Disturbance decoupling control design for Boolean control networks: a Boolean algebra approach

The disturbance decoupling problem (DDP) whereby the system outputs become insensitive to exogenous signals or disturbances plays a vital role in systems engineering and biological systems. Notably, many biological signalling systems with multiple outputs are usually susceptible to external environmental changes. The authors investigate the DDP for Boolean control networks (BCNs) and present a novel technique based on Boolean algebra to solve the DDP. In particular, the results on the DDP solvability are derived by transforming the system dynamics to a simplified form called output-friendly form. Furthermore, a constructive procedure based on the Karnaugh map to design all possible feedback controllers such that the states affecting the outputs are free from disturbances is proposed. Moreover, the presented results are extended to switched BCNs, and design all possible mode-independent feedback controllers. Finally, some examples including a Boolean model of Escherichia coli are provided to validate the main findings.