Specification and Reactive Synthesis of Robust Controllers

Abstract: This paper investigates the synthesis of robust controllers from logical specification of regular properties given in an interval temporal logic QDDC. Our specification encompasses both hard robustness and soft robustness. Here, hard robustness guarantees invariance of commitment under user-specified relaxed (weakened) assumptions. A systematic framework for logically specifying the assumption weakening by means of a formula, called Robustness Criterion, is presented. The soft robustness pertains to the ability of the controller to maintain the commitment for as many inputs as possible, irrespective of any assumption. We present a uniform method for the synthesis of a robust controller which guarantees the specified hard robustness and it optimizes the specified soft robustness. The method is implemented using a tool DCSynth, which provides soft requirement optimized controller synthesis. Through the case study of a synchronous bus arbiter, we experimentally show the impact of hard robustness criteria as well as soft robustness on the ability of the synthesized controllers to meet the commitment "as much as possible". Both, the worst-case and the expected case behaviors are analyzed.