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首页> 外文期刊>Computational Optimization and Applications >Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using a Radau pseudospectral method
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Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using a Radau pseudospectral method

机译：使用Radau伪谱方法的有限水平和无限水平最优控制问题的直接轨迹优化和代价估计

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摘要

A method is presented for direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using global collocation at Legendre-Gauss-Radau (LGR) points. A key feature of the method is that it provides an accurate way to map the KKT multipliers of the nonlinear programming problem to the costates of the optimal control problem. More precisely, it is shown that the dual multipliers for the discrete scheme correspond to a pseudospectral approximation of the adjoint equation using polynomials one degree smaller than that used for the state equation. The relationship between the coefficients of the pseudospectral scheme for the state equation and for the adjoint equation is established. Also, it is shown that the inverse of the pseudospectral LGR differentiation matrix is precisely the matrix associated with an implicit LGR integration scheme. Hence, the method presented in this paper can be thought of as either a global implicit integration method or a pseudospectral method. Numerical results show that the use of LGR collocation as described in this paper leads to the ability to determine accurate primal and dual solutions for both finite and infinite-horizon optimal control problems.
机译：提出了一种在Legendre-Gauss-Radau（LGR）点上使用全局配置的有限水平和无限水平最优控制问题的直接轨迹优化和代价估计方法。该方法的关键特征是它提供了一种将非线性规划问题的KKT乘数映射到最优控制问题的代价的准确方法。更精确地，表明用于离散方案的对偶乘子对应于使用比用于状态方程式小一度的多项式的伴随方程式的伪谱近似。建立状态方程和伴随方程的伪谱方案的系数之间的关系。而且，示出了伪谱LGR微分矩阵的逆恰好是与隐式LGR积分方案相关联的矩阵。因此，本文提出的方法可以被认为是全局隐式积分方法或伪谱方法。数值结果表明，如本文所述，使用LGR配置可以为有限和无限水平的最优控制问题确定精确的原始和对偶解。

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