Abstraction and control by interconnection of linear systems: A geometric approach

摘要

We consider the problem of constructing a controller achieving a desired linear specification, based on a linear abstraction system of the plant system. First, we extend the necessary and sufficient conditions for control by interconnection by bisimulation equivalence to the case of non-deterministic linear systems. Then we apply the controller constructed on the basis of the lower-dimensional abstraction system to the original plant system and show that the closed-loop system is simulated by the given specification system. We distinguish between two forms of abstraction of the plant system. In the first one, the set of variables available for controller interconnection remains the same. In the second, more general form, this is not anymore the case, and we show how an adapted form of interconnection of the controller system to the plant system yields the same result. (C) 2017 Elsevier B.V. All rights reserved.