Guaranteed Pseudospectral Sequential Convex Programming for Accurate Solutions to Constrained Optimal Control Problems

IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS
Keitaro Yamamoto;Kenji Fujimoto;Ichiro Maruta
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引用次数: 0

Abstract

This letter proposes an algorithm for solving finite-time nonlinear optimal control problems. The proposed method employs the Gauss pseudospectral method to transform the optimal control problem into a nonlinear programming problem, and sequential convex programming (SCP) to solve it. Furthermore, by applying the information of the solution obtained by SCP to the indirect shooting method, a more accurate optimal solution can be obtained. There was an attempt to solve a similar class of optimal control problems, but it was only applicable to a restrictive class of problems without state constraints. In contrast, the proposed method can solve a general class of optimal control problems, including those with state constraints, while ensuring the numerical stability of the algorithm. This objective is achieved without losing the numerical stability of the algorithm by introducing a slack variable and incorporating state constraints into the dynamics. Additionally, the proposed method guarantees quadratic convergence by appropriately limiting the update step size of the optimization variables. To demonstrate the effectiveness of the proposed method, we apply the proposed method to an $L^{1}/L^{2}$ -optimal control problem of a two-wheeled rover.
保证伪谱序列凸编程,精确解决受限最优控制问题
本文提出了一种求解有限时间非线性最优控制问题的算法。该方法利用高斯伪谱法将最优控制问题转化为非线性编程问题,并利用顺序凸编程(SCP)对其进行求解。此外,通过将 SCP 得到的解的信息应用于间接射击法,可以得到更精确的最优解。曾有人尝试求解类似的最优控制问题,但只适用于无状态约束的限制性问题。相比之下,所提出的方法可以解决一般类型的最优控制问题,包括有状态约束的问题,同时确保算法的数值稳定性。通过引入一个松弛变量并将状态约束纳入动力学,可以在不损失算法数值稳定性的情况下实现这一目标。此外,所提出的方法通过适当限制优化变量的更新步长,保证了二次收敛。为了证明所提方法的有效性,我们将所提方法应用于双轮漫游车的$L^{1}/L^{2}$最优控制问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
IEEE Control Systems Letters
IEEE Control Systems Letters Mathematics-Control and Optimization
CiteScore
4.40
自引率
13.30%
发文量
471
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