logo

SCIENTIA SINICA Informationis, Volume 50 , Issue 4 : 588-602(2020) https://doi.org/10.1360/N112019-00049

Differential game learning approach for multiple microsatellites takeover of the attitude movement of failed spacecraft

More info
  • ReceivedFeb 28, 2019
  • AcceptedJun 5, 2019
  • PublishedApr 8, 2020

Abstract


Funded by

深圳科创委基金项目(JCYJ20180508151938535)

国家自然科学基金重大项目(61690210,61690211)

西北工业大学博士论文创新基金项目(CX201803)


Supplement

Appendix

可调系数

\begin{align*}&\Psi_{1}=\left[\begin{matrix}-\textstyle\theta_{1m}^{2} \cdots -\textstyle\theta_{Nm}^{2}\end{matrix}\right], \Psi_{21}=\begin{bmatrix} \frac{\lambda_{DM11}^{2}}{2\psi_{121}^{2}}&\cdots &\frac{\lambda_{DM1N}^{2}}{2\psi_{12N}^{2}} \\ \vdots& &\vdots \\ \frac{\lambda_{DMN1}^{2}}{2\psi_{N21}^{2}}&\cdots &\frac{\lambda_{DMNN}^{2}}{2\psi_{N2N}^{2}}\end{bmatrix}, \Psi_{22}=\begin{bmatrix}\textstyle{\sum_{j=1}^{N} \frac{\psi_{12j}^{2}\theta_{1M}^{2}}{2}} \cdots \textstyle{\sum_{j=1}^{N} \frac{\psi_{N2j}^{2}\theta_{NM}^{2}}{2}}\end{bmatrix}, \\ &\Psi_{41}=\begin{bmatrix} &\textstyle{\sum_{j=1}^{N} \frac{\lambda_{EMj1}^{2}}{32\psi_{j41}^{2}}}& & \\ & &\ddots & \\ & & &\textstyle{\sum_{j=1}^{N} \frac{\lambda_{EMjN}^{2}}{32\psi_{j4N}^{2}}}\end{bmatrix}, \Psi_{42}=\begin{bmatrix}\textstyle{\sum_{j=1}^{N} \frac{\psi_{14j}^{2}b_{1M}^{2}}{2}} \cdots \textstyle{\sum_{j=1}^{N} \frac{\psi_{N4j}^{2}b_{NM}^{2}}{2}}\end{bmatrix}, \\ &\Psi_{5}=\begin{bmatrix}\textstyle{\sum_{j=1}^{N} \frac{\psi_{15j}^{2}b_{1M}^{2}}{2}} \cdots \textstyle{\sum_{j=1}^{N} \frac{\psi_{N5j}^{2}b_{NM}^{2}}{2}}\end{bmatrix}+\begin{bmatrix}\textstyle{\sum_{j=1}^{N} \frac{b_{Dj1}^{2}}{8\psi_{j51}^{2}}} \cdots \textstyle{\sum_{j=1}^{N} \frac{b_{DjN}^{2}}{8\psi_{j5N}^{2}}}\end{bmatrix}, \\ &\Psi_{6}=\begin{bmatrix}\textstyle{\sum_{j=1}^{N} \frac{\psi_{16j}^{2}b_{1M}^{2}}{2}} \cdots \textstyle{\sum_{j=1}^{N} \frac{\psi_{N6j}^{2}b_{NM}^{2}}{2}}\end{bmatrix}+\begin{bmatrix}\textstyle{\sum_{j=1}^{N} \frac{b_{Ej1}^{2}}{8\psi_{j61}^{2}}} \cdots \textstyle{\sum_{j=1}^{N} \frac{b_{EjN}^{2}}{8\psi_{j6N}^{2}}}\end{bmatrix}, \\ &\Psi_{71}=\begin{bmatrix} \frac{\psi_{17}^{2}b_{1M}^{2}}{2} \cdots \frac{\psi_{N7}^{2}b_{NM}^{2}}{2}\end{bmatrix}, \Psi_{72}=\sum_{i=1}^{N} \frac{b_{e_{Hi}}^{2}}{2\psi_{i7}^{2}}, \end{align*} 其中$\Psi_{21}$, $\Psi_{41}\in\mathbb{R}^{{N}\times{N}}$, $\Psi_{1}$, $\Psi_{22}$, $\Psi_{42}$, $\Psi_{5}$, $\Psi_{6}$, $\Psi_{71}\in\mathbb{R}^{{1}\times{N}}$, $\Psi_{72}\in\mathbb{R}$.


