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首页> 外文期刊>Automatica Sinica, IEEE/CAA Journal of >Direct trajectory optimization and costate estimation of infinite-horizon optimal control problems using collocation at the flipped legendre-gauss-radau points
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Direct trajectory optimization and costate estimation of infinite-horizon optimal control problems using collocation at the flipped legendre-gauss-radau points

机译：使用翻转后的Legendre-Gauss-radau点处的搭配，对无限水平最优控制问题进行直接轨迹优化和代价估计

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摘要

A pseudospectral method is presented for direct trajectory optimization and costate estimation of infinite-horizon optimal control problems using global collocation at flipped Legendre-Gauss-Radau points which include the end point +1. A distinctive feature of the method is that it uses a new smooth, strictly monotonically decreasing transformation to map the scaled left half-open interval τ ϵ (-1, +1] to the descending time interval t ϵ (+∞, 0]. As a result, the singularity of collocation at point +1 associated with the commonly used transformation, which maps the scaled right half-open interval τ ϵ [-1, +1) to the increasing time interval [0,+∞), is avoided. The costate and constraint multiplier estimates for the proposed method are rigorously derived by comparing the discretized necessary optimality conditions of a finite-horizon optimal control problem with the Karush-Kuhn-Tucker conditions of the resulting nonlinear programming problem from collocation. Another key feature of the proposed method is that it provides highly accurate approximation to the state and costate on the entire horizon, including approximation at t = +∞, with good numerical stability. Numerical results show that the method presented in this paper leads to the ability to determine highly accurate solutions to infinite-horizon optimal control problems.
机译：提出了一种伪谱方法，用于在倒立的Legendre-Gauss-Radau点（包括端点+1）处使用全局配置，对无限水平最优控制问题进行直接轨迹优化和代价估计。该方法的显着特征是它使用新的，严格单调递减的变换将比例缩放后的左半开间隔τϵ（-1，+1]映射到下降时间间隔t ϵ（+∞，0]。结果，与常用变换相关联的点奇异点为+1，该映射将缩放后的右半开间隔τϵ [-1，+1）映射到增加的时间间隔[0，+∞）。避免。通过将有限水平最优控制问题的离散必要最优条件与并置产生的非线性规划问题的Karush-Kuhn-Tucker条件进行比较，可以严格得出所提出方法的代价和约束乘数估计。所提出方法的另一个关键特征是，它提供了整个状态下状态和代价的高度精确的近似值，包括在t = +∞处的近似值，并且具有良好的数值稳定性。数值结果表明，本文提出的方法具有确定无限水平最优控制问题的高精度解决方案的能力。

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