Erzana Berani Abdelwahab

Abstract

Delays arise naturally in feedback loops in modern forms of embedded digital control, like networked control systems where communication between the plant and the controller is crucial. Especially when dealing with safety-critical systems, the communication delay in the feedback loop may however, become significant. In continuous control, delays are modeled by Delay Differential Equations (DDE) and it is already well-known that such delays may cause oscillations which directly affect the stability and control performance of the system. However, despite a large portion of digital control schemes being subject to hybrid state dynamics, there has not been much interest in considering delays in hybrid systems. To the best of our knowledge, neither an established notion of delayed hybrid system nor corresponding verification methods exist. Introducing a formal semantic, i.e., mathematical model for rigorously modeling delays arising in hybrid systems thus constitutes the main objective of this PhD project.

Currently, we are exploiting the idea of using distributed delays as a more relevant model and potentially easier to analyze compared to discrete delays. The smoothing effect embedded in distributed delays implies promising results in reconstructing the history segment based on finite samples. This approach ultimately leads to the reduction of a DDE problem to that of solving an, albeit higher-dimensional, standard ODE. Future work will exploit this reduction for automatic verification of hybrid systems incorporating distributed delays.