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Data-Driven Nonlinear State Observation using Video Measurements (2311.14895v1)

Published 25 Nov 2023 in eess.SY and cs.SY

Abstract: State observation is necessary for feedback control but often challenging for nonlinear systems. While Kazantzis-Kravaris/Luenberger (KKL) observer gives a generic design, its model-based numerical solution is difficult. In this paper, we propose a simple method to determine a data-driven KKL observer, namely to (i) transform the measured output signals by a linear time-invariant dynamics, and (ii) reduce the dimensionality to principal components. This approach is especially suitable for systems with rich measurements and low-dimensional state space, for example, when videos can be obtained in real time. We present an application to a video of the well-known Belousov-Zhabotinsky (B-Z) reaction system with severe nonlinearity, where the data-driven KKL observer recovers an oscillatory state orbit with slow damping.

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References (36)
  1. On the existence of a Kazantzis-Kravaris/Luenberger observer. SIAM J. Control Optim., 45(2), 432–456.
  2. Dynamics and nonlinear control of integrated process systems. Cambridge University Press.
  3. Barzykina, I. (2020). Chemistry and mathematics of the Belousov–Zhabotinsky reaction in a school laboratory. J. Chem. Educ., 97(7), 1895–1902.
  4. Luenberger observers for nonautonomous nonlinear systems. IEEE Trans. Autom. Control, 64(1), 270–281.
  5. Observer design for continuous-time dynamical systems. Ann. Rev. Control, 53, 224–248.
  6. Further remarks on KKL observers. Syst. Control Lett., 172, 105429.
  7. Towards artificial intelligence at scale in the chemical industry. AIChE J., 68(6), e17644.
  8. Christofides, P.D. (2001). Control of nonlinear distributed process systems: Recent developments and challenges. AIChE J., 47(3), 514–518.
  9. Nonlinear observer design for two-time-scale systems. AIChE J., 66(6), e16956.
  10. Science, serendipity, coincidence, and the Oregonator at the University of Oregon, 1969–1974. Chaos, 32(5), 052101.
  11. Nonlinear dynamical systems and control: A Lyapunov-based approach. Princeton University Press.
  12. Honeine, P. (2011). Online kernel principal component analysis: A reduced-order model. IEEE Trans. Pattern Anal. Mach. Intell., 34(9), 1814–1826.
  13. From model-based control to data-driven control: Survey, classification and perspective. Inform. Sci., 235, 3–35.
  14. Convolutional neural nets in chemical engineering: Foundations, computations, and applications. AIChE J., 67(9), e17282.
  15. Principal component analysis: A review and recent developments. Phil. Trans. R. Soc. A, 374(2065), 20150202.
  16. Nonlinear observer design using Lyapunov’s auxiliary theorem. Syst. Control Lett., 34(5), 241–247.
  17. Advances and selected recent developments in state and parameter estimation. Comput. Chem. Eng., 51, 111–123.
  18. Functional observers with linear error dynamics for nonlinear systems. Syst. Control Lett., 157, 105021.
  19. Recursive PCA for adaptive process monitoring. J. Process Control, 10(5), 471–486.
  20. Luenberger, D. (1966). Observers for multivariable systems. IEEE Trans. Autom. Control, 11(2), 190–197.
  21. Learning robust state observers using neural ODEs. In the 5th Learning for Dynamics and Control Conference, 208–219. PMLR.
  22. Nelles, O. (2020). Nonlinear dynamic system identification. Springer, 2nd edition.
  23. Learning-based design of Luenberger observers for autonomous nonlinear systems. In 2023 American Control Conference (ACC), 3048–3055.
  24. Model predictive control: Theory, computation, and design. Nob Hill, 2nd edition.
  25. A tutorial review of neural network modeling approaches for model predictive control. Comput. Chem. Eng., 107956.
  26. On the sample complexity of subspace learning. Advances in Neural Information Processing Systems, 26.
  27. Real-time leak detection using an infrared camera and faster R-CNN technique. Comput. Chem. Eng., 135, 106780.
  28. Sontag, E.D. (1998). Mathematical control theory: Deterministic finite dimensional systems. Springer, 2nd edition.
  29. Tang, W. (2023a). Data-driven state observation for nonlinear systems based on online learning. AIChE J., 69(12), e18224.
  30. Tang, W. (2023b). Synthesis of data-driven nonlinear state observers using Lipschitz-bounded neural networks. arXiv preprint. arXiv:2310.03187.
  31. Dissipativity learning control (DLC): A framework of input–output data-driven control. Comput. Chem. Eng., 130, 106576.
  32. Dissipativity learning control (DLC): Theoretical foundations of input–output data-driven model-free control. Syst. Control Lett., 147, 104831.
  33. Data-driven control: Overview and perspectives. In 2022 American Control Conference (ACC), 1048–1064. IEEE.
  34. Dissipativity learning control through estimation from online trajectories. In 2023 American Control Conference (ACC), 3036–3041.
  35. Predictive control of particlesize distribution of crystallization process using deep learning based image analysis. AIChE J., 68(11), e17817.
  36. Zhabotinsky, A.M. (1991). A history of chemical oscillations and waves. Chaos, 1(4), 379–386.

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