Input design for a cascading system: An approach based on system decomposition and non-influential input detection

This paper addresses the design of the inputs to a mixed logical dynamical system so as to satisfy some specification, while maximizing the number of non-influential inputs, i.e., those inputs that can take an arbitrary value within their admissible range without affecting the satisfaction of the specification. The problem can be rephrased as a reachability problem on an enlarged system and formulated as a robust mixed integer linear program. An iterative procedure that relies on the detection of non-influential inputs is proposed to simplify the solution to the problem for cascading systems. A numerical example shows the efficacy of the approach.