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Steplength Thresholds for Invariance Preserving of Discretization Methods of Dynamical Systems on a Polyhedron

Zoltán Horváth(horvathz***at***szu.hu)
Yunfei Song(yus210***at***lehigh.edu)
Tamás Terlaky(terlaky***at***lehigh.edu)

Abstract: Steplength thresholds for invariance preserving of three types of discretization methods on a polyhedron are considered. For Taylor approximation type discretization methods we prove that a valid steplength threshold can be obtained by finding the first positive zeros of a finite number of polynomial functions. Further, a simple and efficient algorithm is proposed to numerically compute the steplength threshold. For rational function type discretization methods we derive a valid steplength threshold for invariance preserving, which can be computed by using an analogous algorithm as in the first case. The relationship between the previous two types of discretization methods and the forward Euler method is studied. Finally, we show that, for the forward Euler method, the largest steplength threshold for invariance preserving can be computed by solving a finite number of linear optimization problems.

Keywords: Invariant Set, Dynamical System, Discretization, Polyhedron

Category 1: Convex and Nonsmooth Optimization

Category 2: Combinatorial Optimization (Polyhedra )

Category 3: Applications -- Science and Engineering (Control Applications )


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Entry Submitted: 06/25/2014
Entry Accepted: 06/25/2014
Entry Last Modified: 06/25/2014

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