adjoint

adjoint的音标是[ˌdʒeɪdʒɔɪnt]，基本翻译是“共有的；合有的；配偶的；联合的”，速记技巧是“adj+joint（连接）”。

adjoint这个词来源于拉丁语，意为“连接的，联合的”。它的变化形式包括过去式adjointed，过去分词adjointed，现在分词adjointing，形容词adjoint等。

相关单词：intersection（交集），join（连接），joint（连接处），adjunction（结合），adjoin（毗邻），junction（交汇点），adjoinism（毗邻主义），adjoinder（毗连物），adjunct（附属物），adjunctional（结合的）。

这些单词都与adjoint有着密切的联系，因为它们都表示与连接、联合、结合等概念相关的意思。例如，intersection表示交集，即两个集合之间的重叠部分；joint则表示连接处，即两个物体之间的连接部位。这些单词在英语中都得到了广泛的应用，反映了英语词汇的丰富性和多样性。

常用短语：

1. adjoint operator 共轭算子

2. adjoint matrix 共轭矩阵

3. adjoint operator method 共轭算子方法

4. adjoint state 共轭状态

5. adjoint equation 共轭方程

6. adjoint vector 共轭向量

7. adjoint system 共轭系统

双语例句：

1. The adjoint operator of the differential equation was solved to obtain the solution of the original equation. (解微分方程的共轭算子以获得原方程的解)

2. The adjoint matrix of the system was used to analyze its stability and robustness. (利用系统的共轭矩阵来分析它的稳定性和鲁棒性)

3. The adjoint state of the system was used to design optimal control strategies. (利用系统的共轭状态来设计最优控制策略)

4. The adjoint equation was solved to obtain the optimal control input for the system. (解共轭方程以获得系统的最优控制输入)

5. The adjoint vector of the system was used to compute the gradient of the cost function. (利用系统的共轭向量来计算成本函数的梯度)

6. The adjoint operator method was used to solve a complex optimization problem efficiently. (共轭算子方法被用于有效地解决一个复杂的优化问题)

7. The adjoint system of the system was used to design a feedback controller that achieves desired performance. (利用系统的共轭系统来设计一个反馈控制器以实现期望的性能)

英文小作文：

Title: Adjoint Operator and Its Applications in Control Systems

Adjoint operator plays an important role in control systems, which can be used to solve equations, analyze stability and robustness, design optimal control strategies, and compute gradients of cost functions. In this essay, we will introduce the definition and properties of adjoint operator, and discuss its applications in various control systems. Adjoint operator method is particularly useful for solving complex optimization problems efficiently, while adjoint state can be used to design feedback controllers that achieve desired performance. In conclusion, adjoint operator is a powerful tool in control systems that can be used to solve various problems in a systematic and effective way.