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arxiv: 2604.26682 · v1 · submitted 2026-04-29 · 📡 eess.SY · cs.SY· math.OC

Model-Free Dynamic Mode Adaptive Control for Data-Driven Control Synthesis

Parham Oveissi , Ankit Goel This is my paper

Pith reviewed 2026-05-07 11:46 UTC · model grok-4.3

classification 📡 eess.SY cs.SYmath.OC
keywords model-free controldata-driven controladaptive controlrecursive least squaresdynamic mode approximationstabilizing controlonline identification
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The pith

A model-free controller called DMAC approximates local linear dynamics from data and synthesizes a stabilizing feedback law online.

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

This paper proposes dynamic mode adaptive control (DMAC) as a way to design controllers for systems where no mathematical model is available or reliable. The method uses measured data to recursively estimate a local linear approximation of the dynamics and then computes a full-state feedback controller with integral action. Theoretical results establish that the dynamics estimate converges and the closed-loop system remains bounded. Demonstrations on an unstable linear system, the Van der Pol oscillator, and Burgers' equation illustrate its use, with sensitivity analysis showing robustness to parameter variations. If successful, this would allow control design directly from experiments without prior modeling effort.

Core claim

DMAC consists of a dynamics-approximation module that estimates local linear representations using matrix recursive least-squares with a forgetting factor, and a controller-synthesis module that computes an online stabilizing controller. The approach establishes convergence of the recursive approximation and boundedness of the closed-loop system under the DMAC controller.

What carries the argument

The matrix recursive least-squares algorithm with forgetting factor that estimates the local linear dynamics from measurements, which then feeds into the stabilizing controller design.

If this is right

  • The method works for representative systems including unstable linear dynamics, nonlinear oscillators, and fluid models like Burgers' equation.
  • Robustness holds with respect to algorithm hyperparameters and variations in system parameters.
  • The controller provides stabilization using full state feedback and integral action based on the data-driven estimate.

Where Pith is reading between the lines

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

  • DMAC may enable real-time adaptation in environments where system parameters drift over time due to the forgetting factor in the estimator.
  • Similar data-driven approaches could be extended to output-feedback cases when full states are not measurable.
  • Applications in robotics or chemical process control could benefit from reduced reliance on first-principles models.

Load-bearing premise

The system dynamics can be adequately represented by a local linear model estimated from data, with full state measurements available for feedback.

What would settle it

Observing unbounded growth in the system states under the DMAC controller in a scenario where the data is sufficient to estimate the dynamics would falsify the boundedness guarantee.

read the original abstract

This paper presents a model-free, data-driven control synthesis method called dynamic mode adaptive control (DMAC) for systems whose mathematical models are unavailable or unsuitable for classical control design. The proposed approach combines data-driven dynamics approximation with adaptive control synthesis to enable online controller design using measured system data. DMAC comprises two main components: a dynamics-approximation module and a controller-synthesis module. The dynamics approximation module estimates a local linear representation of the system dynamics directly from measurements using a matrix recursive least-squares algorithm with a forgetting factor. The estimated dynamics are then used to compute an online stabilizing controller with full-state feedback and integral action. Theoretical analysis establishes convergence properties of the recursive dynamics approximation and boundedness of the closed-loop system under the DMAC controller. The performance of the proposed method is demonstrated through numerical examples involving representative dynamical systems, including an unstable linear system, the Van der Pol oscillator, and the Burgers' equation. Sensitivity studies further demonstrate the robustness of DMAC with respect to both algorithm hyperparameters and variations in system parameters.

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 / 3 minor

Summary. The manuscript introduces Dynamic Mode Adaptive Control (DMAC), a model-free data-driven method that employs a matrix recursive least-squares estimator with forgetting factor to obtain local linear approximations of system dynamics directly from measurements. These estimates are used to synthesize an online stabilizing controller via full-state feedback augmented with integral action. Theoretical analysis is provided for convergence of the estimator and boundedness of the closed-loop trajectories. The approach is illustrated on an unstable linear system, the Van der Pol oscillator, and a discretized Burgers' equation, accompanied by sensitivity studies on hyperparameters and system parameters.

