Feedback Linearization-Based Guidance with Zero-Dynamics Correction for Guaranteed Interception

Alexander Dorsey; Ankit Goel

arxiv: 2605.03167 · v1 · submitted 2026-05-04 · 📡 eess.SY · cs.SY

Feedback Linearization-Based Guidance with Zero-Dynamics Correction for Guaranteed Interception

Alexander Dorsey , Ankit Goel This is my paper

Pith reviewed 2026-05-08 17:14 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords guidance lawfeedback linearizationzero dynamicsline of sightinterceptionproportional navigationmissile guidance

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The pith

A correction to feedback linearization guidance ensures line-of-sight alignment produces a closing trajectory for interception.

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

This paper develops a guidance law for pursuer-evader interception using input-output feedback linearization to regulate line-of-sight angular rates. The baseline law can achieve alignment without closing the distance because the internal zero dynamics remain uncontrolled. Adding a correction term enforces negative range rate whenever those rates reach zero, so alignment now implies interception. The resulting law stays computationally simple and works for a broad class of initial geometries under point-mass dynamics. Monte Carlo simulations show it improves reliability and reduces miss distance compared with the uncorrected version and classical proportional navigation.

Core claim

The central claim is that a modified input-output feedback linearization law with an added zero-dynamics correction ensures LOS alignment corresponds to a closing trajectory, enabling convergence of the pursuer to the evader for a broad class of initial engagement geometries. This holds while preserving the real-time implementability of feedback linearization and without requiring knowledge of evader acceleration.

What carries the argument

The zero-dynamics correction term, which modifies the feedback-linearized control input to drive range closure when line-of-sight rates are regulated to zero.

If this is right

LOS alignment now directly implies interception rather than possible constant-distance parallel motion.
The law remains simple enough for real-time onboard computation.
Monte Carlo results show consistent convergence and smaller miss distances than baseline IOL or proportional navigation.
The method does not require evader acceleration information.

Where Pith is reading between the lines

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

The same correction idea could apply to other nonlinear output-regulation tasks where zero dynamics decide overall success.
Robustness tests with added disturbances such as drag or sensor noise would check whether the guarantee survives model mismatch.
Hardware trials on small UAVs could confirm whether the simulated performance carries over to real vehicles.

Load-bearing premise

The point-mass dynamics model plus the specific correction term derived from feedback linearization will produce stable range convergence without introducing instability for the tested initial conditions.

What would settle it

A trajectory starting from one of the claimed valid initial conditions in which line-of-sight rates reach zero yet range fails to decrease, producing a positive miss distance.

read the original abstract

This paper develops a guidance law for nonlinear interception using input-output feedback linearization (IOL). The engagement between a pursuer and an evader is modeled using point-mass dynamics, and a baseline IOL-based guidance law is constructed by regulating the angular rates of the line-of-sight (LOS) vector. While this approach yields stable input-output behavior, it does not constrain the internal (zero) dynamics of the system, which can result in non-intercepting trajectories despite successful regulation of the LOS rates. To address this limitation, a modified IOL-based guidance law is proposed that incorporates a correction mechanism to enforce convergence of the range. The resulting formulation ensures that LOS alignment corresponds to a closing trajectory, thereby enabling convergence of the pursuer to the evader for a broad class of initial engagement geometries. The proposed method retains the computational simplicity and real-time implementability of feedback linearization while improving closed-loop performance relative to classical guidance laws. Extensive Monte Carlo simulations over a wide range of initial conditions are conducted to evaluate the proposed method. The results demonstrate improved reliability, reduced miss distance, and consistent convergence compared to the baseline IOL and classical proportional navigation.

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.

Desk Editor's Note private letter to a colleague

They add a zero-dynamics correction to standard IOL guidance and show better Monte Carlo results than baseline or PN, but stability rests only on simulation.

read the letter

The main thing to know is that this paper takes the usual input-output linearization approach to missile guidance and adds a correction term so that driving LOS rates to zero actually produces a closing trajectory instead of letting the range dynamics wander off. They model the pursuer-evader engagement with point-mass dynamics, build the baseline IOL law on the LOS angular rates, then insert the correction to enforce range convergence. The Monte Carlo runs over a wide set of initial geometries show lower miss distances and higher intercept reliability than both the plain IOL version and classical proportional navigation, while keeping the same real-time computational cost. That is the concrete improvement they deliver. The correction itself is a targeted addition rather than a whole new framework, and it directly addresses the known internal-dynamics problem that appears in earlier IOL guidance work. The simulations are the part that works: they are extensive, cover many starting conditions, and give a practical sense that the fix helps in the tested cases. The soft spot is the lack of any analytical stability argument for the corrected zero dynamics. The claim that the method guarantees convergence for a broad class of geometries is supported only by the Monte Carlo envelope, with no Lyapunov function, invariant-set result, or closed-form range dynamics to back it up. This leaves the result dependent on the specific point-mass model and the initial conditions they happened to sample. If evader acceleration or model mismatch enters the picture, it is not clear whether the correction still keeps the system stable. This paper is for people who already work on nonlinear guidance laws or feedback linearization in aerospace applications. A reader looking for a practical tweak to existing IOL methods would get something usable from the simulations and the correction idea. It is worth sending to peer review because the problem it targets is real, the proposed fix is straightforward to implement, and the validation is honest about what it shows.