References

[1] Zhai G, Zhang J R, Zhou Z C. A review of on-orbit life-time extension technologies for GEO satellites. Journal of Astronautics, 2012, 33: 849--859 DOI: 10.3873/j.issn.1000-1328.2012.07.001. Google Scholar

[2] Huang P F, Wang M, Chang H T, et al. Takeover control of attitude maneuver for failed spacecraft. Journal of Astronautics, 2016, 37: 924--935 DOI: 10.3873/j.issn.1000-1328.2016.08.005. Google Scholar

[3] Wang Z, Yuan J, Shi Y. Robust adaptive fault tolerant attitude control for post-capture non-cooperative targets with actuator nonlinearities. Trans Institute Measurement Control, 2018, 40: 2116-2128 CrossRef Google Scholar

[4] Chang H T, Huang P F, Wang M, et al. Distributed control allocation for cellular space robots in takeover control. Acta Aeronaut et Astronaut Sin, 2016, 37: 2864--2873. Google Scholar

[5] Jaeger T, Mirczak W. Satlets - The building blocks of future satellites - and which mold do you use? In: Proceedings of AIAA SPACE 2013 Conference and Exposition, San Diego, 2013. Google Scholar

[6] Goeller M, Oberlaender J, Uhl K, et al. Modular robots for on-orbit satellite servicing. In: Proceedings of IEEE International Conference on Robotics and Biomimetics, Guangzhou, 2012. 2018--2023. Google Scholar

[7] Xue L, Wang Q L, Sun C Y. Game theoretical approach for the leader selection of the second-order multi-agent system. Control Theory Appl, 2016, 33: 1593--1602. Google Scholar

[8] Lin W. Distributed UAV formation control using differential game approach. Aerospace Sci Tech, 2014, 35: 54-62 CrossRef Google Scholar

[9] Vamvoudakis K G, Lewis F L, Hudas G R. Multi-agent differential graphical games: Online adaptive learning solution for synchronization with optimality. Automatica, 2012, 48: 1598-1611 CrossRef Google Scholar

[10] Abouheaf M I, Lewis F L, Vamvoudakis K G. Multi-agent discrete-time graphical games and reinforcement learning solutions. Automatica, 2014, 50: 3038-3053 CrossRef Google Scholar

[11] Ru C J, Wei R X, Guo Q, et al. Guidance control of cognitive game for unmanned aerial vehicleautonomous collision avoidance. Control Theory & Applications, 2014, 31: 1555--1560. Google Scholar

[12] Bopardikar S D, Bullo F, Hespanha J P. On Discrete-Time Pursuit-Evasion Games With Sensing Limitations. IEEE Trans Robot, 2008, 24: 1429-1439 CrossRef Google Scholar

[13] Blasch E P, Pham K, Shen D. Orbital satellite pursuit-evasion game-theoretical control. In: Proceedings of the 11th International Conference on Information Science, Signal Processing and their Applications, Montreal, 2012. 1007--1012. Google Scholar

[14] Vamvoudakis K G, Lewis F L. Multi-player non-zero-sum games: Online adaptive learning solution of coupled Hamilton-Jacobi equations. Automatica, 2011, 47: 1556-1569 CrossRef Google Scholar

[15] Liu D, Li H, Wang D. Online Synchronous Approximate Optimal Learning Algorithm for Multi-Player Non-Zero-Sum Games With Unknown Dynamics. IEEE Trans Syst Man Cybern Syst, 2014, 44: 1015-1027 CrossRef Google Scholar

[16] Vamvoudakis K G. Non-zero sum Nash Q-learning for unknown deterministic continuous-time linear systems. Automatica, 2015, 61: 274-281 CrossRef Google Scholar

[17] Schaub H, Junkins J L. Analytical mechanics of space systems. In: Proceedings of AIAA Education Series, Reston, 2003. 107--142. Google Scholar