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Optimal controller design for state estimation of Boolean control networks

In this paper, a kind of optimal controller is proposed to estimate the state of Boolean control networks (BCNs). Different from the standard observer, the optimal state estimation is completed by designing the control input instead of directly using it, where the maximum-minimum method is employed such that the state of BCNs can be uniquely estimated in possible short time steps. A set observer is first proposed to estimate the state of BCNs at any time steps. Based on the set observer, an initial output-dependent reconstructible state tree is developed, where an algorithm is provided to generate the nodes of such tree and can be implemented offline. The optimal control sequence for uniquely determining the state of BCNs is derived from the reconstructible state tree by a breadth-first search algorithm, where the output of BCNs is dynamically employed. An example is given to illustrate the applicability and usefulness of the developed methods.