Optimal Semicomputable Approximations to Reachable and Invariant Sets

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.

• Type: Journal
• Year: 2007
• Where: MST
• Authors: Pieter Collins
• Keywords: Computations, Discrete-time Systems, Invariance Kernels, MST 2007