Optimal input design for parameter estimation of nonlinear systems: case study of an unstable delta wing. (English) Zbl 1366.93640
Summary: A closed-loop optimal experimental design for online parameter identification approach is developed for nonlinear dynamic systems. The goal of the observer and the nonlinear model predictive control theories is here to perform online computation of the optimal time-varying input and to estimate the unknown model parameters online. The main contribution consists in combining Lyapunov stability theory with an existing closed-loop identification approach, in order to maximize the information content in the experiment and meanwhile to asymptotically stabilize the closed-loop system. To illustrate the proposed approach, the case of an open-loop unstable aerodynamic mechanical system is discussed. The simulation results show that the proposed algorithm allows to estimate all unknown parameters, which was not possible according to previous work, while keeping the closed-loop system stable.
MSC:
| 93E10 | Estimation and detection in stochastic control theory |
| 93C10 | Nonlinear systems in control theory |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93B30 | System identification |
| 93C15 | Control/observation systems governed by ordinary differential equations |
Keywords:
closed-loop identification; optimal experiment design; model predictive control; stability; nonlinear observer; persistent excitation; delta wing; mechanical systemReferences:
| [1] | DOI: 10.1002/aic.14683 · doi:10.1002/aic.14683 |
| [2] | DOI: 10.1109/TAC.2011.2179349 · Zbl 1369.93209 · doi:10.1109/TAC.2011.2179349 |
| [3] | DOI: 10.1002/aic.13957 · doi:10.1002/aic.13957 |
| [4] | Başar T., H-optimal control and related minimax design problems: A dynamic game approach (1995) |
| [5] | Besançon G., Lecture notes in control and information sciences 363 (2007) |
| [6] | on G., Lecture notes in control and information sciences 363 (2007) |
| [7] | DOI: 10.1109/TAC.2006.889867 · Zbl 1366.93193 · doi:10.1109/TAC.2006.889867 |
| [8] | DOI: 10.1016/j.automatica.2010.06.004 · Zbl 1201.93122 · doi:10.1016/j.automatica.2010.06.004 |
| [9] | Bornard G., Lecture notes in control and information sciences 122 pp 130– (1988) |
| [10] | DOI: 10.1109/TAC.1964.1105635 · doi:10.1109/TAC.1964.1105635 |
| [11] | DOI: 10.1109/TAC.2011.2166667 · Zbl 1369.93099 · doi:10.1109/TAC.2011.2166667 |
| [12] | DOI: 10.1016/j.jprocont.2014.03.010 · doi:10.1016/j.jprocont.2014.03.010 |
| [13] | DOI: 10.1016/j.ces.2007.11.034 · doi:10.1016/j.ces.2007.11.034 |
| [14] | DOI: 10.1109/9.256352 · Zbl 0775.93020 · doi:10.1109/9.256352 |
| [15] | Goodwin G.C., Mathematics in science and engineering 136 (1977) |
| [16] | DOI: 10.1016/j.jprocont.2011.01.012 · doi:10.1016/j.jprocont.2011.01.012 |
| [17] | DOI: 10.1016/j.jsv.2004.12.013 · Zbl 1243.93113 · doi:10.1016/j.jsv.2004.12.013 |
| [18] | DOI: 10.1080/00401706.1975.10489332 · doi:10.1080/00401706.1975.10489332 |
| [19] | DOI: 10.1109/TAC.1979.1101943 · Zbl 0399.93054 · doi:10.1109/TAC.1979.1101943 |
| [20] | DOI: 10.1002/047134608X.W1046 · doi:10.1002/047134608X.W1046 |
| [21] | DOI: 10.1109/TAC.2012.2212517 · Zbl 1369.93106 · doi:10.1109/TAC.2012.2212517 |
| [22] | DOI: 10.2514/3.45844 · doi:10.2514/3.45844 |
| [23] | DOI: 10.1109/TAC.1976.1101148 · Zbl 0316.93039 · doi:10.1109/TAC.1976.1101148 |
| [24] | DOI: 10.1016/0005-1098(77)90078-4 · Zbl 0366.93043 · doi:10.1016/0005-1098(77)90078-4 |
| [25] | Walter E., Identification of parametric models from experimental data (1994) |
| [26] | DOI: 10.1080/00207177008905945 · Zbl 0186.48303 · doi:10.1080/00207177008905945 |
| [27] | DOI: 10.1016/j.jprocont.2014.04.023 · doi:10.1016/j.jprocont.2014.04.023 |
| [28] | DOI: 10.1016/j.automatica.2008.06.011 · Zbl 1154.93364 · doi:10.1016/j.automatica.2008.06.011 |
| [29] | DOI: 10.1002/aic.12479 · doi:10.1002/aic.12479 |
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