A Mayer-type optimal control for multivalued logic control networks with undesirable states

A fundamental problem for all dynamical control systems is to determine a control that is optimal in some sense. Based on semi-tensor product, we consider a Mayer-type optimal control problem for multi-valued logical control networks with time delays in states. A necessary condition for a control to be optimal is derived while avoiding a set of forbidden states. Examples are provided to illustrate the effectiveness of the obtained results.