Symbolic Supervisory Control of Resource Allocation Systems

<p>Supervisory control theory (SCT) is a formal model-based methodology for verification and synthesis of supervisors for discrete event systems (DES). The main goal is to guarantee that the closed-loop system fulfills given specifications. SCT has great promise to assist engineers with the generation of reliable control functions. This is, for instance, beneficial to manufacturing systems where both products and production equipment might change frequently.</p> <p>The industrial acceptance of SCT, however, has been limited for at least two reasons: (i) the analysis of DES involves an intrinsic difficulty known as the state-space explosion problem, which makes the explicit enumeration of enormous state-spaces for industrial systems intractable; (ii) the synthesized supervisor, represented as a deterministic finite automaton (FA) or an extended finite automaton (EFA), is not straightforward to implement in an industrial controller.</p> <p>In this thesis, to address the aforementioned issues, we study the modeling, synthesis and supervisor representation of DES using binary decision diagrams (BDDs), a compact data structure for representing DES models symbolically. We propose different kinds of BDD-based algorithms for exploring the symbolically represented state-spaces in an effort to improve the abilities of existing supervisor synthesis approaches to handle large-scale DES and represent the obtained supervisors appropriately.</p> <p>Following this spirit, we bring the efficiencies of BDD into a particular DES application domain -- deadlock avoidance for resource allocation systems (RAS) -- a problem that arises in many technological systems including flexible manufacturing systems and multi-threaded software. We propose a framework for the effective and computationally efficient development of the maximally permissive deadlock avoidance policy (DAP) for various RAS classes. Besides the employment of symbolic computation, special structural properties that are possessed by RAS are utilized by the symbolic algorithms to gain additional efficiencies in the computation of the sought DAP. Furthermore, to bridge the gap between the BDD-based representation of the target DAP and its actual industrial realization, we extend this work by introducing a procedure that generates a set of "guard" predicates to represent the resulting DAP.</p> <p>The work presented in this thesis has been implemented in the SCT tool Supremica. Computational benchmarks have manifested the superiority of the proposed algorithms with respect to the previously published results. Hence, the work holds a strong potential for providing robust, practical and efficient solutions to a broad range of supervisory control and deadlock avoidance problems that are experienced in the considered DES application domain.</p

A correction to the RUN DAP for Conjunctive RAS presented in &quot;Polynomial-Complexity Deadlock Avoidance Policies for Sequential Resource Allocation Systems&quot;, by Reveliotis, Lawley and Ferreira, IEEE TAC, vol. 42, pgs 1344-1357

This technical correspondence first identifies a problem with the correctness of the RUN DAP for Conjunctive RAS, presented in [2], and it subsequently proceeds to the problem correction through an appropriate policy modification. More specifically, the first part of this note provides a counter-example to the policy correctness (i.e., deadlock-freedom of the controlled system), claimed in [2], while the second part introduces the proposed correction, and briefly argues the correctness of the modified DAP. A more detailed mathematical treatment of RUN DAP in the Petri net formalism, and its redefinition so that it covers the broader class of Conjunctive /Disjunctive RAS, can be found in [1]. For the sake of brevity, it is presumed in the following that the reader is familiar with the material of [2