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Dissipative iFIR filters for data-driven design

Zixing Wang, Yi Zhang, Fulvio Forni

TL;DR

This paper proposes a data-driven control design that guarantees closed-loop stability by integrating virtual reference feedback tuning (VRFT) with dissipativity constraints on an iFIR controller. By expressing dissipativity as frequency-domain linear inequalities—implemented via either KYP-based LMIs or sampling-driven inequalities on the FIR coefficients—the approach yields a convex, scalable optimization that decouples stability guarantees from data-driven performance. A 2DOF architecture with a prefilter enhances matching to reference and disturbance models, enabling flexible impedance shaping in applications like soft-gripper control. The method is demonstrated on a gripper impedance-control example, showing stability and accurate tracking even with noisy data, and offering substantial computational savings over traditional LMI-based synthesis. The framework thus provides a practical, scalable pathway for stable data-driven control in single-input single-output, and sets the stage for extensions to nonlinear and multi-input multi-output systems.

Abstract

We tackle the problem of providing closed-loop stability guarantees with a scalable data-driven design. We combine virtual reference feedback tuning with dissipativity constraints on the controller for closed-loop stability. The constraints are formulated as a set of linear inequalities in the frequency domain. This leads to a convex problem that is scalable with respect to the length of the data and the complexity of the controller. An extension of virtual reference feedback tuning to include disturbance dynamics is also discussed. The proposed data-driven control design is illustrated by a soft gripper impedance control example.

Dissipative iFIR filters for data-driven design

TL;DR

This paper proposes a data-driven control design that guarantees closed-loop stability by integrating virtual reference feedback tuning (VRFT) with dissipativity constraints on an iFIR controller. By expressing dissipativity as frequency-domain linear inequalities—implemented via either KYP-based LMIs or sampling-driven inequalities on the FIR coefficients—the approach yields a convex, scalable optimization that decouples stability guarantees from data-driven performance. A 2DOF architecture with a prefilter enhances matching to reference and disturbance models, enabling flexible impedance shaping in applications like soft-gripper control. The method is demonstrated on a gripper impedance-control example, showing stability and accurate tracking even with noisy data, and offering substantial computational savings over traditional LMI-based synthesis. The framework thus provides a practical, scalable pathway for stable data-driven control in single-input single-output, and sets the stage for extensions to nonlinear and multi-input multi-output systems.

Abstract

We tackle the problem of providing closed-loop stability guarantees with a scalable data-driven design. We combine virtual reference feedback tuning with dissipativity constraints on the controller for closed-loop stability. The constraints are formulated as a set of linear inequalities in the frequency domain. This leads to a convex problem that is scalable with respect to the length of the data and the complexity of the controller. An extension of virtual reference feedback tuning to include disturbance dynamics is also discussed. The proposed data-driven control design is illustrated by a soft gripper impedance control example.

Paper Structure

This paper contains 9 sections, 3 theorems, 38 equations, 10 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Data-driven Design of iFIR Controllers
  3. Design of dissipative 1DOF/2DOF iFIR
  4. Stability of dissipative systems
  5. Dissipativity constraints for 1DOF/2DOF iFIR
  6. Proofs
  7. Examples
  8. Gripper reference tracking and impedance shaping
  9. Conclusion

Key Result

Theorem 1

For the closed loops in Figures fig:blockdiag1DOF_P1 or fig:blockdiag2DOF_P1P2, consider the following dissipativity cases for $P_{1}$ Then, the closed loop in Figure fig:blockdiag1DOF_P1 and the closed loop in Figure fig:blockdiag2DOF_P1P2have a finite $\ell_{2}$ gain from $r$ to $y$, if the iFIR controller $C$ satisfies, respectively, where $\epsilon_{1},\epsilon_{2},\epsilon_{3}$ are (small) p

Figures (10)

  • Figure 1: A block diagram of a closed-loop system and of its desired behavior, modeled by the reference model $M_r$.
  • Figure 2: Closed-loop system with disturbance dynamics.
  • Figure 3: A block diagram of a closed-loop system considering disturbance dynamics. A 2DOF controller is used.
  • Figure 4: Graphical interpretation for Cases A-C in Theorem \ref{['thm:dissipativityCases']}. The shaded areas represent the regions where the Nyquist diagram of iFIR controller $C$ must lie.
  • Figure 5: Equation \ref{['eq:freq_conditions_A']} constrains the Nyquist diagram of the controller $C$ within the blue box, to satisfy the passivity property given by the grey disk.
  • ...and 5 more figures

Theorems & Definitions (5)

  • Definition 1
  • Theorem 1
  • proof
  • Theorem 2
  • Theorem 3