The purpose of self-optimizing control (SOC) is minimizing the steady-state economic loss of chemical processes in the presence of disturbances and measurement noises by keeping selected controlled variables (CVs) at constant set-points. In self-optimizing control, by defining a desired objective/loss function and selecting the appropriate combination of process measurements, the average loss, the worst-case loss, or both can be minimized. In general, the optimization problem of self-optimizing control is a non-convex problem and there exist some approaches to change it to a convex form by adding another constraint to the optimization problem, using branch and bound algorithm or mixed integer quadratic programming method to solve the SOC problem. Linear Matrix Inequalities (LMIs) are one of the popular and powerful tools to solve convex optimization problems and changing the optimization problems to the LMI form is gaining popularity. In parallel, for some problems that are non-convex and cannot be transformed to the LMI form, Bilinear Matrix Inequalities (BMI) have been developed. In this paper, we present; first a method to change the convex form of SOC problem to the LMI form and second, reformulate the main and non-convex SOC problem to a BMI form and then change it to the LMI form. The proposed methods are then evaluated on three benchmark processes: a binary distillation column, an evaporator, and a Kaibel column. The LMI/BMI methods are implemented using LMI Control Toolbox and PENBMI of YALMIP toolbox of MATLAB ® software. Results show that the proposed algorithm outperforms other methods in the case of structured measurement matrix H. The main benefit of LMI approach is that the desired structure of matrix H can be directly implemented in the optimization method.

自优化控制 (SOC) 的目的是通过将选定的受控变量 (CV) 保持在恒定的设定点，在存在干扰和测量噪声的情况下最大限度地减少化学过程的稳态经济损失。在自优化控制中，通过定义所需的目标/损失函数并选择适当的过程测量组合，可以最小化平均损失、最坏情况损失或两者。一般来说，自优化控制的优化问题是一个非凸问题，有一些方法可以通过在优化问题上增加另一个约束，使用分支定界算法或混合整数二次规划方法将其变为凸形式。解决SOC问题。线性矩阵不等式 (LMI) 是解决凸优化问题的流行且强大的工具之一，将优化问题转换为 LMI 形式越来越受欢迎。同时，对于一些非凸的且不能转化为LMI形式的问题，已经开发了双线性矩阵不等式（BMI）。在本文中，我们提出；首先是一种将 SOC 问题的凸形式转换为 LMI 形式的方法，其次，将主要和非凸 SOC 问题重新表述为 BMI 形式，然后将其转换为 LMI 形式。然后在三个基准过程上评估所提出的方法：二元蒸馏塔、蒸发器和 Kaibel 塔。LMI/BMI 方法是使用 MATLAB® 软件的 YALMIP 工具箱的 LMI 控制工具箱和 PENBMI 实现的。H。LMI 方法的主要好处是矩阵H的期望结构可以直接在优化方法中实现。