Referee Report

1 major / 2 minor

Summary. The manuscript develops an input-output feedback linearization (IOL) guidance law for nonlinear pursuer-evader interception modeled with point-mass dynamics. A baseline IOL law regulates LOS angular rates but leaves the zero dynamics unconstrained, which can produce non-intercepting trajectories. A correction term is introduced to enforce range closure whenever LOS rates are driven to zero, yielding the claim that LOS alignment implies a closing trajectory and thus interception for a broad class of initial geometries. The method is asserted to retain real-time implementability while outperforming both the baseline IOL and classical proportional navigation, with support provided exclusively by extensive Monte Carlo simulations over varied initial conditions.

Significance. If the zero-dynamics correction can be shown to guarantee asymptotic range convergence, the work would provide a systematic, computationally lightweight extension of feedback linearization to guidance problems that directly addresses a known internal-dynamics limitation. The Monte Carlo campaign over wide initial geometries supplies useful empirical evidence of improved miss-distance statistics and convergence reliability relative to the baselines.

major comments (1)

[Zero-dynamics correction derivation and stability discussion] The central claim that the correction 'ensures that LOS alignment corresponds to a closing trajectory' and enables guaranteed convergence (abstract and title) is load-bearing yet unsupported by analysis. No Lyapunov function, invariant-set argument, or explicit closed-form range dynamics under the corrected control law is derived to prove that r → 0 whenever the LOS rates are regulated to zero. All evidence is Monte Carlo only, leaving open the possibility that stability holds only inside the tested envelope or for the specific point-mass model without evader acceleration.

minor comments (2)

[Control law equations] Clarify the exact form of the correction term (including any dependence on estimated range or relative velocity) and confirm that it introduces no additional real-time computational burden beyond standard IOL.
[Simulation results section] The Monte Carlo results would benefit from explicit reporting of miss-distance statistics (mean, median, standard deviation) and failure-rate counts rather than qualitative statements of 'improved reliability'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The major comment raises a valid point about the need for analytical support beyond simulations, and we address it directly below while committing to a revision that strengthens the theoretical claims.

read point-by-point responses

Referee: [Zero-dynamics correction derivation and stability discussion] The central claim that the correction 'ensures that LOS alignment corresponds to a closing trajectory' and enables guaranteed convergence (abstract and title) is load-bearing yet unsupported by analysis. No Lyapunov function, invariant-set argument, or explicit closed-form range dynamics under the corrected control law is derived to prove that r → 0 whenever the LOS rates are regulated to zero. All evidence is Monte Carlo only, leaving open the possibility that stability holds only inside the tested envelope or for the specific point-mass model without evader acceleration.

Authors: We acknowledge that the manuscript's central claim relies on the design of the correction term (derived from the range-rate equation to drive range closure when LOS rates reach zero) but does not include a formal Lyapunov function, invariant-set argument, or explicit closed-form stability proof for asymptotic range convergence. The evidence presented is indeed limited to Monte Carlo simulations over a wide range of initial conditions. This is a substantive gap. In the revision we will add a new subsection that (i) derives the closed-loop range dynamics under the corrected IOL law, (ii) constructs a Lyapunov function candidate for the range subsystem assuming perfect LOS-rate regulation, and (iii) states the precise assumptions (point-mass kinematics, perfect information, and the tested class of initial geometries). We will also temper the language in the abstract and title from 'guaranteed' to 'ensured under the stated assumptions and validated by extensive simulation,' while retaining the empirical comparison to baseline IOL and PN. These changes will be made without altering the core algorithmic contribution or real-time implementability. revision: yes

