Optimal Semicomputable Approximations to Reachable and Invariant Sets |
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Authors: | Pieter Collins |
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Affiliation: | (1) Centrum voor Wiskunde en Informatica, Postbus 94079, 1090 GB Amsterdam, The Netherlands |
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Abstract: | In this paper we consider the computation of reachable, viable and invariant sets for discrete-time systems. We use the framework
of type-two effectivity, in which computations are performed by Turing machines with infinite input and output tapes, with
the representations of computable topology. We see that the reachable set is lower-semicomputable, and the viability and invariance
kernels are upper-semicomputable. We then define an upper-semicomputable over-approximation to the reachable set, and lower-semicomputable
under-approximations to the viability and invariance kernels, and show that these approximations are optimal. |
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Keywords: | |
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