Model-less Control Framework

• Model-less control is a framework that replaces detailed system modeling with ultra-local, real-time estimation methods.
• It employs integral sliding windows and recursive algebraic estimation to generate adaptive feedback laws in dynamic environments.
• The approach demonstrates robustness and computational efficiency across applications in mechatronics, robotics, and distributed energy systems.

A model-less control framework, sometimes termed "model-free control" (MFC), designates a class of control methodologies that eschew explicit a priori derivation or identification of a plant’s global equations of motion, state-space, or parameterized input-output structure. Instead, these frameworks exploit ubiquitous real-time measurement data and lightweight on-line estimation to derive feedback control actions. The key principle is the continual, local online estimation of minimal-order dynamical relationships (generically, "ultra-local models" or localized empirical system surrogates), which are then leveraged to synthesize effective feedback or optimization-based control laws with minimal reliance on physical plant identification or offline training. Such approaches have found wide application—from high-performance mechatronics and distributed energy resources to robotic soft bodies—delivering robust tracking, disturbance rejection, and guaranteed stability in both finite- and infinite-dimensional, linear and nonlinear, deterministic and stochastic plants (Fliess et al., 2020, Fliess et al., 2013, Vikas et al., 2015, Shahna et al., 18 Sep 2024, Zhang et al., 26 Jun 2024, Gupta et al., 2023, Jiang et al., 2023).

1. The Ultra-Local Model and Fundamental Architecture

Model-less control frameworks rest on the replacement of the unknown system by a minimal-order, ultra-local differential model: $y^{(n)}(t) = F(t) + \alpha u(t),$ where

• $y^{(n)}$ is the $n$th derivative of the measured output $y$ (typically $n=1$ suffices for most physical plants);
• $\alpha\in\mathbb{R}$ is a practitioner-chosen scalar ensuring $\alpha u$ matches $F$ in scale;
• $F(t)$ is a completely unmodeled, time-varying term absorbing all unknown plant dynamics (e.g., inertia, friction, delays, external disturbances, nonlinearities).

At each control instant, the controller only requires an estimate $\hat{F}(t)$, typically obtained by local algebraic estimation (e.g., a sliding window integral or moving-window least-squares), without explicit state-space or transfer function identification (Fliess et al., 2020, Fliess et al., 2013). This local proxy is then used to close the loop with a linear feedback law (e.g., "intelligent" PI/PID, or more general multivariable optimizations). Higher-order extensions ($n=2$) are reserved for plants dominated by light friction or second-order behaviors.

2. Online Algebraic Estimation and Adaptive Control Logic

The cornerstone of model-less control is the real-time estimation of the lumped term $F(t)$ using recursive or integral algebraic schemes, all derived from the ultra-local model. Two representative estimation methods are:

• Integral Sliding Window (Algebraic Filter):

$$\hat{F}(t) = -\frac{6}{\tau^{3}} \int_{t-\tau}^t \left[ (\tau-2\sigma)y(\sigma) + \alpha\sigma(\tau-\sigma)u(\sigma) \right] d\sigma$$

with $\tau$ a small fixed time window. This acts as a real-time low-pass filter, regularizing derivative computations and attenuating sensor noise (Fliess et al., 2020).

• Closed-Loop Mismatch Estimator:

$$\hat{F}(t) = \frac{1}{\tau} \int_{t-\tau}^t \left( \dot{y}_{\text{ref}}(\sigma) - \alpha u(\sigma) - K_P e(\sigma)\right)d\sigma$$

where $e=y - y_{\text{ref}}$. This form is especially convenient when feedback is already operating.

For systems subject to actuator saturations, nonlinear friction, or nontrivial load disturbances (e.g., servo-driven mechanisms with energy conversion), model-less generic robust control (GRC) frameworks decompose the actuation dynamics hierarchically and employ subsystem-wise adaptive control laws: $$u_v = -\frac{1}{2} [k_v + \epsilon_v \hat{h}_v] z_{v+1} - \Theta_v(z_1, \dots, z_v),$$ with gain adaptation and saturation logic, guaranteeing closed-loop robustness and exponential convergence under unknown, bounded disturbances (Shahna et al., 18 Sep 2024).

3. Feedback Law Synthesis and Closed-Loop Performance

Once $F$ is estimated, the feedback law in SISO (or decoupled MIMO) settings is often synthesized as an "intelligent" proportional/integral/derivative (iP/iPI/iPID) controller: $$u(t) = -\frac{\hat{F}(t) - y^{(n)}_{\text{ref}}(t) + K_P e(t) + K_I \int e(\tau)\,d\tau + K_D \dot{e}(t)}{\alpha}$$ with $K_P, K_I, K_D$ chosen for the desired error convergence and bandwidth (Fliess et al., 2013, Moreno-Gonzalez et al., 2023). This law yields simple, linear error dynamics

$e^{(n)} + \cdots + K_P e = F - \hat{F}$

so that as long as $\hat{F} \approx F$, exponential convergence to the reference is achieved.

For broader classes—including nonlinearly parameterized, time-varying, or partially observed systems—finite-time stable (FTS) observers and Lyapunov-based feedback (incorporating sliding or adaptive elements) have been proposed, rendering the approach robust to bounded noise, plant changes, and incomplete knowledge (Sanyal, 2019). Such designs preserve the separation principle and grant formal nonlinear stability certificates.

