Numerical Approach to Computing Nonlinear H-Infinite Control Laws

这个小企业创新研究第一阶段项目旨在开发一种高效的算法来近似计算非线性H(控制律)。非线性H(控制律)的设计归结为求解两个Hamilton-Jacobi-lsaacs(HJI)方程，这是代数Ricatti方程的推广。由于它们的非线性性质，几乎不可能得到HJI方程的闭合解。提出了一种新的求解HJI方程数值解的算法和数据结构。假设HJI方程的解为泰勒级数形式，该算法将通过迭代求解一个代数Ricatti方程和一系列线性代数方程来获得泰勒级数的系数。美国GNC公司的方法是有史以来第一次提供系统的程序来近似求解HJI方程。这个过程可以很容易地用常规的计算机语言和软件包来实现。他们的方法可能是使非线性H(控制)成为实用设计工具的唯一可行方法，并可广泛应用于控制高度不确定的非线性系统，如高性能导弹和/或飞机系统、高精度机器人操作手和大型机动航天器。通过在实时控制/仿真环境下的高性能导弹自动驾驶仪设计实验，验证了该方法的有效性。

This Small Business Innovation Research Phase I project aims to develop an efficient algorithm for approximately computing nonlinear H( control laws. The design of a nonlinear H( control law is reduced to solving two Hamilton-Jacobi-lsaacs (HJI) equations, an extension of the algebraic Ricatti equation. Due to their nonlinear nature, it is almost impossible to obtain the closed-form solution of the HJI equations. An innovative algorithm and data structure is proposed to find a numerical solution of the HJI equations. Assuming the solution of the HJI equation in the Taylor series form, this algorithm will obtain the coefficients of the Taylor series by iteratively solving an algebraic Ricatti equation and a sequence of linear algebraic equations. American GNC Corporation's approach is the first-ever effort for providing a systematic procedure to approximately solve the HJI equations. This procedure can be easily implemented in routine computer languages and software packages. Their approach may be the only feasible method for making the nonlinear H( control a practical design tool and can find a wide range of applications for controlling highly uncertain nonlinear systems such as high performance missile and/or aircraft systems, high accuracy robot manipulators, and large maneuvering spacecraft. The effectiveness of the proposed approach will be illustrated by a high performance missile autopilot design experiment in a real-time control/simulation environment.