Recent developments in Boolean networks control

The aim of this survey paper is to provide the state of the art of the research on control and optimal control of Boolean control networks, under the assumption that all the state variables are accessible and hence available for feedback. Necessary and sufficient conditions for stabilisability to a limit cycle or to an equilibrium point are given. Additionally, it is shown that when such conditions are satisfied, stabilisation can always be achieved by means of state feedback. Analogous results are obtained for the safe control problem that is investigated for the first time in this survey. Finite and infinite horizon optimal control are subsequently considered, and solution algorithms are provided, based on suitable adaptations of the Riccati difference and algebraic equations. Finally, an appropriate definition of the cost function allows to restate and to solve both stabilisation and safe control as infinite horizon optimal control problems.

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