Numerical and Analytical Analysis of Nonlinear Implicit Differential Equations Arising in Control and Mechanics Problems

一个奇异隐式微分方程是一个隐式常微分方程， 形式为F（y '，y，u，t）= 0的微分方程，其中y是向量 值函数，Jacobian Fy'是奇异矩阵，u是向量 函数，t是时间。 这种隐性系统经常 在飞行控制，机器人， 力学中的接触或约束问题。 此外，本发明还提供了一种方法， 隐式微分方程发生在偏微分方程的解 微分方程的直线法和多回路法 模型 奇异系统通常称为微分代数系统 方程（DAE）或描述符系统。 提出了发展分析非线性隐式 微分方程和计算它们的解。 这些结果 当状态方程存在时，也会感兴趣，但是 稀疏性、非线性或对方程参数的依赖性， 使原来的隐式系统优于较低的顺序，但 非稀疏（或难以计算局部）显式状态系统。 控制理论信息的直接数值计算 从原始方程将被调查的一部分， 提议的研究。

A singular implicit differential equation is an implicit ordinary differential equation of the form F(y',y,u,t) = 0 where y is a vector valued function, the Jacobian Fy' is a singular matrix, u is a vector valued function, and t is time. Such implicit systems frequently arise in a variety of control problems in flight control, robotics, and contact or constrained problems in mechanics. In addition, implicit differential equations occur in the solution of partial differential equations by the method of lines and in many circuit models. Singular systems are frequently called differential algebraic equations (DAEs) or discriptor systems. It is proposed to develop methods for analyzing nonlinear implicit differential equations and computing their solutions. These results will also be of interest when the state equations exist, but the sparsity, nonlinearity, or dependence on parameters of the equations, make the original implicit system preferable to a lower order, but non-sparse, (or difficult to compute local) explicit state system. The numerical computation of control theoretic information directly from the original equations will be investigated as part of the proposed research.