Minimum Resource Commitment for Reachability Specifications in a Discrete Time Linear Setting

This paper addresses control input design for a discrete time linear system. The goal is to satisfy a reachability specification and, at the same time, minimize the number of inputs that need to be set (influential inputs). To this purpose, we introduce an appropriate input parametrization so that, depending on the parameter values, some of the inputs act as control variables, while the others are treated as disturbances and can take an arbitrary value in their range. We then enforce the specification while maximizing the number of disturbance inputs. Two approaches are developed: one based on an open-loop scheme and one based on a compensation scheme. In the former, we end up solving a linear program. In the latter, the parametrization is extended so as to allow the influential inputs to depend on the non-influential ones, and the problem is reduced to a mixed integer linear program. A comparison between the two approaches is carried out, showing the superiority of the latter. Possible applications to system design and security of networked control systems are briefly discussed in the introduction.