Self-adaptive software meets control theory: A preliminary approach supporting reliability requirements

This paper investigates a novel approach to derive self-adaptive software by automatically modifying the model of the application using a control-theoretical approach. Self adaptation is achieved at the model level to assure that the model-which lives alongside the application at run-time- continues to satisfy its reliability requirements, despite changes in the environment that might lead to a violation. We assume that the model is given in terms of a Discrete Time Markov Chain (DTMC). DTMCs can express reliability concerns by modeling possible failures through transitions to failure states. Reliability requirements may be expressed as reachability properties that constrain the probability to reach certain states, denoted as failure states. We assume that DTMCs describe possible variant behaviors of the adaptive system through transitions exiting a given state that represent alternative choices, made according to certain probabilities. Viewed from a control-theory standpoint, these probabilities correspond to the input variables of a controlled system-i.e., in the control theory lexicon, "control variables". Adopting the same lexicon, such variables are continuously modified at run-time by a feedback controller so as to ensure continuous satisfaction of the requirements despite disturbances, i.e., changes in the environment. Changes at the model level may then be automatically transferred to changes in the running implementation. The approach is methodologically described by providing a translation scheme from DTMCs to discrete-time dynamic systems, the formalism in which the controllers are derived. An initial empirical assessment is described for a case study. Conjectures for extensions to other models and other requirements.