A simple and efficient algorithm for nonlinear model predictive control
A simple and efficient algorithm for nonlinear model predictive control
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一种简单高效的非线性模型预测控制算法
DOI：
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发表时间：
2017
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通讯作者：
Panagiotis Patrinos
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作者：
L. Stella;Andreas Themelis;Pantelis Sopasakis;Panagiotis Patrinos
我们提出了 PANOC，一种用于解决非线性模型预测控制 (NMPC) 中出现的最优控制问题的新算法。解决此类问题的常用方法是顺序二次规划 (SQP)，它需要在每次迭代时求解二次规划，因此需要内部迭代过程。因此，当问题是病态的或预测范围很大时，每次外部迭代的计算量都变得非常昂贵。我们提出了一种线搜索算法，该算法将前向-后向迭代（FB）和牛顿型步骤结合在最近引入的前向-后向包络（FBE）上，这是原始问题的连续、实值、精确的评价函数。牛顿型方法的曲率信息使得在极限点的温和假设下能够实现渐进超线性率，并且所提出的算法基于非常简单的操作：获取成本和动力学的一阶信息以及低成本直接线性代数。不需要内部迭代过程，也不需要 Hessian 评估，这使得我们的方法在计算上比 SQP 方法更简单。低内存需求和简单的实现使我们的方法特别适合嵌入式 NMPC 应用。
We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of a quadratic program at every iteration and, consequently, inner iterative procedures. As a result, when the problem is ill-conditioned or the prediction horizon is large, each outer iteration becomes computationally very expensive. We propose a line-search algorithm that combines forward-backward iterations (FB) and Newton-type steps over the recently introduced forward-backward envelope (FBE), a continuous, real-valued, exact merit function for the original problem. The curvature information of Newton-type methods enables asymptotic superlinear rates under mild assumptions at the limit point, and the proposed algorithm is based on very simple operations: access to first-order information of the cost and dynamics and low-cost direct linear algebra. No inner iterative procedure nor Hessian evaluation is required, making our approach computationally simpler than SQP methods. The low-memory requirements and simple implementation make our method particularly suited for embedded NMPC applications.