MPC on manifolds with an application to the control of spacecraft attitude on SO(3)

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• 作者：Uro&scaron ; V. Kalabić^a ; ¹ ; ^{kalabic@umich.edu}Author Vitae ; Rohit Gupta^a ; ^{rohitgpt@umich.edu}Author Vitae ; Stefano Di Cairano^b ; ^{dicairano@ieee.org}Author Vitae ; Anthony M. Bloch^c ; ^{abloch@umich.edu}Author Vitae ; Ilya V. Kolmanovsky^a ; ^{ilya@umich.edu}Author Vitae
• 关键词：Model predictive control ; Geometric control ; Manifolds ; Lie groups ; Spacecraft attitude
• 刊名：Automatica
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：76
• 期：Complete
• 页码：293-300
• 全文大小：789 K
• 卷排序：76

文摘

We develop a model predictive control (MPC) design for systems with discrete-time dynamics evolving on smooth manifolds. We show that the properties of conventional MPC for dynamics evolving on RnRn are preserved and we establish a design procedure for achieving similar properties. We also demonstrate that for discrete-time dynamics on manifolds with Euler characteristic not equal to 1, there do not exist globally stabilizing, continuous control laws. The MPC law is able to achieve global asymptotic stability on these manifolds, because the MPC law may be discontinuous. We apply the method to spacecraft attitude control, where the spacecraft attitude evolves on the Lie group SO(3) and for which a continuous globally stabilizing control law does not exist. In this case, the MPC law is discontinuous and achieves global stability.