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Less Conservative Robust Reference Governors and Their Applications

Miguel Castroviejo-Fernandez, Huayi Li, Andrés Cotorruelo, Emanuele Garone, Ilya Kolmanovsky

TL;DR

This work develops a less-conservative robust Reference Governor (RG) for discrete-time linear systems with unmeasured, set-bounded disturbances by incorporating online disturbance estimation and cancellation in the nominal control. It introduces time-varying, error-bounding sets derived from observer dynamics to replace the traditional invariant set, enabling a sequence of constraint-admissible regions $ ilde{O}_{ ext{inf},n}$ that adapt as estimation errors shrink. Two error-bounding strategies—ellipsoidal and polyhedral—are analyzed, with polyhedral bounding offering reduced conservatism at the cost of more complex bounding geometry; a finite-determined subset of the infinite safety set is constructed to maintain tractable online implementation. The framework is extended to unmatched disturbances and validated through aerospace-relevant simulations, including short-period aircraft dynamics and icing scenarios, demonstrating improved performance over classical RG approaches and practical applicability to real-world constrained control problems.

Abstract

The applications of reference governors to systems with unmeasured set-bounded disturbances can lead to conservative solutions. This conservatism can be reduced by estimating the disturbance from output measurements and canceling it in the nominal control law. In this paper, a reference governor based on such an approach is considered and time-varying, disturbance and state estimation errors bounding sets are derived. Consequently, the traditional implementation of a reference governor, which exploits a constraint admissible positively-invariant set of constant commands and initial states, is replaced by one which utilizes a time-dependent sequence of similar sets (which are not necessary nested). Examples are reported which include two applications to longitudinal control of aircraft that illustrate handling of elevator uncertainty and wing icing.

Less Conservative Robust Reference Governors and Their Applications

TL;DR

This work develops a less-conservative robust Reference Governor (RG) for discrete-time linear systems with unmeasured, set-bounded disturbances by incorporating online disturbance estimation and cancellation in the nominal control. It introduces time-varying, error-bounding sets derived from observer dynamics to replace the traditional invariant set, enabling a sequence of constraint-admissible regions that adapt as estimation errors shrink. Two error-bounding strategies—ellipsoidal and polyhedral—are analyzed, with polyhedral bounding offering reduced conservatism at the cost of more complex bounding geometry; a finite-determined subset of the infinite safety set is constructed to maintain tractable online implementation. The framework is extended to unmatched disturbances and validated through aerospace-relevant simulations, including short-period aircraft dynamics and icing scenarios, demonstrating improved performance over classical RG approaches and practical applicability to real-world constrained control problems.

Abstract

The applications of reference governors to systems with unmeasured set-bounded disturbances can lead to conservative solutions. This conservatism can be reduced by estimating the disturbance from output measurements and canceling it in the nominal control law. In this paper, a reference governor based on such an approach is considered and time-varying, disturbance and state estimation errors bounding sets are derived. Consequently, the traditional implementation of a reference governor, which exploits a constraint admissible positively-invariant set of constant commands and initial states, is replaced by one which utilizes a time-dependent sequence of similar sets (which are not necessary nested). Examples are reported which include two applications to longitudinal control of aircraft that illustrate handling of elevator uncertainty and wing icing.
Paper Structure (14 sections, 5 theorems, 55 equations, 6 figures)

This paper contains 14 sections, 5 theorems, 55 equations, 6 figures.

Table of Contents

  1. Introduction
  2. System with a Disturbance Input and a Nominal Controller
  3. Observer and Prediction Model for Reference Governor Design
  4. Observer Error Bounding
  5. Ellipsoidal bounding
  6. Polyhedral bounding
  7. Safe Sets
  8. Reference governor
  9. Unmatched Disturbances
  10. Simulation results
  11. Comparison of different error bounding schemes
  12. Short period dynamics of transport aircraft
  13. Aircraft under icing conditions
  14. Conclusion

Key Result

Proposition 1

Suppose $(C_{\tt cl}, A_{\tt cl})$ is observable, $A_{\tt cl}$ is Schur, and $Y_{\tt cl}$ is compact. Then there exists $k^*(n) \in \mathbb{Z}_{\geq 0}$ such that i.e., $\tilde{O}_{\infty,n}$ is a finitely-determined subset of ${O}_{\infty,n}$.

Figures (6)

  • Figure 1: Top: Time histories of the actual and estimated disturbance and of the control inputs for the polyhedral and ellipsoidal bounding-based RGs. Bottom: Time histories of the actual and estimated position, desired reference and modified by RG reference for the polyhedral and ellipsoidal bounding based RGs.
  • Figure 2: Error bounding sets $\Omega_{200}$ obtained using ellipsoidal and polyhedral error bounding.
  • Figure 3: Time histories of states, constraints, desired reference and referencemodified by RG reference for the aircraft short period dynamics with RG based on disturbance estimation (case a) and conventional robust RG (case b).
  • Figure 4: Time histories of the input, disturbance and constraints for the aircraft short period dynamics with RG making use of disturbance estimation (case a) and conventional robust RG (case b).
  • Figure 5: Projections of several error bounding sets $\Omega_n$ onto the $(e_\alpha,e_\theta,e_w)$ error space.
  • ...and 1 more figures

Theorems & Definitions (7)

  • Remark 1
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Remark 2