Finite-horizon optimal control of Boolean control networks

In this paper we address the finite-horizon optimal control problem for Boolean control networks (BCNs). By resorting to the algebraic approach recently introduced by D. Cheng and co-authors, we first pose the problem of finding the input sequences that minimize a given quadratic cost function. Then, by resorting to the semi-tensor product, we rewrite the cost function as a linear one. The problem solution is obtained by means of a recursive algorithm that represents the analogue for BCNs of the difference Riccati equation for linear systems. A number of apparently more general optimal control problems for BCNs can be easily reframed into the present set-up. In particular, the cost function can be adjusted so as to include penalties on the switchings, provided that we redefine the BCN state variable.