Bounded stabilisation of stochastic port-Hamiltonian systems. (English) Zbl 1317.93265
Summary: This paper proposes a stochastic bounded stabilisation method for a class of stochastic port-Hamiltonian systems. Both full-actuated and underactuated mechanical systems in the presence of noise are considered in this class. The proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability. The bounded region and achieving probability are both assignable, and a stochastic Lyapunov function is explicitly provided based on a Hamiltonian structure. Although many conventional stabilisation methods assume that the noise vanishes at the origin, the proposed method is applicable to systems under persistent disturbances.
MSC:
| 93E15 | Stochastic stability in control theory |
| 93E03 | Stochastic systems in control theory (general) |
| 70Q05 | Control of mechanical systems |
| 93C10 | Nonlinear systems in control theory |
Keywords:
stochastic stability; stochastic Hamiltonian systems; bounded stability; nonlinear stochastic controlReferences:
| [1] | DOI: 10.1109/9.100932 · Zbl 0758.93007 · doi:10.1109/9.100932 |
| [2] | DOI: 10.1109/9.746260 · Zbl 0958.93095 · doi:10.1109/9.746260 |
| [3] | DOI: 10.1109/9.940927 · Zbl 1008.93068 · doi:10.1109/9.940927 |
| [4] | DOI: 10.1007/978-3-662-00031-1 · doi:10.1007/978-3-662-00031-1 |
| [5] | DOI: 10.1137/S0363012995279961 · Zbl 0874.93092 · doi:10.1137/S0363012995279961 |
| [6] | DOI: 10.1137/S0363012997317478 · Zbl 0942.60052 · doi:10.1137/S0363012997317478 |
| [7] | DOI: 10.1016/S0167-6911(00)00091-8 · Zbl 1032.93007 · doi:10.1016/S0167-6911(00)00091-8 |
| [8] | Khalil H.K., Nonlinear systems, 3. ed. (1996) |
| [9] | Kushner H.J., Stochastic stability and control (1967) · Zbl 0244.93065 |
| [10] | DOI: 10.1155/2009/145213 · Zbl 1207.34074 · doi:10.1155/2009/145213 |
| [11] | DOI: 10.1007/s10255-007-7005-x · Zbl 1142.93034 · doi:10.1007/s10255-007-7005-x |
| [12] | Maschke B., Proceedings of the 2nd IFAC Symposium on Nonlinear Control Systems pp 282– (1992) |
| [13] | DOI: 10.1007/978-3-662-03620-4 · doi:10.1007/978-3-662-03620-4 |
| [14] | DOI: 10.1109/TAC.2002.800770 · Zbl 1364.93662 · doi:10.1109/TAC.2002.800770 |
| [15] | DOI: 10.1016/S0005-1098(01)00278-3 · Zbl 1009.93063 · doi:10.1016/S0005-1098(01)00278-3 |
| [16] | DOI: 10.1109/TAC.2012.2229791 · Zbl 1369.93581 · doi:10.1109/TAC.2012.2229791 |
| [17] | Satoh S., Proceedings of the 20th Symposium on Mathematical Theory of Networks and Systems (2012) |
| [18] | DOI: 10.1016/0167-6911(94)00050-6 · Zbl 0877.93121 · doi:10.1016/0167-6911(94)00050-6 |
| [19] | Thygesen U., A survey of Lyapunov techniques for stochastic differential equations (1997) |
| [20] | DOI: 10.1080/002071798221632 · Zbl 0953.93073 · doi:10.1080/002071798221632 |
| [21] | DOI: 10.1007/3-540-76074-1 · doi:10.1007/3-540-76074-1 |
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