Formal Control Synthesis via Simulation Relations and Behavioral Theory for Discrete-Time Descriptor Systems

The control and verification of industrial processes, modeled as discrete-time descriptor systems, is often computationally hard due to the presence both algebraic couplings difference equations. In this article, we introduce a new synthesis method for systems which based on formal abstractions enables design over related reduced-order models. We leverage notions exact approximate similarity relations, hold that are inherent systems. Using behavioral framework, extend refinement scheme classical dynamical develop corresponding notion systems: show any given well-posed controller abstract (reduced-order) system can be refined original system. resulting controlled preserves same output behavior in case similarity, whereas shown have bounded deviation from model where designed.