A metamodel of operational control for discrete event logistics systems

State Machines can implement a collection of ‘next-state functions’ that would define a set of control functions for the domain and express how the transition system evolves [223]. There is not a definitive way to construct these functions, and they “follow no general rules, but depend on the logic of the specific problem at hand and the desired system behavior” [284]. While implementing supervisory control requires some external decision process to be applied to the system to guide its evolution, there is no formal, canonical specification or design methodology for this external process. However, due to the dynamic nature of DELS, the design of optimal control models shares many characteristics with engineering other dynamical systems. This has led to the incorporation of theories and mathematical tools from control theory to support the specification and optimization of dynamic aspects of DELS behavior [237]. In control theory, the controller uses the reference point and measured output from the system to determine a control decision or input to the system (Figure 1). In classical control theory, the controller is implemented using transfer functions based in the frequency domain. However as the systems evolved, it became difficult to design and deploy more complicated controller architectures such as multiple input, multiple output (MIMO) control methods. In modern control engineering, the physical system is modeled as a set of input, output, and state variables related by first-order differential equations, a form known as the statespace representation. The set of state variables is defined as the minimal subset of system variables that can represent the entire state of the system at any given time [195]. Figure 1: Classic Control Theory Block Diagram Whereas in classic control theory the controller’s design is static, adaptive control is a technique that allows the parameters of the controller to be adjusted using feedback obtained during the operation of the plant [239]. Sastry and Bodson [239] informally define