Design of Digital Control Networks for Continuous Passive Plants Subject To Delays and Data Dropouts

We present a framework to synthesize lm 2 -stable control networks which are subject to delays and data dropouts. This framework can be applied to control systems which use “soft-real-time” cooperative schedulers and wired or wireless network feedback. The approach applies to passive plants and controllers that can be either linear, nonlinear, and (or) time-varying. This framework is based on fundamental results presented here related to passive control, and scattering theory. It loosens the requirements for the passive systems to possess specialized storage functions and state space descriptions as is typically done in showing Lyapunov stability for passive force-feedback telemanipulation systems, of which we provide a short review. The benefits of loosening these requirements will become quite obvious to the reader as we make connections between the general input-output definitions of passivity and the more specific passive dissipative system definitions. Theorem 4 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 5(6) provide new sufficient conditions for lm 2 (and L m 2 )-stability in which a strictly-output passive controller and plant are interconnected with only wavevariables. 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. Proposition 1 shows how to synthesize a discrete passive LTI system from a continuous passive LTI system, which leads to Corollary 1 that shows how to synthesize a discrete strictly-output passive LTI system from a continuous passive LTI system. Corollary 2 provides a suitable method to appropriately scale the synthesized discrete strictly-output passive LTI system. Corollaries 3 and 4 show how to integrate the discrete strictly-output passive LTI system with wave variables. Proposition 2 shows how a LTI strictly-output passive observer can be implemented for a strictly-output passive LTI continuous plant. Corollaries 5 and 6 result from Proposition 2 as they relate to an observer using wave variables. We then present a new cooperative scheduler algorithm to implement a lm 2 -stable control network. We also provide an illustrative simulated example followed by a discussion of future research.