1. 状态空间建模
状态空间方程是现代控制理论的基础，用一阶微分方程组描述系统的内部动态。对于一个线性时不变（LTI）系统，其状态空间模型为：
$$\begin{aligned}
\dot{x}(t) &= A x(t) + B u(t) \quad &\text{(状态方程)} \\
y(t) &= C x(t) + D u(t) \quad &\text{(输出方程)}
\end{aligned}
$$其中：
$x(t) \in \mathbb{R}^n$：状态向量(系统内部变量)
$u(t) \in \mathbb{R}^m$：输
2025-12-066.2k 字39 分钟
C++ Practical Advanced Topics
ref: https://github.com/0voice/cpp-learning-2025
The Practical Advanced Topics section focuses on the core competencies of C++ engineering development, covering four key modules: Design Patterns, Multithreaded Programming, Performance Optimization, and Engineering Practices. It helps developers prog
2025-12-055.1k 字33 分钟
C++ Object-Oriented Programming
ref: https://github.com/0voice/cpp-learning-2025
I. Classes and Objects
1. Class vs. Struct
In C++, class and struct are the core constructs for object-oriented programming. Their only essential difference is the default access control, as their syntax is nearly identical:
Feature
class
struct
2025-12-047.4k 字47 分钟
C++ Advanced Fundamentals
ref: https://github.com/0voice/cpp-learning-2025
I. STL (Standard Template Library)
The STL (Standard Template Library) is a core C++ library that encapsulates common data structures (containers) and algorithms, following the “generic programming” paradigm. It is a high-frequency topic in technical
2025-12-033.7k 字24 分钟
C++ Basic Syntax Guide
ref: https://github.com/0voice/cpp-learning-2025
I. Variables and Data Types
1. Basic Data Types
C++ provides fundamental data types to store different kinds of data for various scenarios:
Type Category
Specific Type
Description
Example
Integer
int
Basic integer (typically 4 bytes)
int age
2025-12-02795 字5 分钟
Convex Optimization Notes
1. Duality
1.1 Lagrangian and Dual Function
Lagrangian for a primal problem:$$L(x, \lambda, \nu) = f_0(x) + \sum_{i=1}^m \lambda_i f_i(x) + \sum_{i=1}^p \nu_i h_i(x)
$$
Dual function:$$g(\lambda, \nu) = \inf_{x \in D} L(x, \lambda, \nu)
$$
Always concave (regardless of convexi
