Huixia Liu

Optimal Petri-Net-Based Polynomial-Complexity Deadlock-Avoidance Policies for Automated Manufacturing Systems

Even for a simple automated manufacturing system (AMS), such as a general single-unit resource allocation system, the computation of an optimal or maximally permissive deadlock-avoidance policy (DAP) is NP-hard. Based on its Petri-net model, this paper addresses the deadlock-avoidance problem in AMSs, which can be modeled by systems of simple sequential processes with resources. First, deadlock is characterized as a perfect resource-transition circuit that is saturated at a reachable state. Second, for AMSs that do not have one-unit resources shared by two or more perfect resource-transition circuits that do not contain each other, it is proved that there are only two kinds of reachable states: safe states and deadlock. An algorithm for determining the safety of a new state resulting from a safe one is then presented, which has polynomial complexity. Hence, the optimal DAP with polynomial complexity can be obtained by a one-step look-ahead method, and the deadlock-avoidance problem is polynomially solved with Petri nets for the first time. Finally, by reducing a Petri-net model and applying the design of optimal DAP to the reduced one, a suboptimal DAP for a general AMS is synthesized, and its computation is of polynomial complexity.

Resource-Transition Circuits and Siphons for Deadlock Control of Automated Manufacturing Systems

The resource-transition circuit ( RTC) and siphon are two different structural objects of Petri nets and used to develop deadlock control policies for automated manufacturing systems. They are related to the liveness property of Petri net models and thus used to characterize and avoid deadlocks. Based on them, there are two kinds of methods for developing deadlock controllers. Such methods rely on the computation of all maximal perfect RTCs and strict minimal siphons (SMSs), respectively. This paper concentrates on a class of Petri nets called a system of simple sequential processes with resources, establishes the relation between two kinds of control methods, and identifies maximal perfect RTCs and SMSs. A graph-based technique is used to find all elementary RTC structures. They are then used to derive all RTCs. Next, an iterative method is developed to recursively construct all maximal perfect RTCs from elementary ones. Finally, a one-to-one correspondence between SMSs and maximal perfect RTCs and, hence, an equivalence between two deadlock control methods are established.

Transition Cover-Based Design of Petri Net Controllers for Automated Manufacturing Systems

In automated manufacturing systems (AMSs), deadlock problems must be well solved. Many deadlock control policies, which are based on siphons or Resource-Transition Circuits (RTCs) of Petri net models of AMSs, have been proposed. To obtain a live Petri net controller of small size, this paper proposes for the first time the concept of transition covers in Petri net models. A transition cover is a set of Maximal Perfect RTCs (MPCs), and the transition set of its MPCs can cover the set of transitions of all MPCs. By adding a control place with the proper control variable to each MPC in an effective transition cover to make sure that it is not saturated, it is proved that deadlocks can be prevented, whereas the control variables can be obtained by linear integer programming. Since the number of MPCs in an effective transition cover is less than twice that of transition vertices, the obtained controller is of small size. The effectiveness of a transition cover is checked, and ineffective transition covers can be transformed into effective ones. Some examples are used to illustrate the proposed methods and show the advantage over the previous ones.

Deadlock prevention for flexible manufacturing systems via controllable siphon basis of Petri nets

Siphons are a kind of special structural objects in a Petri net, and plays a key role in synthesizing a live Petri net controller for flexible manufacturing systems. In order to obtain a small size Petri net controller, this paper introduces the concept of a controllable siphon basis. It then proves that a live Petri net controller can be established by adding a control place and related arcs to each strict minimal siphon (SMS) in a controllable siphon basis. The initial markings of control places are determined by an integer linear program. The number of control places in the obtained controllers is the same as the number of SMSs in the controllable siphon basis, while the latter is no more than that of the activity places in a Petri net model. An algorithm for constructing a controllable siphon basis is proposed, and a new deadlock prevention policy based on it is established. A few examples are provided to demonstrate the proposed concepts and policy and used to compare them with the state-of-the-art methods.

Comment on "On Siphon Computation for Deadlock Control in a Class of Petri Nets

It was claimed recently in the paper by Li and Zhou that ldquoa polynomial time algorithm for finding the set of elementary siphons in S3PRs is proposed, which avoids complete siphon enumerationrdquo. However, this is incorrect because Proposition 1 and Corollary 6 of the aforementioned paper, which lead to the claim, are both incorrect. In this correspondence paper, Proposition 1 and Corollary 6 are disproved. As a consequence, some claims of the aforesaid paper are denied. Two examples are presented to disprove some claims of the previously mentioned paper.

