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arxiv: 2605.23354 · v1 · pith:WI3E77FFnew · submitted 2026-05-22 · 📡 eess.SY · cs.SY

Physics-informed sparse identification-based tube model predictive control for aerial vehicles

Tayyab Manzoor , Yasir Ali , Yuanqing Xia , Lijie You , Yan Wang This is my paper

Pith reviewed 2026-05-25 03:55 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords model predictive controlphysics-informed machine learningsparse identificationtube MPCquadrotorrobust controlaerial vehiclesadaptive tube
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The pith

A physics-informed sparse model supports adaptive-tube MPC that guarantees stability while reducing computation for aerial vehicles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a model predictive control framework for autonomous aerial vehicles that uses physics-informed machine learning to identify a sparse, control-affine dynamic model. The model embeds first-principles knowledge and learns residual uncertainties from data, then feeds into a robust MPC scheme that employs high-order Runge-Kutta discretization and adapts the tube radius online from the residual error. Theoretical results establish recursive feasibility and stability of the closed-loop system. Experiments on a quadrotor show the approach lowers computational load relative to nonlinear MPC and high-fidelity robust MPC while delivering better tracking and robustness than PID, nonlinear MPC, neural-network MPC, and fixed-tube robust MPC.

Core claim

The central claim is that a sparse control-affine model obtained via physics-informed machine learning, when placed inside a tube-based robust MPC with residual-error-driven tube adaptation and high-order Runge-Kutta integration, yields a control law that is both computationally lighter than full nonlinear or high-fidelity robust MPC and provably recursively feasible and stable under uncertainty.

What carries the argument

The PIML-derived sparse control-affine model whose residual error directly sets the time-varying tube radius inside a Runge-Kutta-discretized robust MPC.

If this is right

  • Recursive feasibility and asymptotic stability hold for the adaptive-tube closed loop.
  • Online computation is lower than that of nonlinear MPC or robust MPC built on a high-fidelity model.
  • Tracking error and robustness metrics exceed those of PID, nonlinear MPC, neural-network MPC, and fixed-tube robust MPC on the tested quadrotor.
  • The scheme remains suitable for resource-constrained aerial platforms because the sparse model keeps prediction cheap while the adaptive tube avoids excess conservatism.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Learning only the residual mismatch rather than the entire dynamics may keep the model interpretable and fast enough for real-time embedded use.
  • The same residual-driven tube adaptation could be tested on other partially known robotic platforms such as manipulators or ground vehicles.
  • If the adaptation rule proves reliable across wider uncertainty classes, designers may be able to drop fixed conservative tubes in many robust MPC applications.

Load-bearing premise

The residual error learned by the PIML model can be used directly to adapt the tube radius in a way that guarantees constraint satisfaction and recursive feasibility without introducing excessive conservatism.

What would settle it

A closed-loop quadrotor experiment in which the proposed controller produces a state or input constraint violation under disturbances that the residual model was trained to capture would falsify the robustness guarantee.

Figures

Figures reproduced from arXiv: 2605.23354 by Lijie You, Tayyab Manzoor, Yan Wang, Yasir Ali, Yuanqing Xia.

Figure 1
Figure 1. Figure 1: Aerial vehicle’s inertial and body-fixed frame [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: PIML framework tions of ℓ-th column in Ψ(xˆ,uˆ) and weighted coefficient of δℓ(xˆ,uˆ) concerned with j-th state, i.e., Sj = [Sj0, Sj1, Sj2, . . . , Sjncf ] ⊤, respectively. Next, sparse optimization is used as follows: Sj = arg min Sj [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overall architecture of the control strategy (read with Algorithm [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Disturbance profile used in numerical results [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Trajectory tracking response for different types of trajectories [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Simulation to hardware deployment and hovering experiments [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Real-time indoor experiments related to state response [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Control input during hovering experiment [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
read the original abstract

Autonomous aerial vehicles necessitate control strategies that balance computational efficiency with robust performance in dynamic operational environments. This paper proposes a model predictive control (MPC) framework for aerial platforms that leverages physics-informed machine learning (PIML) to achieve an optimal balance between computational tractability and robust performance. At the core of the proposed approach lies a sparse, control-affine model identified via the PIML method, which provides a parsimonious yet interpretable representation of the system dynamics by embedding first-principles knowledge and learning residual uncertainties from operational data. This model is incorporated within a robust MPC scheme that adopts a high-order Runge-Kutta discretization to ensure prediction accuracy and an adaptive tube-based mechanism to guarantee constraint satisfaction under uncertainty. The online adaptation of the tube, directly informed by the residual error of the PIML model, ensures robust stability without introducing excessive conservatism. Rigorous theoretical proofs are provided to establish recursive feasibility and stability. Numerical simulations and experiments on a quadrotor demonstrate that our method significantly reduces computational load compared to nonlinear MPC and robust MPC using a high-fidelity model, while outperforming PID, nonlinear MPC, neural-network-based MPC, and fixed-tube robust MPC in tracking performance and robustness, showcasing the practical efficiency of the proposed PIML-based control synthesis for resource-constrained aerial systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a physics-informed machine learning (PIML) method to identify a sparse control-affine dynamic model for aerial vehicles by embedding first-principles knowledge and learning residuals from data. This model is embedded in a tube MPC controller that uses high-order Runge-Kutta discretization and adapts the tube radius online from the PIML residual error, with claimed proofs of recursive feasibility and stability. Numerical simulations and quadrotor experiments are reported to show lower computational load than nonlinear or high-fidelity robust MPC and better tracking/robustness than PID, nonlinear MPC, neural-network MPC, and fixed-tube robust MPC.

