268
Views
6
CrossRef citations to date
0
Altmetric
Articles

Non-asymptotic numerical differentiation: a kernel-based approach

ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 2090-2099 | Received 30 Mar 2017, Accepted 14 May 2018, Published online: 28 Jun 2018

References

  • Abramowitz, M., & Stegun, I. A. (1964). Handbook of mathematical functions: With formulas, graphs, and mathematical tables (Vol. 55). Washington, DC: United States Department of Commerce, National Bureau of Standards.
  • Bartolini, G., Pisano, A., & Usai, E. (2000). First and second derivative estimation by sliding mode technique. Journal of Signal Processing, 4(2), 167–176.
  • Burton, T. (2005). Volterra integral and differential equations. Amsterdam: Elsevier.
  • Chai, G., Lin, Z., & Fu, M. (2013). Consensus-based cooperative source localization of multi-agent systems. Proceedings of the 32nd Chinese Control Conference (CCC), Xi'an, China. (pp. 6809–6814). IEEE.
  • Chen, C.-K., & Lee, J.-H. (1995). Design of high-order digital differentiators using l/sub 1/error criteria. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 42(4), 287–291. doi: 10.1109/82.378044
  • Duncan, T. E., Mandl, P., & Pasik-Duncan, B. (1996). Numerical differentiation and parameter estimation in higher-order linear stochastic systems. IEEE Transactions on Automatic Control, 41(4), 522–532. doi: 10.1109/9.489273
  • Fliess, M., & Sira-Ramirez, H. (2004). Control via state estimations of some nonlinear systems. IFAC symposium on Nonlinear Control Systems (NOLCOS’04), Stuttgart, Germany. Elsevier.
  • Ibrir, S. (2004). Linear time-derivative trackers. Automatica, 40(3), 397–405. doi: 10.1016/j.automatica.2003.09.020
  • Ibrir, S., & Diop, S. (2004). A numerical procedure for filtering and efficient high-order signal differentiation. International Journal of Applied Mathematics and Computer Science, 14(2), 201–208.
  • Levant, A. (1998). Robust exact differentiation via sliding mode technique. Automatica, 34(3), 379–384. doi: 10.1016/S0005-1098(97)00209-4
  • Levant, A. (2003). Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control, 76(9–10), 924–941. doi: 10.1080/0020717031000099029
  • Liu, D.-Y., Gibaru, O., & Perruquetti, W. (2011a). Differentiation by integration with Jacobi polynomials. Journal of Computational and Applied Mathematics, 235(9), 3015–3032. doi: 10.1016/j.cam.2010.12.023
  • Liu, D.-Y., Gibaru, O., & Perruquetti, W. (2011b). Error analysis of Jacobi derivative estimators for noisy signals. Numerical Algorithms, 58(1), 53–83. doi: 10.1007/s11075-011-9447-8
  • Mboup, M., Join, C., & Fliess, M. (2007). A revised look at numerical differentiation with an application to nonlinear feedback control. 2007 Mediterranean Conference on Control & Automation, Athens, Greece (pp. 1–6). IEEE.
  • Mboup, M., Join, C., & Fliess, M. (2009). Numerical differentiation with annihilators in noisy environment. Numerical Algorithms, 50(4), 439–467. doi: 10.1007/s11075-008-9236-1
  • Pin, G., Assalone, A., Lovera, M., & Parisini, T. (2016). Non-asymptotic kernel-based parametric estimation of continuous-time linear systems. IEEE Transactions on Automatic Control, 61(2), 360–373.
  • Pin, G., Chen, B., & Parisini, T. (2015). The modulation integral observer for linear continuous-time systems. 2015 European Control Conference (ECC), Linz, Austria (pp. 2932–2939). IEEE.
  • Pin, G., Lovera, M., Assalone, A., & Parisini, T. (2013). Kernel-based nonasymptotic state estimation for linear continuous-time systems. 2013 American Control Conference, Washington, DC (pp. 3123–3128). IEEE.
  • Polyakov, A., Efimov, D., & Perruquetti, W. (2014). Homogeneous differentiator design using implicit Lyapunov function method. 2014 European Control Conference (ECC), Strasbourg, France (pp. 288–293). IEEE.
  • Rader, C. M., & Jackson, L. B. (2006). Approximating noncausal IIR digital filters having arbitrary poles, including new Hilbert transformer designs, via forward/backward block recursion. IEEE Transactions on Circuits and Systems I: Regular Papers, 53(12), 2779–2787. doi: 10.1109/TCSI.2006.883877
  • Reger, J., & Jouffroy, J. (2009). On algebraic time-derivative estimation and deadbeat state reconstruction. Proceedings of the 48th IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, Shanghai, China (pp. 1740–1745). IEEE.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.