线性二次型调节器算法研究

LQR 即线性二次型调节器，其对象是现代控制理论中以状态空间形式给出的线性系统,而目标函数为对象状态和控制输入的二次型函数。LQR的最优解可以写成统一的解析表达式， 且可导致一个简单的状态反馈控制律。线性二次型控制理论已成为反馈设计系统的一种重要工具， 其特点是：为多变量反馈系统的设计提供了一种有效地分析方法；它可以适应于时变系统；它可以处理扰动信号和测量噪声问题；它可以处理有限和无限的时间区间。在处理可精确数学描述的对象时取得了很大的成功。对研究无人机的自动飞行控制技术具有十分重要的现实意义。

Research on Linear Quadratic Regulator Algorithm

LQR is a linear quadratic regulator whose object is a linear system given in the form of state space in modern control theory, and the objective function is a quadratic function of the object state and control input. The optimal solution of LQR can be written as a unified analytical expression and can lead to a simple state feedback control law. Linear quadratic control theory has become an important tool for feedback design systems. It is characterized by an effective analysis method for the design of multivariable feedback systems and it can be adapted to time-varying systems and generate disturbance signals and solve measuring noise problems and finally it can handle finite and infinite time intervals.