|
|
Pure Mathematics 2024
基于几何QSR-耗散性和线性静态输出反馈控制器的非线性随机离散系统的几何镇定
|
Abstract:
本文研究了非线性随机离散系统的几何镇定问题。 首先，引入了非线性随机离散系统的几何随机增量QSR耗散的概念，并给出了该概念的线性矩阵不等式(LMI)表示形式；其次，基于几何随机 增量QSR耗散性和线性静态输出反馈控制器，提出了该系统的概率意义下的几何均方增量稳定的 充要条件。 最后，通过进行数值模拟，展示了所得结论的有效性。
In this paper, the geometric stabilization problem of nonlinear stochastic discrete-
time systems is studied. Firstly, the concept of geometric stochastic incremental
QSR dissipativity for nonlinear stochastic discrete-time systems is introduced, and
the expression of the concept of linear matrix inequality (LMI) is given. Secondly,
based on the geometric stochastic incremental QSR dissipativity and the linear static
output feedback controller, the sufficient and necessary conditions for the geometric
mean square incremental stability in probability of the system are proposed. Finally,
the validity of the results is demonstrated by numerical simulation.
| [1] | Brogliato, B., Lozano, R., Maschke, B. and Egeland, O. (2007) Dissipative Systems Analysis
and Control. Theory and Applications, 2, 2-5. https://doi.org/10.1007/978-1-84628-517-2 1 |
| [2] | Willems, J.C. (1972) Dissipative Dynamical Systems Part I: General Theory. Archive for Ra-
tional Mechanics and Analysis, 45, 321-351. https://doi.org/10.1007/BF00276493 |
| [3] | Willems, J.C. (1972) Dissipative Dynamical Systems Part II: Linear Systems with Quadratic
Supply Rates. Archive for Rational Mechanics and Analysis, 45, 352-393.
https://doi.org/10.1007/BF00276494 |
| [4] | Haddad, W. and Chellaboina, V. (2008) Nonlinear Dynamical Systems and Control: A
Lyapunov-Based Approach. Princeton University Press, Princeton.
https://doi.org/10.1515/9781400841042 |
| [5] | Rajpurohit, T. and Haddad, W.M. (2016) Dissipativity Theory for Nonlinear Stochastic Dy-
namical Systems. IEEE Transactions on Automatic Control, 62, 1684-1699.
https://doi.org/10.1109/TAC.2016.2598474 |
| [6] | Berman, N. and Shaked, U. (2006) H/sub/spl infin//Control for Discrete-Time Nonlinear
Stochastic Systems. IEEE Transactions on Automatic Control, 51, 1041-1046.
https://doi.org/10.1109/TAC.2006.876808 |
| [7] | Liu, T., Hill, D.J. and Zhao, J. (2015) Output Synchronization of Dynamical Networks with
Incrementally-Dissipative Nodes and Switching Topology. IEEE Transactions on Circuits and
Systems I: Regular Papers, 62, 2312-2323. https://doi.org/10.1109/TCSI.2015.2451891 |
| [8] | Aghannan, N. and Rouchon, P. (2003) An Intrinsic Observer for a Class of Lagrangian Systems.
IEEE Transactions on Automatic Control, 48, 936-945.
https://doi.org/10.1109/TAC.2003.812778 |
| [9] | Richter, J.H., Heemels, W.P.M.H., van de Wouw, N. and Lunze, J. (2011) Reconfigurable
Control of Piecewise Affine Systems with Actuator and Sensor Faults: Stability and Tracking.
Automatica, 47, 678-691. https://doi.org/10.1016/j.automatica.2011.01.048 |
| [10] | Madeira, D.D.S. (2021). Necessary and Sufficient Dissipativity-Based Conditions for Feedback
Stabilization. IEEE Transactions on Automatic Control, 67, 2100-2107.
https://doi.org/10.1109/TAC.2021.3074850 |
