Optimal control of Boolean control networks: a data-driven perspective

Data-driven approaches have recently emerged in the analysis of Boolean control networks (BCNs), with the aim of addressing fundamental control problems, such as state-feedback stabilization, safe control, and output regulation, without requiring an explicit model, provided that a sufficiently informative dataset is available. This paper develops a data-based framework for the finite-horizon and infinite-horizon optimal control problems in BCNs. For the finite-horizon problem, the conditions for solvability are relatively mild. In contrast, solving the infinite-horizon problem from data imposes stricter requirements on both the generating BCN and the collected dataset. Our analysis builds on the concept of data informativity, which ensures that any proposed solution is feasible for all BCNs consistent with the data. While the resulting controllers may not be optimal for every such BCN, they represent the best performance attainable given the available information. The degree of sub-optimality is characterized in detail, and the effectiveness of the proposed (both finite- and infinite-horizon) methods is illustrated through an example based on a biological system of practical relevance.