Digital Control Networks for Continuous Passive Plants Which Maintain Stability Using Cooperative Schedulers

This paper provides a sufficient framework to synthesize l-stable networks in which the controller and plant can be subject to delays and data dropouts. This framework can be applied to control systems which use “soft-real-time” cooperative schedulers as well as those which use wired and wireless network feedback. The framework applies to plants and controllers which are passive, therefore these passive systems can be either linear, nonlinear, and (or) time-varying. This framework arises from fundamental results related to passive control, and scattering theory which are used to design passive force-feedback telemanipulation systems, in which we provide a short review. Theorem 3 states how a (non)linear (strictly input or strictly output) passive plant can be transformed to a discrete (strictly input) passive plant using a particular digital sampling and hold scheme. Furthermore, Theorem 4(5) provide new sufficient conditions for l (and L)-stability in which a strictly-output passive controller and plant are interconnected with only wave-variables. Lemma 2 shows it is sufficient to use discrete wave-variables when data is subject to fixed time delays and dropouts in order to maintain passivity. Lemma 3 shows how to safely handle time varying discrete wave-variable data in order to maintain passivity. Based on these new theories, we provide an extensive set of new results as they relate to LTI systems. For example, Proposition 2 shows how a LTI strictly-output passive observer can be implemented. We then present a new cooperative scheduler algorithm to implement an l-stable control network. We also provide an illustrative simulated example which uses a passive observer followed with a discussion for future research.