Fast quadratic model predictive control based on sensitivity analysis and Wolfe method

IF 2.2 4区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

IET Control Theory and Applications Pub Date : 2024-04-14 DOI:10.1049/cth2.12642

Hamid Kalantari, Mohsen Mojiri, Javad Askari, Najmeh Zamani

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Abstract

This paper proposes a new algorithm based on sensitivity analysis and the Wolfe method to solve a sequence of parametric quadratic programming (QP) problems such as those that arise in quadratic model predictive control (QMPC). The Wolfe method, based on Karush–Kuhn–Tucker conditions, has been used to convert parametric QP problems to parametric linear programming (LP) problems, and then the sensitivity analysis is applied to solve the sequence of the parametric LP problems. This strategy obtains sensitivity analysis-based QMPC (SA-QMPC) algorithm. It is proved that the computational complexity of SA-QMPC is $O (N n^{2})$ for a region of the initial conditions and $O (N^{2} n^{2})$ for sufficiently small sampling time and all initial conditions, where $N$ and $n$ are the horizon time and dimension of the state vector, respectively. Numerical results indicate the potential and properties of the proposed algorithm.

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基于灵敏度分析和沃尔夫法的快速二次模型预测控制

本文提出了一种基于灵敏度分析和沃尔夫法的新算法，用于求解参数二次编程（QP）问题序列，如二次模型预测控制（QMPC）中出现的问题。Wolfe 方法基于 Karush-Kuhn-Tucker 条件，用于将参数 QP 问题转换为参数线性规划（LP）问题，然后应用灵敏度分析来求解参数 LP 问题序列。这种策略得到了基于灵敏度分析的 QMPC（SA-QMPC）算法。研究证明，SA-QMPC 的计算复杂度是在初始条件区域内，以及在足够小的采样时间和所有初始条件下的计算复杂度。数值结果表明了所提算法的潜力和特性。

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来源期刊

IET Control Theory and Applications 工程技术-工程：电子与电气

CiteScore

5.70

自引率

7.70%

发文量

167

审稿时长

5.1 months

期刊介绍： IET Control Theory & Applications is devoted to control systems in the broadest sense, covering new theoretical results and the applications of new and established control methods. Among the topics of interest are system modelling, identification and simulation, the analysis and design of control systems (including computer-aided design), and practical implementation. The scope encompasses technological, economic, physiological (biomedical) and other systems, including man-machine interfaces. Most of the papers published deal with original work from industrial and government laboratories and universities, but subject reviews and tutorial expositions of current methods are welcomed. Correspondence discussing published papers is also welcomed. Applications papers need not necessarily involve new theory. Papers which describe new realisations of established methods, or control techniques applied in a novel situation, or practical studies which compare various designs, would be of interest. Of particular value are theoretical papers which discuss the applicability of new work or applications which engender new theoretical applications.