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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

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

Abstract

Takeover of the attitude control function of a failed spacecraft suffering from fuel exhaustion or actuator failures enables recycling of on-board valuable reusable payloads. Microsatellites can provide cost-efficient ways for the attitude takeover control through coordination. Differential games are used to study the individual optimal decision problem, where each player optimizes their local performance index function to obtain the control policy, and the game's predefined global objective can be achieved. In this paper, the failed spacecraft attitude takeover control problem is transformed into a multi-microsatellite differential game problem. First, the multi-microsatellite differential game model is established, the performance index function is designed for each microsatellite, and the mathematical description of the multi-microsatellite differential game problem is realized. Second, the Hamilton-Jacobi (HJ) equations are provided and solved through the single neural network (NN) based policy iteration (PI) algorithm to learn the multi-microsatellite game equilibrium control strategies. Finally, numerical simulations are carried out to validate the effectiveness of the multi-microsatellite differential game learning method. The results have shown that the predefined global objective of the takeover of the attitude control of the failed spacecraft can be realized through the approximate game equilibrium control strategies of multiple microsatellites.


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$\Psi_{21}$, $\Psi_{41}\in\mathbb{R}^{{N}\times{N}}$, $\Psi_{1}$, $\Psi_{22}$, $\Psi_{42}$, $\Psi_{5}$, $\Psi_{6}$, $\Psi_{71}\in\mathbb{R}^{{1}\times{N}}$, $\Psi_{72}\in\mathbb{R}$.


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