Intrinsic Optimal Control for Mechanical Systems on Lie Group

Chao Liu, Shengjing Tang and Jie Guo

Advances in Mathematical Physics, 2017, vol. 2017, 1-8

Abstract:

The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on , the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:6302430

DOI: 10.1155/2017/6302430

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