论文标题
使用正交多项式的转向非语言集成器
Steering nonholonomic integrator using orthogonal polynomials
论文作者
论文摘要
我们考虑了最低的能量最佳控制问题，该问题与时间相关的Lagrangian在非单位集成符上，并使用Sturm-Liouville理论找到分析解决方案。此外，我们还考虑了Lie Group $ \ Mathbb {so}（3）$的最小能量问题，其依赖时间为Lagrangian。 我们表明，可以通过使用各种正交多项式的家族（例如Chebyshev，legendre和Jacobi多项式）来实现非方面集成商和广义的非世俗集成剂的转向，除了在文献中考虑了三角族的多项式。最后，我们展示了如何 当成本函数由输入的$ \ Mathcal {l} _1 $ norm for时，使用正交函数家族的元素查找次优输入。
We consider minimum energy optimal control problem with time dependent Lagrangian on the nonholonomic integrator and and find the analytical solution using Sturm-Liouville theory. Furthermore, we also consider the minimum energy problem on the Lie group $\mathbb{SO}(3)$ with time dependent Lagrangian. We show that the steering of nonholonomic integrator and generalized nonholonomic integrator can be achieved by using various families of orthogonal polynomials such as Chebyshev, Legendre and Jacobi polynomials apart from trigonometric polynomials considered in the literature. Finally, we show how to find sub-optimal inputs using elements from a family of orthogonal functions when the cost function is given by the $\mathcal{L}_1$ norm of the input.
