منابع مشابه
Taylor Approximation for Hybrid Systems
Wepropose a new approximation technique forHybridAutomata. Given anyHybridAutomatonH, we callApprox(H , k) the Polynomial Hybrid Automaton obtained by approximating each formula in H with the formulae k obtained by replacing the functions in with their Taylor polynomial of degree k. We prove that Approx(H , k) is an over-approximation ofH. We study the conditions ensuring that, given any > 0, s...
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In [10, 11] we proposed a technique to approximate Hybrid Automata (HA) with Polynomial HA. The idea was to replace functions appearing in formulae with their Taylor Polynomials. Here we extend this technique to HA with formulae admitting integral functions. We prove that we get over-approximations of the original HA. We study the conditions ensuring that: 1. the “distance” between the formulae...
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It is known that stability properties of delay-differential equations are not preserved by Taylor series expansion of the delayed term. Still, this technique is often used to approximate delayed systems by ordinary differential equations in different engineering and biological applications. In this brief, it is demonstrated through some simple second-order scalar systems that low-order Taylor s...
متن کاملHybrid Regenerating Codes for Distributed Storage Systems
Distributed storage systems are mainly justified due to their ability to store data reliably over some unreliable nodes such that the system can have long term durability. Recently, regenerating codes are proposed to make a balance between the repair bandwidth and the storage capacity per node. This is achieved through using the notion of network coding approach. In this paper, a new variation ...
متن کاملReachability Analysis of Non-Linear Hybrid Systems Using Taylor Models
With the ubiquitous use of computers in controlling physical systems, it requires to have a new formalism that could model both continuous flows and discrete jumps. Hybrid systems are introduced to this purpose. A hybrid system, which is modeled by a hybrid automaton in the thesis, is equipped with finitely many discrete modes and continuous real-valued variables. A state of it is then represen...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2007
ISSN: 0890-5401
DOI: 10.1016/j.ic.2007.05.004