Symbolic Computation of Nonblocking Control Function for Timed Discrete Event Systems

In this paper, we symbolically compute a minimally restrictive nonblocking supervisor for timed discrete event systems, in the supervisory control theory context. The method is based on Timed Extended Finite Automata, which is an augmentation of extended finite automata (EFAs) by incorporating discrete time into the model. EFAs are ordinary automaton extended with discrete variables, guard expressions and action functions. To tackle large problems all computations are based on binary decision diagrams (BDDs). The main feature of this approach is that the BDD-based fixed-point computations is not based on “tick” models that have been commonly used in this area, leading to better performance in many cases. As a case study, we effectively computed the minimally restrictive nonblocking supervisor for a well-known production cell

Non-blocking supervisory control for initialised rectangular automata

We consider the problem of supervisory control for a class of rectangular automata and more specifically for compact rectangular automata with uniform rectangular activity, i.e. initialised. The supervisory controller is state feedback and disables discrete-event transitions in order to solve the non-blocking forbidden state problem. The non-blocking problem is defined under both strong and weak conditions. For the latter maximally permissive solutions that are computable on a finite quotient space characterised by language equivalence are derived

Symbolic Supervisory Control of Timed Discrete Event Systems

With the increasing complexity of computer systems, it is crucial to have efficient design of correct and well-functioning hardware and software systems. To this end, it is often desired to control the behavior of systems to possess some desired properties. A specific class of systems is called discrete event systems (DES). DES deal with `discrete' quantities, e.g., ``number of robots in a manufacturing cell'', and their processes are driven by instantaneous `events', e.g., ``start of a machine''. In this thesis, the focus is on DES and an extension of such systems, which also considers the time points at which the events may occur, called \emph{timed DES (TDES)}. Real-time applications such as communication networks, manufacturing facilities, or the execution of a computer program, can be considered into TDES. Having a DES or TDES, with some given specifications, by utilizing a well-known mathematical framework, called supervisory control theory (SCT), it is possible to automatically generate a supervisor that restricts the system's behavior towards the specifications, only when it is necessary. Applying the SCT to large and complex systems, typically follows with some issues, concerning computational complexity and modeling aspects, which is tackled in this thesis. We model DES by extended finite automata (EFAs), state transition models that contain discrete-valued variables. TDES are modeled by an augmentation of EFAs, called timed EFAs (TEFAs), which contain a set of discrete-valued clocks. Based on EFAs or TEFAs, the supervisor can be symbolically computed, using binary decision diagrams (BDDs), data structures that could, in many cases, lead to smaller representation of the state space. For complex systems, the computed supervisor may consist of many states, causing representation and implementation difficulties. To tackle this, based on the states of the supervisor, we symbolically compute logical constraints that will be attached to the original models to restrict the system's behavior. Consequently, we present a framework, where given a set of EFAs or TEFAs, the supervisor is computed using BDDs, and represented in a modular manner based on the computed logical constraints. The framework has been developed, implemented, and applied to industrial case studies

Certainly Unsupervisable States

This paper proposes an abstraction method for compositional synthesis. Synthesis is a method to automatically compute a control program or supervisor that restricts the behaviour of a given system to ensure safety and liveness. Compositional synthesis uses repeated abstraction and simplification to combat the state-space explosion problem for large systems. The abstraction method proposed in this paper finds and removes the so-called certainly unsupervisable states. By removing these states at an early stage, the final state space can be reduced substantially. The paper describes an algorithm with cubic time complexity to compute the largest possible set of removable states. A practical example demonstrates the feasibility of the method to solve real-world problems

Robust State-Based Supervisory Control of Hierarchical Discrete-Event Systems

Model uncertainty due to unknown dynamics or changes (such as faults) must be addressed in supervisory control design. Robust supervisory control, one of the approaches to handle model uncertainty, provides a solution (i.e., supervisor) that simultaneously satisfies the design objectives of all possible known plant models. Complexity has always been a challenging issue in the supervisory control of discrete-event systems, and different methods have been proposed to mitigate it. The proposed methods aim to handle complexity either through a structured solution (e.g. decentralized supervision) or by taking advantage of computationally efficient structured models for plants (e.g., hierarchical models). One of the proposed hierarchical plant model formalisms is State-Tree-Structure (STS), which has been successfully used in supervisor design for systems containing up to 10^20 states. In this thesis, a robust supervisory control framework is developed for systems modeled by STS. First, a robust nonblocking supervisory control problem is formulated in which the plant model belongs to a finite set of automata models and design specifications are expressed in terms of state sets. A state-based approach to supervisor design is more convenient for implementation using symbolic calculation tools such as Binary Decision Diagrams (BDDs). In order to ensure that the set of solutions for robust control problem can be obtained from State Feedback Control (SFBC) laws and hence suitable for symbolic calculations, it is assumed, without loss of generality, that the plant models satisfy a mutual refinement assumption. In this thesis, a set of necessary and sufficient conditions is derived for the solvability of the robust control problem, and a procedure for finding the maximally permissive solution is obtained. Next, the robust state-based supervisory framework is extended to systems modeled by STS. A sufficient condition is provided under which the mutual refinement property can be verified without converting the hierarchical model of STS to a flat automaton model. As an illustrative example, the developed approach was successfully used to design a robust supervisor for a Flexible Manufacturing System (FMS) with a state set of order 10^8