^\top, \quad h=-p_d.$$9

where $r=[V_{a,c},h_c,\psi_c]$0 when the most probable IOHMM hidden state is the abnormal state $r=[V_{a,c},h_c,\psi_c]$1, and $r=[V_{a,c},h_c,\psi_c]$2 otherwise. The method combines TD3 with behavioral cloning through a Cycle of Learning, trains only on relevant abnormal data, and uses mixed replay $r=[V_{a,c},h_c,\psi_c]$3. In the Tennessee Eastman process, the paper reports that architectures with specialization outperform those without and that CoL-SDRPRL performs best in the MISO disturbance setting (Abbas et al., 2023).

In autonomous driving, predicates are implemented by decision-tree splits. The residual model is decomposed as

$r=[V_{a,c},h_c,\psi_c]$4

where $r=[V_{a,c},h_c,\psi_c]$5 is the nonlinear, nonconvex, nondifferentiable tree-routing map on non-control features and $r=[V_{a,c},h_c,\psi_c]$6 is a leaf-wise linear regression on control variables. The resulting switched linear residual augments a nominal linear dynamic bicycle model while preserving a QP formulation for MPC. The random forest therefore acts as an interpretable predicate layer that selects the local residual model (Zhao et al., 2023).

A different precursor appears in residual reinforcement learning for robot control, where the basic superposition law is

$r=[V_{a,c},h_c,\psi_c]$7

That work does not use explicit predicates, but it provides the control decomposition later elaborated by predicate-gated variants. In the block assembly task, the baseline handles geometric motion while the residual addresses contacts, friction, and unstable objects (Johannink et al., 2018). This suggests a lineage in which predicate-derived mechanisms narrow when and how the residual is permitted to act.

4. Safety, stability, and certifiable residuals

A central theme in predicate-derived residual control is that residual freedom is deliberately bounded. In the UAV formulation, exploration risk is reduced because learning is confined to command references rather than actuator torques, command projection $r=[V_{a,c},h_c,\psi_c]$8 enforces admissible speed, altitude, and heading bounds, CLF/CBF-inspired runtime predicates block risky choices, and the finite-action shield always retains the no-op fallback (Iscan et al., 31 May 2026). The paper is explicit, however, that these are structural assurances rather than formal certificates: it provides bounded commands, no-op fallback, and finite per-step evaluation, but “no formal safety/stability certificates.”

For mechatronic systems, constrained residual reinforcement learning pushes the stability analysis further. Absolute residual control uses

$r=[V_{a,c},h_c,\psi_c]$9

whereas relative residual control uses

$$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$0

The paper proves Lyapunov-based stability results for a broad class of mechanical systems and derives parameter inequalities for $$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$1, $$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$2, $$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$3, and $$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$4 or $$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$5. In the relative case, the admissible residual is proportional to the base controller output, which keeps exploration inside a tube around the nominal action and leverages the base controller’s robustness (Staessens et al., 2021).

In risk-sensitive safety, a related direction uses Discrete-Time Control Barrier Functions with a learned generative disturbance model. The Online Risk-Informed Optimization controller combines DT-CBFs with a CVAE disturbance model and, according to the abstract, can be run at 100Hz on an embedded computer while exhibiting less conservative behavior and retaining theoretical safety properties (Cosner et al., 2023). Although the detailed equations are unavailable in the supplied source material, the alignment with predicate-derived residual control is direct: a safety predicate defines the admissible set, and a learned residual distribution determines the risk margin.

In parametric PDE regression, the predicate is variational rather than logical. For each parameter $$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$6, the residual $$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$7 induces the pointwise loss

$$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$8

Under uniform continuity and inf-sup bounds,

$$\mathcal A_r=\{a_0,a_{V+},a_{V-},a_{h+},a_{h-},a_{\psi+},a_{\psi-}\},$$9

The residual loss is therefore “variationally correct”: its value is uniformly proportional to the squared solution error in the SVF-induced norm. In ultraweak SVFs with optimal test norms, the summary states that $a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$0, which gives perfect conditioning (Bachmayr et al., 2024).