Significance. If the adaptive-tube construction from the learned residual supplies a rigorously bounded uncertainty set that preserves recursive feasibility under discretization, the method would combine the parsimony of sparse models with reduced conservatism relative to fixed-tube or high-fidelity robust MPC, offering a practical route to robust control on resource-constrained aerial platforms.

major comments (2)
  1. [§4] §4 (Recursive feasibility and stability proofs): the central claim that the online tube adaptation from the PIML residual guarantees constraint satisfaction and recursive feasibility requires an explicit set-valued bound on the residual (including its propagation through the high-order Runge-Kutta scheme) rather than a pointwise error; without this, the invariant-tube property used in the proof is not secured.
  2. [§3.2] §3.2 (Tube adaptation law) and Eq. (tube radius update): the adaptation rule is stated to be “directly informed by the residual error,” but no Lipschitz or interval bound is supplied to ensure the adapted tube remains a robust positively invariant set when the identified model is control-affine and the discretization error is present; this is load-bearing for the stability theorem.
minor comments (2)
  1. Notation for the PIML residual and the tube radius should be unified across the model-identification and control sections to avoid ambiguity in the feasibility argument.
  2. The experimental section would benefit from reporting the actual CPU times and constraint-violation statistics (not only qualitative outperformance) to substantiate the computational-load claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have identified important aspects where the theoretical analysis can be strengthened. We address each major comment below.

read point-by-point responses

  1. Referee: [§4] §4 (Recursive feasibility and stability proofs): the central claim that the online tube adaptation from the PIML residual guarantees constraint satisfaction and recursive feasibility requires an explicit set-valued bound on the residual (including its propagation through the high-order Runge-Kutta scheme) rather than a pointwise error; without this, the invariant-tube property used in the proof is not secured.

    Authors: We acknowledge that the proof requires an explicit set-valued bound on the residual (including propagation through the Runge-Kutta scheme) to rigorously establish the invariant-tube property. The original manuscript relies on the online adaptation from the pointwise PIML residual, but we agree this is insufficient without the set-valued characterization. In the revision we will derive and insert the required bound in Section 4, using Lipschitz constants of the control-affine dynamics and interval estimates for the discretization error. revision: yes

  2. Referee: [§3.2] §3.2 (Tube adaptation law) and Eq. (tube radius update): the adaptation rule is stated to be “directly informed by the residual error,” but no Lipschitz or interval bound is supplied to ensure the adapted tube remains a robust positively invariant set when the identified model is control-affine and the discretization error is present; this is load-bearing for the stability theorem.

    Authors: We agree that a Lipschitz or interval bound on the residual is needed to guarantee that the adapted tube remains a robust positively invariant set. The manuscript states the adaptation is informed by the residual but does not supply the supporting bound. We will revise Section 3.2 to include the necessary Lipschitz/interval analysis for the control-affine model and discretization, thereby securing the invariance property used in the stability theorem. revision: yes

Circularity Check

0 steps flagged

No circularity: model from data, MPC with proofs, validated externally

full rationale

The derivation begins with PIML-based sparse identification of a control-affine model from operational data, followed by incorporation into an adaptive-tube MPC scheme whose radius update uses the learned residual. Recursive feasibility and stability are asserted via provided theoretical proofs rather than by redefinition or fitting. Performance claims rest on numerical simulations and quadrotor experiments against external baselines (PID, NMPC, NN-MPC, fixed-tube RMPC), not on any internal renaming or self-referential prediction. No self-citations, ansatzes smuggled via prior work, or fitted inputs relabeled as predictions appear in the supplied text; the chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach depends on the assumption that system dynamics admit a sparse control-affine representation with learnable residuals, plus standard robust MPC assumptions on bounded uncertainty; no new physical entities are introduced.

free parameters (1)
  • PIML model coefficients
    Learned from operational flight data to capture residual dynamics
axioms (1)
  • domain assumption Aerial vehicle dynamics admit a sparse control-affine form with additive residual uncertainties that can be identified from data
    This underpins the PIML sparse identification step

pith-pipeline@v0.9.0 · 5772 in / 1322 out tokens · 29393 ms · 2026-05-25T03:55:12.315087+00:00 · methodology

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Reference graph

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