Abstract-Programmable logic controllers (PLCs) are widely used in embedded systems. A timer plays a pivotal role in PLC real-time applications. The paper presents a formalization of TON-timers of PLC programs in the theorem proving system Coq. The behavior of a timer is characterized by a set of axioms at an abstract level. PLC programs with timers are modeled in Coq. As a case study, the quiz machine problem with timer is investigated. Relevant timing properties of practical interests are proposed and proven in Coq. This work unveils the hardness of timer modeling in embedded systems. It is an attempt of formally proving the correctness of PLC programs with timer control.
To deal with the problem of resource integration and optimal scheduling in cloud manufacturing, based on the analyzation of the existing literatures, multitask oriented virtual resource integration and optimal scheduling problem is presented from the perspective of global optimization based on the consideration of sharing and correlation among virtual resources. The correlation models of virtual resources in a task and among tasks are established. According to the correlation model and characteristics of resource sharing, the formulation in which resource time-sharing scheduling strategy is employed is put forward, and then the formulation is simplified to solve the problem easily. The genetic algorithm based on the real number matrix encoding is proposed. And crossover and mutation operation rules are designed for the real number matrix. Meanwhile, the evaluation function with the punishment mechanism and the selection strategy with pressure factor are adopted so as to approach the optimal solution more quickly. The experimental results show that the proposed model and method are feasible and effective both in situation of enough resources and limited resources in case of a large number of tasks.
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