Control of Discrete Event Systems by Using Symbolic Transition Model: An Application to Power Grids

Abstract

In this paper, a new symbolic modeling framework is proposed for the control of discrete event systems (discrete controller synthesis). Reactive infinite-state systems are generally dynamic systems with inputs and outputs. Modeling the outputs in existing symbolic modeling methods for reactive infinite-state systems has not been extensively discussed in the literature. It is crucial to realistically model the outputs and obtain reliable controllers. One of the main contributions and innovations in this study is the ability to symbolically model their output. In this direction, symbolic transition models are offered, where events are defined as guarded symbolic transitions. The framework considers input/output reactive infinite-state systems to satisfy safety and optimization objectives. Effective algorithms and safety control policies are offered to solve the safety control problem (i.e., satisfy the safety objective) for input/output infinite-state systems. Another contribution in this work provides optimization targets within a given cost function based on state transitions, without specifying the target states. The framework is then applied to power grids to demonstrate the effectiveness of the symbolic transition models and experimentally evaluate the new control algorithms. The results showed that the approach is very effective compared to other approaches found in the literature. The computation times required to achieve both safety and optimization objectives are obtained relatively quickly compared to other deterministic methods found in the literature.