Control

Abstract

Whenever a system S _a fails to conform to its specification S _b , in the sense that $S_a \npreceq S_b$, we may ask if there exists another system S _c , the controller, such that $S_c \times_I S_b \preceq$ or even $S_c \times_I S_a \cong S_b$. In this chapter we discuss these control problems in the behavioral and similarity contexts. We show how to reduce controller synthesis problems from the behavioral context to the similarity context and we solve the later by computing _xed-points of suitably de_ned operators. In addition to these general control problems we also present _xed-point solutions specialized for safety and reachability control problems that frequently arise in applications.