Observer design and state-feedback stabilization for nonlinear systems via equilibrium manifold expansion linearization. (English) Zbl 07902961
Summary: Linearization remodeling and state-feedback control for a class of autonomous nonlinear systems based on equilibrium manifold expansion (EME) are visited and explicated in this paper, including linearization approximation, state-feedback stabilization and state estimation. More precisely, firstly, EME linearized remodels of nonlinear systems are explained and their existence is validated rigorously; secondly, EME-based state-feedback control and observer design are developed analytically with EME remodeling and gain scheduling; thirdly, stabilization under EME-based state feedback and observers are tackled, respectively; finally, feasibility and efficiency of the EME approach are illustrated by numerical simulations.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93B53 | Observers |
| 93C10 | Nonlinear systems in control theory |
| 93B18 | Linearizations |
References:
| [1] | Rugh, WJ; Shamma, JS, Research on gain scheduling, Automatica, 32, 10, 1401-1425, 2000 · Zbl 0976.93002 · doi:10.1016/S0005-1098(00)00058-3 |
| [2] | Coutinho, PHS; Palhares, M., Codesign of dynamic event-triggered gain-scheduling control for a class of nonlinear systems, IEEE Trans. Autom. Control, 67, 8, 4186-4193, 2022 · Zbl 1537.93463 · doi:10.1109/TAC.2021.3108498 |
| [3] | Shi, KH; Petersen, IR; Vladimirov, IG, Making nonlinear systems negative imaginary via state feedback, Automatica, 155, 111127, 2023 · Zbl 1520.93407 · doi:10.1016/j.automatica.2023.111127 |
| [4] | Baumann, WT; Rugh, WJ, Feedback control of nonlinear systems by extended linearization, IEEE Trans. Autom. Control, 31, 1, 40-46, 1986 · Zbl 0582.93031 · doi:10.1109/TAC.1986.1104100 |
| [5] | Baumann, WT; Rugh, WJ, Feedback control of analytic nonlinear systems by extended linearization, SIAM J. Control. Optim., 25, 5, 1341-1352, 1987 · Zbl 0631.93029 · doi:10.1137/0325073 |
| [6] | Baumann, WT, Feedback control of multiinput nonlinear systems by extended linearization, IEEE Trans. Autom. Control, 33, 2, 193-197, 1988 · Zbl 0633.93032 · doi:10.1109/9.389 |
| [7] | Yu, DR; Sui, YF, Expansion model based on equilibrium manifold for nonlinear systems, J. Syst. Simul., 18, 9, 2415-2418, 2006 |
| [8] | Chen, C.; Zhao, J., Switching control of acceleration and safety protection for turbo fan aero-engines based on equilibrium manifold expansion model, Asian J Control, 20, 5, 1689-1700, 2018 · Zbl 1407.93157 · doi:10.1002/asjc.1745 |
| [9] | Zhu, LH; Liu, JF; Ma, YJ; Zhou, WX; Yu, DR, A corrected equilibrium manifold expansion model for gas turbine system simulation and control, Energies, 13, 18, 4904-4904, 2020 · doi:10.3390/en13184904 |
| [10] | Rotondo, D.; Ponsart, J.; Theilliol, D., Gain-scheduled observer-based consensus for linear parameter varying multi-agent systems, Automatica, 135, 109979, 2022 · Zbl 1478.93641 · doi:10.1016/j.automatica.2021.109979 |
| [11] | Arezki, H.; Zemouche, A.; Bedouhene, F.; Alessandri, A.; Laleg-Kirati, MT, State observer design method for a class of nonlinear systems, IFAC-Papers OnLine, 53, 2, 4935-4940, 2020 · doi:10.1016/J.IFACOL.2020.12.1074 |
| [12] | Venkateswaran, S.; Kravaris, C., Design of linear unknown input observers for sensor fault estimation in nonlinear systems, Automatica, 155, 111152, 2023 · Zbl 1520.93557 · doi:10.1016/j.automatica.2023.111152 |
| [13] | Khalil, H., Nonlinear Systems, 2000, New Jersey: Pearson Education International Inc, New Jersey |
| [14] | Chen, WH, An Introduction to Differentiable Manifold, 1998, Beijing: Advanced Education Press Inc, Beijing |
| [15] | Rong, PX; Lu, N.; Lu, HL, Certificated method of the unity of bass-Gura, Ackerman and controllable standard form formulas, J. Harbin Univ. Sci. Technol., 01, 4, 22-24, 1999 |
| [16] | Mathematical Sciences, E.C.N.U. (ed.): Mathematical Analysis. Advanced Education Press Inc, Beijing (2018) |
| [17] | Chen, C., Linear System Theory and Design, 1999, New York: Oxford University Press, New York |
| [18] | Oleinik, OA, Lecure of Partial Differential Equations, 2008, Beijing: Advanced Education Press Inc, Beijing · Zbl 1234.35004 |
| [19] | Sadamatsu, T., On the Cauchy-Kowalewski theorem for general system of differential equations, J. Math. Kyoto Univ., 24, 4, 593-609, 1984 · Zbl 0575.35002 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