In stochastic constrained decision-making, RCML defines projected pressure and a pressure-memory residual,

$a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$1

This residual has an exact feasibility-complementarity interpretation: $a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$2 The multiplier memory is then updated as a finite-gain tracker of current projected pressure rather than as an accumulator of raw mini-batch violations (Liu et al., 5 Jun 2026).

5. Empirical behavior and characteristic trade-offs

The empirical record across domains is notably consistent on one point: predicate-derived residuals often improve the targeted quantity, but the gain is usually localized and comes with a trade-off. In the UAV study, long-horizon path tracking and altitude RMS improved substantially, yet airspeed RMS increased from 10.546 m/s for the baseline to 15.191 m/s for the HJB residual, and the baseline won every scenario on airspeed RMS (Iscan et al., 31 May 2026). In the short-horizon 8 s sweep, baseline path RMS was 0.866 m, compared with 1.174 m for HJB and 1.183 m for Q; predicate-derived supervision was advantageous mainly in the more difficult long-duration disturbance cases.

In inverse manipulation, the symbolic prefix alone leaves a measurable continuous gap. With $a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$3 cm handoff perturbation over 10 seeds, the symbolic prefix without RL yielded $a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$4 mm mean pose error and 10% success at 1 cm, symbolic plus random action yielded $a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$5 mm and 50% success, and symbolic plus RL yielded $a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$6 mm and 90% success. Ablations showed that fences with two-sided $a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$7 dropped success to 10%, while removing $a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$8 altogether gave 0% success and value-function divergence (Yildirim et al., 3 Jun 2026).

In the Tennessee Eastman process, the hybrid residual design produced “autonomous synchronization” in SISO disturbance rejection and early activation in the MISO setting. At 65% and 70% disturbances, average episode reward after 150 episodes was $a_{V+}\mapsto [+2\,\mathrm{m/s},0,0]$9 and $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$0 for PID, $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$1 and $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$2 for CoL, and $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$3 and $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$4 for CoL+DRPRL. In the MISO disturbance-65% comparison, CoL-SDRPRL was reported around $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$5, outperforming PID around $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$6 and substantially outperforming TD3 alone around $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$7 (Abbas et al., 2023).

In contact-rich robot assembly, residual RL improved robustness to environment variation. With aligned blocks, both the hand-engineered controller and residual RL achieved 20/20 success. With misaligned blocks, the hand-engineered controller achieved 2/20 while residual RL achieved 15/20. The real-world task was learned in under 3 hours, approximately 8000 samples, and the sim-to-real variant solved the task in under one thousand timesteps of real-world interaction (Johannink et al., 2018).

In autonomous driving, the random-forest-switched residual MPC reduced lateral tracking MAE from 0.0206 for nominal MPC to 0.0172 for MPC+RFL, while mean computation time was 0.695 s versus 15.434 s for NMPC+GP in the reported simulation. Residual-fitting test RMSE improved from 1.48‰ for RF to 0.1477‰ for RFL, and test ME improved from 2.81 cm to 0.32 cm (Zhao et al., 2023).

In hybrid PINN training, the benefit of predicate targeting is even more literal. In the 3D annular heat-conduction benchmark, a body-fitted shell near the wavy outer wall served as the predicate region. Across seeds 0–5 and 100k epochs under the Kourkoutas-beta optimizer regime, a fixed shell weight of $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$8 reduced mean outer-wall BC RMSE from $a_{h+}\mapsto [0,+10\,\mathrm{m},0]$9 to $a_{\psi+}\mapsto [0,0,+3^\circ]$0 and mean wall-flux RMSE from $a_{\psi+}\mapsto [0,0,+3^\circ]$1 to $a_{\psi+}\mapsto [0,0,+3^\circ]$2 relative to a matched run without the shell term (Kassinos, 15 Apr 2026).

