A generalization of the Riccati recursion for equality‐constrained linear quadratic optimal control

Lander Vanroye, Joris De Schutter, Wilm Decré
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引用次数: 2

Abstract

Abstract This paper introduces a generalization of the well‐known Riccati recursion for solving the discrete‐time equality‐constrained linear quadratic optimal control problem. The recursion can be used to compute problem solutions as well as optimal feedback control policies. Unlike other tailored approaches for this problem class, the proposed method does not require restrictive regularity conditions on the problem. This allows its use in nonlinear optimal control problem solvers that use exact Lagrangian Hessian information. We demonstrate that our approach can be implemented in a highly efficient algorithm that scales linearly with the horizon length. Numerical tests show a significant speed‐up of about one order of magnitude with respect to state‐of‐the‐art general‐purpose sparse linear solvers. Based on the proposed approach, faster nonlinear optimal control problem solvers can be developed that are suitable for more complex applications or for implementations on low‐cost or low‐power computational platforms. The implementation of the proposed algorithm is made available as open‐source software.

Abstract Image

等式约束线性二次最优控制的Riccati递推推广
摘要介绍了Riccati递推的推广,用于求解离散时间等式约束线性二次型最优控制问题。递归可以用来计算问题的解以及最优反馈控制策略。与针对这类问题的其他定制方法不同,所提出的方法不需要问题的限制性规则条件。这允许它在使用精确拉格朗日黑森信息的非线性最优控制问题求解中使用。我们证明了我们的方法可以在一个高效的算法中实现,该算法与视界长度线性扩展。数值测试表明,相对于最先进的通用稀疏线性解算器,速度显著提高了约一个数量级。基于所提出的方法,可以开发出更快的非线性最优控制问题求解器,适用于更复杂的应用或在低成本或低功耗计算平台上实现。所提出的算法的实现作为开源软件提供。
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