Stability Analysis for a Class of Resource-Aware, Co-Regulated Systems

Abstract

In this paper we develop four methods for proving stability for a subclass of co-regulated systems – finite-state, co-regulated systems with restrictions on possible sampling rates. “Co-regulation” is a control strategy we previously developed wherein cyber and physical effectors are dynamically adjusted in response to holistic system performance. The cyber effector, sampling rate, is adjusted in response to off-nominal conditions in the controlled system, and the physical effector adjusts control outputs corresponding to the current (changing) sampling rate. The resulting computer-control system is a discrete-time-varying system with changing zero-order holds and sampling periods, and unknown delays over discrete intervals. This makes performance guarantees such as stability difficult to obtain. We address this difficulty by drawing from specialized results in the control community to develop four methods for proving asymptotic stability of finite-state, co-regulated systems. Each successive method relaxes the assumptions needed to guarantee stability. This lays the groundwork for a more all-encompassing analytical framework for co-regulated systems. We use the results to demonstrate stability for a co-regulated multicopter unmanned aircraft system.