RCML exhibits the same pattern on constrained optimization tasks. On a convex QP, DualTV dropped from approximately $a_{\psi+}\mapsto [0,0,+3^\circ]$3 for Projected-ALM to approximately $a_{\psi+}\mapsto [0,0,+3^\circ]$4 for Residual-I, while ViolTail improved from $a_{\psi+}\mapsto [0,0,+3^\circ]$5 to $a_{\psi+}\mapsto [0,0,+3^\circ]$6. In neural fair ranking, RCML-Robust satisfied the fairness tolerance with soft gap approximately $a_{\psi+}\mapsto [0,0,+3^\circ]$7, achieved the highest feasible NDCG@10 approximately $a_{\psi+}\mapsto [0,0,+3^\circ]$8, and kept the dual state markedly smaller than Projected-ALM, approximately $a_{\psi+}\mapsto [0,0,+3^\circ]$9 versus $$\tilde r_k=\Pi_{\mathcal C}\big(r_k+\Delta r(a_k)\big),\quad \mathcal C=[20,140]~\mathrm{m/s}\times[0,450]~\mathrm{m}\times[-180^\circ,180^\circ).$$0 (Liu et al., 5 Jun 2026).

6. Limitations, misconceptions, and open directions

A recurring misconception is that residual control simply means learned actuation layered over a nominal controller. The surveyed formulations are more restrictive. In the UAV design, the autopilot remains the only actuator-facing controller and the supervisor adjusts only the commanded references. In inverse manipulation, the residual does not superpose on the symbolic prefix; it takes control after the symbolic plan reaches a valid handoff. In CRRL, relative residuals are explicitly constrained by the base controller magnitude (Iscan et al., 31 May 2026).

A second misconception is that predicates automatically imply hard formal guarantees. Several papers explicitly deny that implication. The UAV method reports “no formal safety/stability certificates,” and its filters and critics are heuristic over normalized features. The Tennessee Eastman residual controller reports no formal stability guarantees. The autonomous-driving residual MPC does not provide explicit uncertainty quantification or formal stability proofs. Even when theoretical guarantees exist, they are conditional: RCML’s finite-gain convergence is established for the convex-affine backbone, while its nonconvex result is a local KKT-residual interpretation near regular KKT points (Iscan et al., 31 May 2026).

Predicate engineering itself is a limitation. In inverse manipulation, predicates, margins, temperatures, and scales are hand-designed, and the framework depends on scripted low-level action primitives. In residual MPC for autonomous driving, poor linear fitting on some leaves can degrade local accuracy. In PINN shell regularization, misaligned predicates can improve residual smoothness without improving the quantity of interest, and large auxiliary weights can hurt field accuracy (Yildirim et al., 3 Jun 2026).

The evidence base is also uneven. The UAV benchmark is simulation-based and uses one seed per scenario in the primary benchmark; hardware-in-the-loop and flight tests remain to be done. The PushCube validation is on one task family. The autonomous-driving results are reported in joint simulation rather than on a real vehicle. Optimizer sensitivity is substantial in the PINN shell study, where Adam with the default learning-rate regime is unreliable and Kourkoutas remains the recommended regime (Iscan et al., 31 May 2026).

The future directions reported by the papers follow naturally from these limits. For UAV command supervision, proposed extensions include continuous residuals with projection-based safety filters and learned barrier functions, adaptive envelopes and disturbance-aware gains, integration with MPC or certified CBF-QP at the command layer, and multi-seed full-duration hardware validation. For inverse manipulation, the stated next steps are learned predicates and parameters from demonstrations, replacement of scripted primitives with learned movement primitives, and expansion to more tasks and richer operator sets. For residual MPC, suggested extensions include online adaptation, uncertainty-aware predicates, and hybrid terminal ingredients. For variationally correct residual regression, higher-order SVFs, adaptive meshes and test-search spaces, and nonlinear PDE extensions are identified as natural next steps (Iscan et al., 31 May 2026).

The concept therefore occupies a specific methodological niche. Predicate-Derived Residual Control preserves a nominal structure, introduces a residual only where that structure is insufficient, and uses predicates to determine when the residual is admissible, useful, or certifiable. The practical effect, across the surveyed works, is not universal improvement but targeted improvement with auditable trade-offs: better long-horizon path tracking at the cost of airspeed error, more accurate inverse restoration after symbolic planning, safer adaptive correction around a base controller, regime-switched residual prediction in MPC, residual-loss control aligned with variational error, and finite-gain multiplier stabilization under stochastic feedback (Liu et al., 5 Jun 2026).