Logical specification and uniform synthesis of robust controllers

Abstract

This paper investigates the synthesis of robust controllers from a 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 the invariance of commitment under relaxed (weakened) assumptions. A systematic framework for logically specifying the assumption weakening by means of a QDDC formula Rb(A), called Robustness criterion, is presented. This can be used with any user specified assumption DA to obtain a relaxed (weakened) assumption Rb(DA). A variety of robustness criteria encompassing some existing notions such as k, b resilience as well as some new notions like tolerating non-burst errors and recovery from transient errors are formulated logically. 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 invariance of specified hard robustness and it optimizes the expected value of occurrence of commitment across input sequences. Through the case study of a synchronous bus arbiter, we experimentally show the impact of variety of hard robustness criteria as well as the soft robustness on the ability of the synthesized controllers to meet the commitment "as much as possible".