Significance. If the convergence and boundedness results hold, the work provides a useful addition to data-driven control by delivering an adaptive, online synthesis procedure with explicit stability guarantees that does not require an a priori model. The combination of RLS-with-forgetting and integral-action feedback is practically relevant for systems where dynamics are only partially known or slowly time-varying, and the numerical examples across linear and nonlinear cases support broader applicability.

major comments (2)
  1. [§4] §4, Theorem 1: The convergence proof for the matrix RLS estimator invokes a persistent-excitation condition on the regressor; however, the subsequent boundedness argument for the closed-loop system (Theorem 2) does not explicitly verify that the adaptive controller maintains this excitation once the loop is closed, which is load-bearing for the global stability claim.
  2. [§5.3] §5.3 (Burgers' equation example): The local-linear approximation is applied to a spatially discretized nonlinear PDE, yet the manuscript provides no quantitative bound on the approximation error induced by the spatial discretization or by the forgetting factor; this gap weakens the extension of the boundedness result from finite-dimensional ODEs to the reported PDE case.
minor comments (3)
  1. [§3.1] The notation for the estimated state matrix Â(k) and input matrix B̂(k) is introduced without an explicit statement of their dimensions relative to the original system order; adding this clarification in §3.1 would improve readability.
  2. [Figure 4] Figure 4 (sensitivity plots) uses different vertical scales across subplots without comment; uniform scaling or explicit mention of the plotted quantities would aid interpretation.
  3. [§3.2] The abstract states that 'full state measurements are available,' but the controller diagram in §3.2 does not label the measurement noise or sensor dynamics; a brief remark on this modeling choice would be helpful.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation and the detailed comments, which help clarify the scope and limitations of the stability results. We address each major comment below and will revise the manuscript to strengthen the presentation of the theoretical claims.

read point-by-point responses

  1. Referee: [§4] §4, Theorem 1: The convergence proof for the matrix RLS estimator invokes a persistent-excitation condition on the regressor; however, the subsequent boundedness argument for the closed-loop system (Theorem 2) does not explicitly verify that the adaptive controller maintains this excitation once the loop is closed, which is load-bearing for the global stability claim.

    Authors: We agree that the link between the PE condition in Theorem 1 and the closed-loop boundedness in Theorem 2 requires explicit attention. The current proof of Theorem 2 assumes that the regressor remains persistently exciting under the adaptive feedback law. In the revision we will insert a remark immediately after Theorem 2 that (i) recalls the role of the integral action in generating a non-zero reference-tracking error that sustains excitation and (ii) notes that the forgetting factor prevents the covariance matrix from collapsing, thereby preserving the PE property once the estimator has converged. We will also add a brief sentence in the statement of Theorem 2 making this standing assumption explicit. revision: yes

  2. Referee: [§5.3] §5.3 (Burgers' equation example): The local-linear approximation is applied to a spatially discretized nonlinear PDE, yet the manuscript provides no quantitative bound on the approximation error induced by the spatial discretization or by the forgetting factor; this gap weakens the extension of the boundedness result from finite-dimensional ODEs to the reported PDE case.

    Authors: We acknowledge that the Burgers' example is presented as a finite-dimensional discretization to which the ODE theory directly applies, without quantitative bounds on the discretization or forgetting-factor errors. In the revised manuscript we will add a short paragraph at the end of §5.3 that (i) states the spatial discretization error is controlled by the mesh size (with a reference to standard finite-difference convergence results) and (ii) reports additional numerical sensitivity plots showing that the closed-loop trajectories remain bounded for a range of forgetting factors. We will also insert a sentence clarifying that the boundedness guarantee is for the discretized system and that extension to the infinite-dimensional PDE remains an open question. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives its DMAC method from standard matrix RLS-with-forgetting-factor estimation of local linear dynamics directly from measurements, followed by separate online controller synthesis using full-state feedback plus integral action. Convergence of the estimator and closed-loop boundedness are established via independent theoretical analysis (not by re-using the estimator output as its own proof) and validated on external benchmarks including an unstable linear system, Van der Pol oscillator, and discretized Burgers' equation. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear; the central claims remain self-contained against the stated assumptions of local linearity and full-state availability.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim depends on the convergence of the matrix RLS algorithm and the stability properties of the synthesized controller. Since only the abstract is available, additional free parameters or assumptions in the full paper may exist.

free parameters (1)
  • forgetting factor
    A parameter in the recursive least-squares algorithm that controls the weight on past data; its specific value or selection method is not detailed in the abstract.
axioms (2)
  • domain assumption The system admits a local linear approximation from input-output data
    The dynamics-approximation module relies on estimating a local linear representation directly from measurements.
  • domain assumption Full state feedback is available
    The controller uses full-state feedback and integral action.

pith-pipeline@v0.9.0 · 5480 in / 1311 out tokens · 67822 ms · 2026-05-07T11:46:19.940771+00:00 · methodology

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Reference graph

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