Circularity Check

0 steps flagged

No circularity detected; derivation is constructive design from standard IOL

full rationale

The paper applies input-output feedback linearization to point-mass engagement dynamics to regulate LOS angular rates, then introduces an explicit correction term whose purpose is to enforce range closure in the zero dynamics. This is a direct, constructive modification rather than a self-referential loop. No parameters are fitted to a data subset and then re-predicted, no load-bearing self-citations appear in the abstract or description, and the central claim (that the corrected law produces closing trajectories) follows from the stated design objective and is evaluated via Monte Carlo rather than by re-deriving the inputs. The chain is therefore self-contained against external benchmarks and does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the standard point-mass engagement model and the assumption that the derived correction term produces the desired internal dynamics without further tuning.

axioms (1)

domain assumption Point-mass dynamics accurately capture pursuer and evader motion
Invoked to model the engagement; standard but excludes aerodynamic or actuator effects.

pith-pipeline@v0.9.0 · 5500 in / 1123 out tokens · 26195 ms · 2026-05-08T17:14:34.294117+00:00 · methodology

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Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

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Zarchan, P., Tactical and strategic missile guidance, American Institute of Aeronautics and Astronautics, Inc. , 2012

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Optimal inter cept missile guidance strategies with autopilot lag,

Chen, R. H., Speyer, J. L., and Lianos, D., “Optimal inter cept missile guidance strategies with autopilot lag,” Journal of guidance, control, and dynamics , Vol. 33, No. 4, 2010, pp. 1264–1272

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Augmented po lynomial guidance with terminal speed constraints for unpo wered aerial vehicles,

Tahk, M.-J., Moon, G.-H., and Shim, S.-W., “Augmented po lynomial guidance with terminal speed constraints for unpo wered aerial vehicles,” International Journal of Aeronautical and Space Sciences , Vol. 20, 2019, pp. 183–194

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Alkaher, D., Moshaiov, A., and Or, Y ., “Guidance laws bas ed on optimal feedback linearization pseudocontrol with ti me-to-go estimation,” Journal of Guidance, Control, and Dynamics , Vol. 37, No. 4, 2014, pp. 1298–1305

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Portella Delgado, J. M., and Goel, A., “Circumventing un stable zero dynamics in input-output linearization of long itudinal ﬂight dynamics,” AIAA SCITECH 2024 Forum, 2024, p. 0321

work page 2024

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Adaptive Nonlinear Cont rol of a Bicopter with Unknown Dynamics,

Delgado, J. M. P., and Goel, A., “Adaptive Nonlinear Cont rol of a Bicopter with Unknown Dynamics,” 2024 American Control Conference (ACC), IEEE, 2024, pp. 3867–3872

work page 2024

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T., and Girard, A

Kabamba, P. T., and Girard, A. R., Fundamentals of Aerospace navigation and guidance, Cambridge University Press, 2014

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Feedback Linearization-bas ed Guidance Law for Guaranteed Interception,

Dorsey, A., and Goel, A., “Feedback Linearization-bas ed Guidance Law for Guaranteed Interception,” , 2025. URL https://arxiv.org/abs/2509.07843

work page arXiv 2025

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Minimum Time-of-Fl ight Interceptor Guidance Using Real-Time-Implementable Model- Predictive Guidance,

Islam, S. A. U., and Bernstein, D., “Minimum Time-of-Fl ight Interceptor Guidance Using Real-Time-Implementable Model- Predictive Guidance,” AIAA SCITECH 2022 Forum, 2022, p. 1377

work page 2022

[12] [12]

Circumventing Unstabl e Zero Dynamics in Input-Output Linearization of Longitudinal Flight Dynamics,

Delgado, J. M. P., and Goel, A., “Circumventing Unstabl e Zero Dynamics in Input-Output Linearization of Longitudinal Flight Dynamics,” Aerospace Research Central, 2023. URL https://arxiv.org/abs/2205.06192

work page arXiv 2023

[13] [13]

Cooperative G uidance Law for High-Speed and High- Maneuverability Air Targets,

Cevher, F. Y ., and Leblebicioğlu, M. K., “Cooperative G uidance Law for High-Speed and High- Maneuverability Air Targets,” Aerospace, Vol. 10, No. 2, 2023. https://doi.org/10.3390/aerospace10020155, URL https://www.mdpi.com/2226-4310/10/2/155

work page doi:10.3390/aerospace10020155 2023

[14] [14]

Mode rn Homing Missile Guidance The- ory and Techniques,

Palumbo, N. F., Blauwkamp, R. A., and Lloyd, J. M., “Mode rn Homing Missile Guidance The- ory and Techniques,” Johns Hopkins APL Technical Digest , Vol. 29, No. 1, 2010. URL https://secwww.jhuapl.edu/techdigest/Home/Detail?Journal=J&VolumeID=29&IssueID=1. 14

work page 2010