Observer Design for Nonlinear Networked Control Systems With Persistently Exciting Protocols

Abstract

We study the design of state observers for nonlinear networked control systems (NCSs) affected by disturbances and measurement noise, via an emulation-like approach. That is, given an observer designed with a specific stability property in the absence of communication constraints, we implement it over a network and we provide sufficient conditions on the latter to preserve the stability property of the observer. In particular, we provide a bound on the maximum allowable transmission interval (MATI) that guarantees an input-to-state stability (ISS) property for the corresponding estimation error system. The stability analysis is trajectory-based, utilises small-gain arguments, and exploits a persistently exciting (PE) property of the scheduling protocols. This property is key in our analysis and allows us to obtain significantly larger MATI bounds in comparison to the ones found in the literature. Our results hold for a general class of NCSs, however, we show that these results are also applicable to NCSs implemented over a specific physical network called WirelessHART (WH). The latter is mainly characterised by its multi-hop structure, slotted communication cycles, and the possibility to simultaneously transmit over different frequencies. We show that our results can be further improved by taking into account the intrinsic structure of the WH-NCS model. That is, we explicitly exploit the model structure in our analysis to obtain an even tighter MATI bound that guarantees the same ISS property for the estimation error system. Finally, to illustrate our results, we present analysis and numerical simulations for a class of Lipschitz non-linear systems and high-gain observers.

On state estimation for nonlinear systems under random access wireless protocols

“…We note that Assumption 3 ensures an ISS property on the designed observer so that it is robust with respect to (e, v, w), which is satisfied by various observer designs in the literature, see e.g., [57,58] and the references therein. These ISS conditions are the stochastic counterpart of the ones often adopted when using emulation-based design, see e.g., [14,40]. Similar stochastic ISS notions have been used in the literature, see e.g., [59].…”

“…We assume the upper bound on |ỹ| to be independent of z in this paper. However, this can be relaxed as done in our previous deterministic work [40], at the expense of getting weaker stability properties. To avoid obscuring the main message of this paper, we adopt Assumption 2(b), as this already holds for a large class of observers, see the example in Section 4 for instance.…”

“…In this context, a different analysis that uses tools such as dominated convergence theorem is performed. • This proposal also serves as the stochastic counterpart of our previous work on observer design in a deterministic setting [40]. We note that in [40], successive transmissions are uniformly (deterministically) bounded by a maximum allowable transmission interval (MATI).…”

“…• This proposal also serves as the stochastic counterpart of our previous work on observer design in a deterministic setting [40]. We note that in [40], successive transmissions are uniformly (deterministically) bounded by a maximum allowable transmission interval (MATI). We highlight that wireless networks naturally exhibit stochastic phenomena.…”

“…We highlight that wireless networks naturally exhibit stochastic phenomena. Therefore, in order to tackle observer design in WNCS settings, this work provides a more suitable framework than [40], for which the structure of the wireless network given by multiple channel probabilities of success and random transmission times are taken into account. • Lastly, we extend our recent stochastic work [41] on observer design to a more general case where each node is subject to its own packet loss process.…”