Dynamic observer error linearization. (English) Zbl 1104.93017
Summary: A new framework of observer error linearization problem is proposed. The main idea of our approach is twofold. The one is to introduce an auxiliary dynamics whose input is the system output, and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics. It is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output. It is also shown that whenever an \(n\)-dimensional system is immersible into an \(n+d\)-dimensional linear system up to an output injection, then it can be also dynamically observer error linearizable in our sense with a \(d\)-dimensional auxiliary dynamics. Moreover, we show that the converse is not true by providing a counterexample, which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method.
References:
| [1] | Back, J., & Seo, J. H. (2004a). A constructive algorithm for system immersion into nonlinear observer form. In Proceedings of the IFAC symposium on nonlinear control systems; Back, J., & Seo, J. H. (2004a). A constructive algorithm for system immersion into nonlinear observer form. In Proceedings of the IFAC symposium on nonlinear control systems |
| [2] | Back, J.; Seo, J. H., Immersion of nonlinear systems into linear systems up to output injection: Characteristic equation approach, International Journal of Control, 77, 8, 723-734 (2004) · Zbl 1069.93006 |
| [3] | Bestle, D.; Zeitz, M., Canonical form observer for non-linear time-variable systems, International Journal of Control, 38, 419-431 (1983) · Zbl 0521.93012 |
| [4] | Bossane, D., Rakotopara, D., & Gauthier, J. P. (1989). Local and global immersion into linear systems up to output injection. In 28th IEEE conference on decision and control; Bossane, D., Rakotopara, D., & Gauthier, J. P. (1989). Local and global immersion into linear systems up to output injection. In 28th IEEE conference on decision and control |
| [5] | Charlet, B.; Lévine, J.; Marino, R., On dynamic feedback linearization, Systems & Control Letters, 13, 143-151 (1989) · Zbl 0684.93043 |
| [6] | Charlet, B.; Lévine, J.; Marino, R., Sufficient conditions for dynamic state feedback linearization, SIAM Journal on Control and Optimization, 29, 38-57 (1991) · Zbl 0739.93021 |
| [7] | Fliess, M.; Kupka, I., A finiteness criterion for nonlinear input-output differential systems, SIAM Journal on Control and Optimization, 21, 5, 721-728 (1983) · Zbl 0529.93031 |
| [8] | Guay, M., Observer linearization by output-dependent time-scale transformations, IEEE Transactions on Automatic Control, 47, 10, 1730-1735 (2002) · Zbl 1364.93087 |
| [9] | Hou, M.; Pugh, A. C., Observer with linear error dynamics for nonlinear multi-output systems, Systems & Control Letters, 37, 1-9 (1999) · Zbl 0917.93010 |
| [10] | Jouan, P., Immersion of nonlinear systems into linear systems modulo output injection, SIAM Journal on Control and Optimization, 41, 6, 1756-1778 (2003) · Zbl 1036.93006 |
| [11] | Keller, H., Non-linear observer design by transformation into a generalized observer canonical form, International Journal of Control, 46, 6, 1915-1930 (1987) · Zbl 0634.93012 |
| [12] | Krener, A. J.; Isidori, A., Linearization by output injection and nonlinear observers, Systems & Control Letters, 3, 47-52 (1983) · Zbl 0524.93030 |
| [13] | Krener, A. J.; Respondek, W., Nonlinear observers with linearizable error dynamics, SIAM Journal on Control and Optimization, 23, 2, 197-216 (1985) · Zbl 0569.93035 |
| [14] | Levine, J.; Marino, R., Nonlinear system immersion, observers and finite-dimensional filters, Systems & Control Letters, 7, 133-142 (1986) · Zbl 0592.93030 |
| [15] | Noh, D.; Jo, N. H.; Seo, J. H., Nonlinear observer design by dynamic observer error linearization, IEEE Transactions on Automatic Control, 49, 10, 1746-1750 (2004) · Zbl 1365.93060 |
| [16] | Phelps, A. R., On constructing nonlinear observers, SIAM Journal on Control and Optimization, 29, 516-534 (1991) · Zbl 0738.93032 |
| [17] | Plestan, F.; Glumineau, A., Linearization by generalized input-output injection, Systems & Control Letters, 31, 115-128 (1997) · Zbl 0901.93013 |
| [18] | Respondek, W.; Pogromsky, A.; Nijmeijer, H., Time scaling for observer design with linearizable error dynamics, Automatica, 40, 2, 277-285 (2004) · Zbl 1055.93010 |
| [19] | Xia, X.-H.; Gao, W.-B., Nonlinear observer design by observer error linearization, SIAM Journal on Control and Optimization, 27, 1, 199-216 (1989) · Zbl 0667.93014 |
| [20] | Yu, K. T., Back, J., & Seo, J. H. (2005). An algorithm for dynamic linearization by generalized output injection. In Proceedings of the CDC and ECC; Yu, K. T., Back, J., & Seo, J. H. (2005). An algorithm for dynamic linearization by generalized output injection. In Proceedings of the CDC and ECC |
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