Straightening out rectangular di erential inclusions

نویسندگان

  • George J. Pappas
  • Shankar Sastry
چکیده

In this paper, the classic straightening out theorem from di erential geometry is used to derive necessary and su cient conditions for locally converting rectangular di erential inclusions to constant rectangular di erential inclusions. Both scalar and coupled di erential inclusions are considered. The results presented in this paper have use in the area of computer aided veri cation of hybrid systems where they represent the frontier of the known decidable models of in nite state systems. c © 1998 Elsevier Science B.V. All rights reserved.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Straightening out Trajectories near Singular Points of Implicit Differential Equations

Under appropriate assumptions, it is shown that there is a di eomorphism that transforms solutions of the implicit di erential equation

متن کامل

Differential Inclusions and Monotonicity Conditions for Nonsmooth Liapunov Functions

In this paper we address the problem of characterizing the in nitesimal properties of functions which are non-increasing along all the trajectories of a di erential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous di erential inclusions. Moreover, we show that the same criterion applies also in the ...

متن کامل

Discovery of Differential Equations from Numerical Data

This paper proposes a method of discovering some kinds of di erential equations with interval coe cients, which characterize or explain numerical data obtained by scienti c observations and experiments. Such numerical data inevitably involve some ranges of errors, and hence they are represented by closed intervals in this paper. Based on these intervals, we design some interval inclusions which...

متن کامل

Numerical Solution of fuzzy differential equations of nth-order by Adams-Bashforth method

So far, many methods have been presented to solve the rst-order di erential equations. But, not many studies have been conducted for numerical solution of high-order fuzzy di erential equations. In this research, First, the equation by reducing time, we transform the rst-order equation. Then we have applied Adams-Bashforth multi-step methods for the initial approximation of one order di erentia...

متن کامل

Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems

In this paper we describe an experimental system called d dt for approximating reachable states for hybrid systems whose con tinuous dynamics is de ned by linear di erential equations We use an approximation algorithm whose accumulation of errors during the con tinuous evolution is much smaller than in previously used methods The d dt system can so far treat non trivial continuous systems hybri...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1998