Control Input Design: Detecting Non Influential Inputs While Satisfying a Reachability Specification

We address the problem of designing the control input for a discrete time dynamical system so as to make its state reach some target set in finite time. Among the feasible solutions to the reachability problem, we look for those where only few input variables need to be set to some specic value, whereas the others can take an arbitrary value within their admissible range without compromising the desired reachability condition. This input design problem is not standard and the optimality criterion cannot be easily expressed in terms of some performance index to be optimized. Here, we propose a solution that rests on an appropriate parametrization of the input variables as set-valued signals, and rephrase the input design problem as a robust optimization program. In turn, if the target set is a polytope, the optimization problem reduces to a linear program for linear system, and to a mixed integer linear program for mixed logical dynamical systems. Some numerical examples show the ecacy of the approach.