Singular mix-valued logical networks and its optimal control

Singular mix-valued logical control network is a natural generalization of singular Boolean control network. In this paper, the optimal control problem of singular mix-valued logical control networks is studied. Via semi-tensor product, a singular mix-valued control network can be converted to an algebraic form. On this basis, a necessary condition for the existence of the optimal control is presented and the result can also be applied to singular Boolean control networks and the k-valued case. Then, to compute an optimal control, an algorithm is supplied. Finally, an illustrative example is delivered to show that the result is feasible.