Research on identification algorithm of Hammerstein model

This paper presents a parameter identification method of nonlinear Hammerstein model with two-segment piecewise nonlinearities. Its basic idea is that: First of all, expressing the output of the Hammerstein nonlinear models as a regressive equation in all parameters based on the key term separation principle and separating key term from linear block and nonlinear block. Then, the unknown true outputs in the information vector are replaced with the outputs of an auxiliary model, the unknown internal variables and the unmeasured noise terms are replaced with the estimated internal variables and the estimated residuals, respectively. Accordingly, the problem of the nonlinear system identification is cast as function optimization problem over parameter space; a particle swarm optimization (PSO) algorithm is adopted to solve the optimization problem. In order to further enhance the precision and robust of identification, an improved particle swarm optimization (IPSO) algorithm is applied to search the parameter space to find the optimal estimation of the system parameters. Finally, the feasibility and efficiency of the presented algorithm are demonstrated using numerical simulations.

Two-stage deadlock prevention policy based on resource-transition circuits

This paper presents a suboptimal deadlock controller for a class of manufacturing systems of sequential processes with resources, where deadlocks are characterized by saturated maximal perfect resource-transition circuits (MPRT-circuits), and the controller consists of two parts. In the maximally permissive Petri net controller, which avoids all MPRT-circuits being saturated, some control places are redundant. By deleting all redundant control places and their related arcs, the first part of our controller, non-redundant controller, is obtained. In the controlled system with the non-redundant controller, deadlocks may occur if the system contains crucial resources. Then we propose for the first time the concept of the maximal perfect control-transition circuits (MPCT-circuits), which is used to characterize the deadlock in the controlled system with the non-redundant controller. When deadlock occurs under a reachable marking, some MPCT-circuits in the controlled system become empty. The Petri net controller to prevent all MPCT-circuits from being empty is the second part of our controller. It is proved that the controller consisting of two parts can guarantee the liveness of the controlled system.

Robust deadlock control for automated manufacturing systems with a single type of unreliable resources

In automated manufacturing systems, resource failures are often inevitable. They reduce the number of available resources and may cause some processing routes of parts to halt and sometimes the whole system to shutdown. This article focuses on the robust deadlock control problem in automated manufacturing systems with multiple resource failures. To obtain such a robust controller, we first put forward a new concept of blocked states of automated manufacturing systems. From such a state, the production of some part types through one of their routes is blocked as caused by resource failures, and only after some failed resources are repaired, these parts can resume their normal processing. Then, these blocked states are characterized in terms of emptied siphons caused by resource failures. In order to prevent the system from deadlocks and blocked states, a robust controller is proposed by the following two steps. First, for siphons without unreliable resources, optimal deadlock control places are added. Then for siphons which contain unreliable resources, new control places are devised to ensure that they could be marked even when resource failures happen. It is proved that the proposed controller can guarantee that all types of parts can be processed repeatedly as long as one unit of unreliable resources can still work. This means that the proposed controller is of greatest robustness, that is, it can tolerate a maximum number of resource failures. Some examples are provided to illustrate the proposed method and show the advantage over the previous ones.

Liveness Analysis and Deadlock Control for Automated Manufacturing Systems With Multiple Resource Requirements

This paper focuses on the liveness analysis and deadlock control for automated manufacturing systems (AMSs) with multiple resource requirements. Such an AMS is modeled by a class of generalized Petri nets called systems of simple sequential processes with multiple resources (S3PMR). It is shown that a deadlock of the considered AMSs can be characterized by the saturation of a structural object in S3PMR, called perfect resource transition-circuit (PRT-circuit). As a consequence, an S3PMR is live if and only if no PRT-circuit is saturated at any reachable marking. To ensure the system liveness, one has to prevent all PRT-circuits from being saturated at all reachable markings. To develop a structurally simple Petri net deadlock controller, we present the concept of an effective transition cover, which is a special subset of PRT-circuits that may be saturated. Then by designing a control place with a proper control variable for each PRT-circuit in an effective transition cover, we obtain a deadlock controller for the system. The needed control variables are determined by an integer linear program. Since the number of PRT-circuits in an effective transition cover is much less than that of all PRT-circuits that need to control, our controller is of small structural size. For an AMS with saturable PRT-circuits, there exists at least a transition cover. An algorithm is presented for checking the effectiveness of transition covers, and transforming noneffective transition covers into effective ones. Finally, some examples are used to illustrate the proposed method.

An identification approach of Hammerstein model

An identification method of Hammerstein model is investigated in this paper. First of all, the key term separation technique is introduced. Next, an auxiliary model is established. Accordingly, the identification problem of the Hammerstein model is cast as nonlinear function optimization problem over parameter space. Then, the estimation values of the parameters of the model are obtained based on particle swarm optimization (PSO) algorithm. In order to further enhance the precision and stability of the identification algorithm, a modified particle swarm optimization (MPSO) algorithm is applied to search the parameter space to find the optimal parametric estimation values of the model. Finally, simulation experiments show that the proposed algorithm is effective and reasonable.