Using p-invariants to transform inadmissible constraints into admissible constraints

In this paper we propose a new approach that not only enforces the admissible constraints but also transforms inadmissible constraints into admissible ones. This approach is based on an efficient method that constructs new p-invariants. Through this method dealing with transitions is more convenience because creating new p-invariants in this way utilizes transitions to create a new p-invariant. Therefore, designers are easily able to deal with transitions including uncontrollable or unobservable transitions. Constructing p-invariants will be executed by introducing one theorem and two lemmas; besides, by taking advantages of this theorem and two lemmas a complementary lemma will be established to show when a maximal permissive controller would exist. Finally, we propose a new algorithm which uses the theorem and lemmas to transform inadmissible constraints into admissible ones. In contrast to other methods, this algorithm which we call it “transforming algorithm” can easily transform inadmissible constraints into admissible constraints without needing to solve an integer linear programming (ILP) problem. The correctness of this algorithm will be evaluated through an example, and result shows that transforming inadmissible constraints into admissible ones using this method dose not need solving an integer linear programming and requires less computation to implement a proper controller.