Biblio

We consider a compositional construction of approximate abstractions of interconnected control systems. In our framework, an abstraction acts as a substitute in the controller design process and is itself a continuous control system. The abstraction is related to the concrete control system via a so-called simulation function: a Lyapunov-like function, which is used to establish a quantitative bound between the behavior of the approximate abstraction and the concrete system. In the first part of the paper, we provide a small gain type condition that facilitates the compositional construction of an abstraction of an interconnected control system together with a simulation function from the abstractions and simulation functions of the individual subsystems. In the second part of the paper, we restrict our attention to linear control system and characterize simulation functions in terms of controlled invariant, externally stabilizable subspaces. Based on those characterizations, we propose a particular scheme to construct abstractions for linear control systems. We illustrate the compositional construction of an abstraction on an interconnected system consisting of four linear subsystems. We use the abstraction as a substitute to synthesize a controller to enforce a certain linear temporal logic specification.

Due to the growing performance requirements, embedded systems are increasingly more complex. Meanwhile, they are also expected to be reliable. Guaranteeing reliability on complex systems is very challenging. Consequently, there is a substantial need for designs that enable the use of unverified components such as real-time operating system (RTOS) without requiring their correctness to guarantee safety. In this work, we propose a novel approach to design a controller that enables the system to restart and remain safe during and after the restart. Complementing this controller with a switching logic allows the system to use complex, unverified controller to drive the system as long as it does not jeopardize safety. Such a design also tolerates faults that occur in the underlying software layers such as RTOS and middleware and recovers from them through system-level restarts that reinitialize the software (middleware, RTOS, and applications) from a read-only storage. Our approach is implementable using one commercial off-the-shelf (COTS) processing unit. To demonstrate the efficacy of our solution, we fully implement a controller for a 3 degree of freedom (3DOF) helicopter. We test the system by injecting various types of faults into the applications and RTOS and verify that the system remains safe.