Reference Output Tracking in Boolean Control Networks
Giorgia Disarò, Maria Elena Valcher
TL;DR
This work tackles the problem of tracking time-varying Boolean reference outputs in Boolean control networks using an algebraic framework based on the semi-tensor product. It first generalizes finite-length trajectory tracking to arbitrary initial conditions by developing forward and backward vector sequences (α and β) and a set-based methodology to enumerate all compatible state/input trajectories, then extends the results to periodic reference trajectories with a pruning algorithm that identifies feasible initial states. The key contributions include formal solvability criteria, algorithms to compute all exact-tracking controls, and a clear separation of compatibility and reachability conditions, enabling delayed tracking when exact tracking from all initial states is not possible. The results provide a practical procedure for designing control sequences in BCNs and are demonstrated via a numerical example, highlighting the approach’s applicability to periodic tracking tasks.
Abstract
In this paper, the problem of tracking a given reference output trajectory is investigated for the class of Boolean control networks, by resorting to their algebraic representation. First, the case of a finite-length reference trajectory is addressed, and the analysis and algorithm first proposed in [17] are extended to be able to deal with arbitrary initial conditions and to identify all possible solutions. The approach developed for the finite-length case is then adjusted to cope with periodic reference output trajectories. The results of the paper are illustrated through an example.