一类带初始输入的线性循环终止性分析

本文针对带初始输入的二维齐次线性循环的终止性问题进行研究。通过分析该类循环所有非终止点组成集合(即NT集)的性质,将该类循环NT集的构造问题转化为一类非线性优化求解问题,并给出了此类优化问题的数学模型。最终,通过验证该类循环的初始输入是否位于所构造的NT集合内,判定了带初始输入的二维齐次线性循环的终止性, 并建立了用来完备判定该类循环终止性的算法。     

Interactions Between PVS and Maple in Symbolic Analysis of Control Systems

This paper presents a decision procedure for problems relating polynomial and transcendental functions. The procedure applies to functions that are continuously differentiable with a finite number of points of inflection in a closed convex set. It decides questions of the form ‘is f0?’, where {=,>,<}. An implementation of the procedure in Maple and PVS exploits the existing Maple, PVS and QEPCAD connections. It is at present limited to those twice differentiable functions whose derivatives are rational functions (rationally differentiable). This procedure is particularly applicable to the analysis of control systems in determining important properties such as stability.