Theory of Computing Systems

, Volume 41, Issue 1, pp 33–48 | Cite as

Optimal Semicomputable Approximations to Reachable and Invariant Sets

Open Access


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.

Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Centrum voor Wiskunde en Informatica, Postbus 940791090 GB AmsterdamThe Netherlands

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