Computational Procedures for Robust Nonblocking Supervisory Control of Discrete-Event Systems

The concept of robust control arises in control theory in dealing with modeling uncertainties and model changes. In the study of supervisory control of discrete-event systems (DES), one approach to robustness is to assume that the exact plant model is unknown but it belongs to a finite family of DES models. The design objective is to find a supervisor such that any of the plant DES models in the aforementioned family, under the supervision of the designed supervisor, meets its design specifications. The set of solutions of the robust nonblocking supervisory control problem (RNSCP) is available in the literature in terms of a class of languages. For the case of control with full event observation, RNSCP has an optimal (maximally permissive) solution. In the case of control under partial event observation (RNSCP-PO), a maximally permissive solution does not necessarily exist; however suboptimal solutions (in terms of normal languages) that are generally more suitable for computational procedures have been identified. In this thesis, computational algorithms are developed for finding the solution of RNSCP in the form of finite-state automaton. First, a computational algorithm for supremal G-nonblocking languages is presented. Next this algorithm is used to develop an iterative algorithm that obtains the maximally permissive solution of RNSCP as the largest fixed point of a suitable operator. It is shown that the algorithm converges in a bounded number of steps for finite-state plant models and regular specification languages. The computational complexities of the algorithms are also derived. The resulting algorithms have been implemented in MATLAB environment using Discrete Event Control Kit (DECK) and applied to solve a problem of control and fault recovery in a simplified spacecraft propulsion system. Next the computational algorithm for RNSCP is extended to the case of control under partial event observation. In this case the maximally permissive solution of RNSCP-PO among the solutions that have the normality property is obtained