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Sample-based detectability and moving horizon state estimation of continuous-time systems

Isabelle Krauss, Victor G. Lopez, Matthias A. Müller

Abstract

In this paper we propose a detectability condition for nonlinear continuous-time systems with irregular/infrequent output measurements, namely a sample-based version of incremental integral input/output-to-state stability (i-iIOSS). We provide a sufficient condition for an i-iIOSS system to be sample-based i-iIOSS. This condition is also exploited to analyze the relationship between sample-based i-iIOSS and sample-based observability for linear systems, such that previously established sampling strategies for linear systems can be used to guarantee sample-based i-iIOSS. Furthermore, we present a sample-based moving horizon estimation scheme, for which robust stability can be shown. Finally, we illustrate the applicability of the proposed estimation scheme through a biomedical simulation example.

Sample-based detectability and moving horizon state estimation of continuous-time systems

Abstract

In this paper we propose a detectability condition for nonlinear continuous-time systems with irregular/infrequent output measurements, namely a sample-based version of incremental integral input/output-to-state stability (i-iIOSS). We provide a sufficient condition for an i-iIOSS system to be sample-based i-iIOSS. This condition is also exploited to analyze the relationship between sample-based i-iIOSS and sample-based observability for linear systems, such that previously established sampling strategies for linear systems can be used to guarantee sample-based i-iIOSS. Furthermore, we present a sample-based moving horizon estimation scheme, for which robust stability can be shown. Finally, we illustrate the applicability of the proposed estimation scheme through a biomedical simulation example.
Paper Structure (11 sections, 7 theorems, 44 equations, 8 figures)

This paper contains 11 sections, 7 theorems, 44 equations, 8 figures.

Table of Contents

  1. Conclusion
  2. Conclusion
  3. Introduction
  4. Preliminaries and setup
  5. Sample-based i-iIOSS
  6. Sample-based MHE
  7. Setup
  8. Robust stability analysis
  9. Linear systems and sample-based i-iIOSS
  10. Simulation example
  11. Conclusion

Key Result

Theorem 35

Let system (eq:sys) be i-iIOSS and let Assumption ass:f hold. Consider some set $K$ according to Definition def:K. The system is sample-based i-iIOSS if there exist a finite $t^*$ and $\alpha_w, \alpha_y, \alpha_v \in \mathcal{K}_{\infty}$ such that for any two initial conditions $\chi_1, \chi_2$ an

Figures (8)

  • Figure 1: Noisy system output $y$ (blue) and infrequently sampled discrete measurements (green) used in the sample-based MHE scheme.
  • Figure 2: Real system states (blue) and sample-based MHE estimates (red) of the hormone concentrations that are directly measurable.
  • Figure 3: Real system states (blue) and sample-based MHE estimates (red) of the unmeasured hormone concentrations.
  • Figure 4: Real system states (blue) and sample-based MHE estimates (red) of the hormone concentrations that are directly measurable.
  • Figure 5: Real system states (blue) and sample-based MHE estimates (red) of the unmeasured hormone concentrations.
  • ...and 3 more figures

Theorems & Definitions (13)

  • Definition 31: i-iIOSS
  • Definition 32: Sampling set $K$ Kra25
  • Definition 33: Sample-based i-iIOSS
  • Theorem 35: Sufficient Condition
  • Definition 36
  • Theorem 38: sample-based MHE is RGES
  • Theorem 39
  • Definition 40: Sample-based observability matrix Kra25b
  • Lemma 41
  • Remark 42
  • ...and 3 more