4. Model-Less Control in Distributed and Large-Scale Systems

In large-scale energy networks and grid applications, model-less control replaces conventional admittance- or topology-based network models with real-time, measurement-based sensitivity estimation. For distribution grids, this involves:

• Estimation of Voltage Sensitivity Coefficients: Local regression or recursive least squares (RLS) infers real-time sensitivities $K_{ij}^P, K_{ij}^Q$ quantifying the effect of DER $j$ on node $i$'s voltage, with uncertainty quantification via covariance propagation (Gupta et al., 2023, Gupta et al., 2022, Majumdar et al., 2021).
• Robust Optimization: Setpoint optimization problems for DER actuation (curtailment, reactive support) are solved via quadratic or linear programming, accounting for coefficient uncertainty using robust, budgeted ambiguity sets. The resulting model-less voltage regulation ensures statutory compliance without explicit electrical models, and is validated experimentally in full-scale microgrids.

In soft robotics and continuum manipulators, the model-less paradigm circumvents intractable or inaccurate infinite-dimensional mechanics by (a) locally discretizing the actuation/interaction space, (b) empirically updating Jacobians via minimal perturbations and convex updates, and (c) synthesizing tip motion through convex quadratic programs with slack avoidance, geometric, and internal force constraints (Vikas et al., 2015, Rajneesh et al., 7 Dec 2025).

5. Comparative Analysis: Model-Less vs. Model-Based/ML Approaches

Compared to classical model-based and modern machine learning-based controllers (ANN/RL), model-less control frameworks offer:

• No system identification or offline training: All feedback laws depend solely on real-time filtered input-output data streams.
• Minimal parameter tuning: Only a gains vector $(K_P, \ldots)$ and the scale parameter $\alpha$ need to be hand-selected or optimized for the desired bandwidth or convergence rate.
• Computational efficiency: All updates (F estimation, PID law) can be realized as simple recursive digital filters or moving window integrals, enabling deployment on lightweight embedded hardware.
• Robustness: Demonstrated resilience to disturbances, unmodeled nonlinearities, delays, and plant or sensor faults with rapid recovery (even under severe network packet loss or hardware failure) (Join et al., 2020).
• Stability guarantees: Error decay is direct and exponential under standard conditions; Lyapunov-based nonlinear generalizations deliver global uniform (or finite-time) convergence (Shahna et al., 18 Sep 2024, Sanyal, 2019).

Rather than seeking universal optimality over large system classes, as in deep RL, model-less control emphasizes rapid real-world adaptability, analytical stability, and ease of deployment (Fliess et al., 2020, Lawrence et al., 2023, Zhang et al., 26 Jun 2024).

6. Representative Implementations and Case Studies

The model-less control framework has been validated across a spectrum of domains:

• High-bandwidth mechatronics: Laboratory half-quadrotor (Quanser AERO) with decoupled ultralocal models for azimuth and pitch; perfect tracking and rapid adaptation to load disturbances (4 g payload) without retuning (Fliess et al., 2020).
• Robust voltage regulation: Real CIGRE LV microgrid using PMUs and RLS sensitivity estimation, with convex robust QP ensuring all bus voltages within [0.96, 1.04] pu despite significant measurement noise and estimation uncertainty (Gupta et al., 2023).
• Soft multi-limb robotics: Data-driven graph-theoretic gait synthesis via discretization, reward learning from state transitions, and periodic gait optimization with integer programming (Vikas et al., 2015).
• Continuum manipulation: Empirical Jacobian update and real-time QP actuation for tension-constrained tendon-driven robots operating in unstructured, uncertain environments; sub-millimeter steady-state accuracy without model calibration (Rajneesh et al., 7 Dec 2025).
• Distribution grids: Model-less linear OPF for low-voltage feeders, providing P–Q flexibility capability curves and near-optimal hosting capacity extensions (Majumdar et al., 2021).

Extensive simulation and industrial-scale experimental deployments across energy, robotics, and IIoT domains confirm the universality, computational tractability, and practical robustness of the model-less control paradigm.

7. Practical Considerations, Tuning, and Limitations

The following practical issues govern the deployment and effectiveness of model-less control frameworks:

• Scale parameter $\alpha$: Chosen so that $\alpha u$ and $F$ are commensurate; trial-and-error or order-of-magnitude estimates suffice.
• Derivative/order selection ($n$): $n=1$ suffices unless dominant inertial or friction effects necessitate $n=2$.
• Gains ($K_P,\ldots$): Directly shape exponential decay rate; integral/derivative terms added as needed for offset-free tracking or improved transient noise rejection.
• Estimation window $\tau$: Set small enough to follow fast changes yet large enough to filter sensor noise; typically 10–100 ms.
• MIMO/coupled systems: Each channel can be regulated independently in the SISO case; diagonal or MIMO extensions are possible but require more elaborate estimation and decoupling strategies.
• Limitations: Does not provide intrinsic fault detection; estimation performance degrades with low excitation or poor SNR; sudden structural changes (e.g., faults, topological reconfiguration) may necessitate manual or algorithmic intervention.

The methodology is less suited to systems with minimal excitation, heavy coupling without diagonal dominance, or where global performance constraints dominate local transient performance. In such cases, hybrid or hierarchical approaches may be favorable.

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The model-less control framework, particularly as epitomized by the ultra-local model and online algebraic estimation, thus establishes a universal, practical, and mathematically rigorous foundation for high-performance feedback in both classical and emerging control domains—without resorting to explicit model identification or resource-intensive machine learning (Fliess et al., 2020, Fliess et al., 2013, Vikas et al., 2015, Rajneesh et al., 7 Dec 2025, Shahna et al., 18 Sep 2024, Zhang et al., 26 Jun 2024, Gupta et al., 2023).