Robust data-driven model-reference control of linear perturbed systems via sliding mode generation

This paper introduces a data-based integral sliding mode control scheme for robustification of model-reference controllers, accommodating generic multivariable linear systems with unknown dynamics and affected by matched disturbances. Specifically, an integral sliding mode control (ISMC) law is recast into a data-based framework relying on an integral sliding variable depending only on the reference model, without the need of modeling the plant. The main strength of the proposed approach is the enforcement of the desired reference model in closed-loop under sliding mode conditions, despite the lack of knowledge of the model dynamics and the presence of the matched disturbances. Moreover, the conditions required to guarantee an integral sliding mode generation and the closed-loop stability are formally analyzed in the paper, remarking the generality of the proposed data-driven integral sliding mode control (DD-ISMC) with respect to the related model-based counterpart. Finally, the main practices for the data-based design of the proposed control scheme are deeply discussed in the paper, and the proposed method is tested in simulation on a benchmark example, and experimentally on a real laboratory setup. Simulation and experimental evidence fully corroborates the theoretical analysis, thus motivating further research in this direction.

💡 Research Summary

This paper proposes a novel data‑driven integral sliding‑mode control (DD‑ISMC) framework that achieves robust model‑reference tracking for multivariable continuous‑time linear systems with unknown dynamics and matched disturbances. The authors start by reviewing the limitations of existing indirect (identify‑then‑control) and direct (data‑only) model‑reference methods such as VRFT, IFT, FRIT, and recent data‑based sliding‑mode approaches. While these techniques can match a desired closed‑loop behavior, they generally lack explicit mechanisms to reject unknown disturbances once the controller is deployed.

To overcome this gap, the paper combines two ideas: (i) the sliding variable is defined solely from the reference model, independent of plant states or parameters, and (ii) the continuous “ideal” control part is synthesized via a multivariable VRFT procedure that uses a single batch of open‑loop input‑output data to match the reference model. The overall control law reads
(u(t)=K,e(t)+G,v(t)+u_s(t)),
where (K) and (G) are the VRFT‑derived gains, (e(t)) is the tracking error, (v(t)) the virtual reference, and (u_s(t)) the discontinuous sliding term. The sliding term is expressed as (u_s(t)=-L,\text{sign}(\sigma(t)),\eta), with (\sigma(t)) the integral sliding variable built from the reference model output.

A key contribution is the derivation of sufficient LMI conditions—via Petersen’s Lemma—that guarantee (a) the existence of an integral sliding mode from the initial instant, and (b) asymptotic stability of the closed‑loop system while the sliding mode is active. The authors prove that, under these conditions, the closed‑loop dynamics exactly follow the reference model regardless of matched disturbances and of any residual disturbance generated by the imperfect data‑driven ideal controller. The residual disturbance is explicitly characterized, and the discontinuous term is shown to cancel it.

The design procedure consists of: (1) collecting a rich open‑loop dataset, (2) solving the VRFT optimization to obtain (K) and (G), (3) constructing the LMI using the reference model and a known bound on the disturbances, and (4) solving for the sliding‑mode gain matrix (L) and scalar (\eta). This systematic approach ensures that the sliding mode is generated immediately (no reaching phase) and that the controller is implementable with only input‑output measurements.

Simulation results on a 2‑input‑2‑output benchmark system with injected matched disturbances demonstrate that DD‑ISMC achieves near‑zero tracking error, outperforming standard VRFT and classical ISMC (which requires exact plant models). Experimental validation on a laboratory electro‑mechanical setup confirms the theoretical findings: the sliding mode appears instantly, the plant output follows the reference model precisely, and robustness to disturbances is maintained in real‑time operation.

In summary, the paper delivers a rigorous, practically applicable solution to the open problem of robust data‑driven model‑reference control. It extends the classical integral sliding‑mode paradigm to a model‑free, output‑feedback setting, integrates multivariable VRFT for the continuous part, and provides LMI‑based tuning rules for the discontinuous part. The work opens avenues for applying the methodology to higher‑order, nonlinear, or large‑scale systems where model identification is infeasible but robust performance is required.