Control of switched boolean control networks by state feedback

Control of infectious diseases using bacteriophage therapy is regaining interests in modern medicine and systems biology as an alternative treatment for antibiotic-resistant bacteria. A key issue is to control the phage's replication process: indeed, phage may switch either towards lytic state or lysogeny state during its reproduction due to some conditions. However, only lytic state is relevant for bacteria elimination. In this paper, we model switching replication dynamics of the lambda phage, i.e., a class of bacteriophage, as a switched Boolean control network (SBCN) and we address the problem of designing all possible switching signal-dependent state feedback controllers to stabilize the phage system at lytic developmental pathway. An algebraic state-space representation method is adopted to determine all possible families of reachable sets. Necessary and sufficient conditions for the stabilization of SBCN to a given equilibrium point under arbitrary switching signals are presented, where the control input is switching signal-dependent. Moreover, all possible switching signal-dependent state feedback controllers are obtained based on all complete families of reachable sets. Results are relevant for both the development of SBCN theory and for practical applications. At last, the example of bacteriophage lambda is analyzed to show the effectiveness of the main results.