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arXiv · 1503.07021

Minimal Reachability Problems

Vasileios Tzoumas·Ali Jadbabaie·George J. Pappas
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Abstract

In this paper, we address a collection of state space reachability problems, for linear time-invariant systems, using a minimal number of actuators. In particular, we design a zero-one diagonal input matrix B, with a minimal number of non-zero entries, so that a specified state vector is reachable from a given initial state. Moreover, we design a B so that a system can be steered either into a given subspace, or sufficiently close to a desired state. This work extends the recent results of Olshevsky and Pequito, where a zero-one diagonal or column matrix B is constructed so that the involved system is controllable. Specifically, we prove that the first two of our aforementioned problems are NP-hard; these results hold for a zero-one column matrix B as well. Then, we provide efficient polynomial time algorithms for their general solution, along with their worst case approximation guarantees. Finally, we illustrate their performance over large random networks.

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Vasileios Tzoumas, Ali Jadbabaie, George J. Pappas. 2015-03-24. Minimal Reachability Problems. https://arxiv.org/abs/1503.07021

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