在分布曲线控制中，传统的积分平方误差指标仅考虑输出曲线与目标曲线的误差面积，忽略了分布曲线的内在特征结构。该文从曲线相似度度量出发，提出了一种基于梯度特征的分布曲线模型预测控制算法。该算法采用B样条模型描述分布曲线对象，基于梯度特征度量曲线相似度，综合曲线数值信息与梯度信息构造优化命题，并通过复合梯形方法对优化命题进行离散化，求解得到最优控制策略。仿真结果表明：该算法可提高曲线切换过程中输出曲线与目标曲线的相似度，实现了曲线形状的自然过渡。
Abstract
In the control of distribution processes, the traditional integral square error performance index only considers the area between the output curve and the target curve, which ignores the structural features of the distribution curve. A gradient feature-based model predictive control algorithm that takes into account the curve similarities is developed for distribution processes. The algorithm first models the distribution process curve with B-splines. Then, the algorithm quantifies the similarity between the curves based on gradient features and optimizes the design by combining numerical and gradient information. The composite trapezoidal rule is then used to discretize the optimization proposition. Finally, the optimization proposition is solved to get the optimal solution. Simulations show that this algorithm improves the similarity between the output curve and the target curve during curve switching with natural transitions of the curve shape.
关键词
模型预测控制 /
分布曲线 /
曲线相似度 /
梯度特征
Key words
model predictive control /
distribution process /
curve similarity /
gradient feature
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基金
国家重点研发计划（2017YFB0603703）；国家自然科学基金-浙江两化融合联合基金项目（U1509209）；国家自然科学基金项目（61773340）；中央高校基本科研业务费专项（2018QNA5011）
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