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首页> 外文期刊>Journal of Spacecraft and Rockets >Exploiting Sparsity in Direct Collocation Pseudospectral Methods for Solving Optimal Control Problems
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Exploiting Sparsity in Direct Collocation Pseudospectral Methods for Solving Optimal Control Problems

机译：在直接配置伪谱方法中利用稀疏性来解决最优控制问题

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摘要

In a direct collocation pseudospectral method, a continuous-time optimal control problem is transcribed to a finite-dimensional nonlinear programming problem. Solving this nonlinear programming problem as efficiently as possible requires that sparsity at both the first- and second-derivative levels be exploited. In this paper, a computationally efficient method is developed for computing the first and second derivatives of the nonlinear programming problem functions arising from a pseudospectral discretization of a continuous-time optimal control problem. Specifically, in this paper, expressions are derived for the objective function gradient, constraint Jacobian, and Lagrangian Hessian arising from the previously developed Radau pseudospectral method. It is shown that the computation of these derivative functions can be reduced to computing the first and second derivatives of the functions in the continuous-time optimal control problem. As a result, the method derived in this paper reduces significantly the amount of computation required to obtain the first and second derivatives required by a nonlinear programming problem solver. The approach derived in this paper is demonstrated on an example where it is found that significant computational benefits are obtained when compared against direct differentiation of the nonlinear programming problem functions. The approach developed in this paper improves the computational efficiency of solving nonlinear programming problems arising from pseudospectral discretizations of continuous-time optimal control problems.
机译：在直接配置伪谱方法中，将连续时间最优控制问题转化为有限维非线性规划问题。尽可能有效地解决此非线性规划问题，需要利用一阶和二阶导数级的稀疏性。在本文中，开发了一种计算有效的方法，用于计算由连续时间最优控制问题的伪谱离散化引起的非线性规划问题函数的一阶和二阶导数。具体而言，在本文中，从先前开发的Radau伪谱方法中导出了目标函数梯度，约束Jacobian和Lagrangian Hessian的表达式。结果表明，在连续时间最优控制问题中，这些导数函数的计算可以简化为计算函数的一阶和二阶导数。结果，本文得出的方法大大减少了获得非线性编程问题求解器所需的一阶和二阶导数所需的计算量。本文得出的方法在一个示例中得到了证明，该示例发现与非线性编程问题函数的直接微分相比，可以获得显着的计算优势。本文开发的方法提高了解决由连续时间最优控制问题的伪谱离散化引起的非线性规划问题的计算效率。

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