Asymptotical Stabilization of Logic Dynamical Systems via Output-Based Random Control

This study focuses on the problem of asymptotical stabilization of logic dynamical systems (LDSs) under the situation where the only available measurable information is the real-time output. We propose a novel time-invariant control strategy called output-based random control (OBRC), which breaks through the limitation of time-invariant deterministic output feedback (TIDOF). The TIDOF can be regarded as a special type of the OBRC, but the OBRC is capable of stabilizing some LDSs that cannot be stabilized by any TIDOF. A necessary and sufficient condition for asymptotical stabilizability by the OBRC and a method of finding an optimal OBRC that minimizes a quadratic cost function are proposed. The proposed OBRC was applied to a reduced gene network for the lac operon in the bacterium Escherichia coli. The results of numerical computations and time-domain simulations indicate that the OBRC outperforms the TIDOF.