In recent years, microprocessors have invaded the physical world, resulting in sophisticated but complicated networked embedded systems that defy theoretical understanding, resulting in inadequate design tools for the modern embedded system engineer. Embedded systems require the development of new theories, methods, and tools providing the correct understanding of these systems and accelerated analysis and design methods in order to ensure safety but also substantially decrease their design time. Embedded systems require very novel, very challenging specifications that have to deal with synchronization, sequencing, and temporal ordering of different tasks. Mathematically formulating such desired specifications cannot be achieved using traditional mathematical formulations in control theory. On the other hand, computer aided verification has popularized the use of several temporal logics to describe complex specifications. However, the emphasis has been on verification of these properties for purely discrete systems, and not on synthesis for systems with a continuous component.
In this research, a novel approach for automatically synthesizing hybrid controllers is pursued in order to satisfy specifications that are expressed in temporal logics. In particular, methodologies are developed to extract finite abstractions of linear control systems, that will be used to design controllers meeting the desired temporal logic specifications. Contrary to other approaches, this project considers specification dependent abstractions for continuous control systems as opposed to continuous dynamical systems. The proposed framework will provide algorithms and tools for the computation of discrete controllers, which by refinement will lead to embedded, hybrid controllers for the original system while providing performance and correctness guarantees.
The educational agenda of the proposal focuses on the development of a cross- departmental, undergraduate, signals and systems course that broadens the definition of systems in order to capture software and hardware systems in addition to traditional control or communication systems. This course has been carefully coordinated with recent curriculum changes and aims at the educational uniformity of signals and systems concepts in both the discrete and the continuous world.
