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Derivative-Free Data-Driven Control of Continuous-Time Linear Time-Invariant Systems

Alessandro Bosso, Marco Borghesi, Andrea Iannelli, Giuseppe Notarstefano, Andrew R. Teel

Abstract

This paper develops a data-driven stabilization method for continuous-time linear time-invariant systems with theoretical guarantees and no need for signal derivatives. The framework, based on linear matrix inequalities (LMIs), is illustrated in the state-feedback and single-input single-output output-feedback scenarios. Similar to discrete-time approaches, we rely solely on input and state/output measurements. To avoid differentiation, we employ low-pass filters of the available signals that, rather than approximating the derivatives, reconstruct a non-minimal realization of the plant. With access to the filter states and their derivatives, we can solve LMIs derived from sample batches of the available signals to compute a dynamic controller that stabilizes the plant. The effectiveness of the framework is showcased through numerical examples.

Derivative-Free Data-Driven Control of Continuous-Time Linear Time-Invariant Systems

Abstract

This paper develops a data-driven stabilization method for continuous-time linear time-invariant systems with theoretical guarantees and no need for signal derivatives. The framework, based on linear matrix inequalities (LMIs), is illustrated in the state-feedback and single-input single-output output-feedback scenarios. Similar to discrete-time approaches, we rely solely on input and state/output measurements. To avoid differentiation, we employ low-pass filters of the available signals that, rather than approximating the derivatives, reconstruct a non-minimal realization of the plant. With access to the filter states and their derivatives, we can solve LMIs derived from sample batches of the available signals to compute a dynamic controller that stabilizes the plant. The effectiveness of the framework is showcased through numerical examples.

Paper Structure

This paper contains 12 sections, 7 theorems, 28 equations, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement and Preliminaries
  3. Data-Driven Control from Input-State Data
  4. Non-Minimal System Realization
  5. Controller Design
  6. Data-Driven Control from Input-Output Data
  7. Non-Minimal System Realization
  8. Controller Design
  9. Numerical Examples
  10. Design with Input-State Data
  11. Design with Input-Output Data
  12. Conclusion

Key Result

Lemma 1

Under Assumption hyp:ctrb, for all $\lambda$ and all $\gamma \neq 0$, the observable and controllable subsystem of eq:filter_state_compact obeys the same dynamics of eq:plant_state, with state $\xi \in {\mathbb{R}}^n$.

Theorems & Definitions (10)

  • Definition 1
  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Remark 1
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Theorem 2
  • Remark 2