Minimal-time uncertain output final value of unknown DT-LTI systems with application to the decentralised network consensus problem
Ye Yuan, Guy-Bart V. Stan, Ling Shi, Mauricio Barahona, Jorge M. Gonçalves · Cambridge University Engineering Department Publications Database · 2010
For an unknown discrete-time linear time- invariant (DTLTI) autonomous system, this paper characterises the minimal number of steps necessary to compute the asymp- totic final value of an output observed with uncertainty. We show that this minimal number of steps can also be obtained directly from a graphical representation of the DTLTI system using Mason's rule. Moreover, we provide heuristic algorithms to compute the final value in a minimal amount of time with uncertain observations. The general structure of these algorithms is as follows. Step one, by introducing a one-step prediction error metric, we characterise the minimal length of recursion for the outputs of the considered DTLTI system. Step two, by constructing a new data set close to the original uncertain output data set satisfying certain conditions, we estimate the final value of the original output set by computing the final value associated with this new data set. Step three, we characterise the difference between the estimated final values obtained from different estimated data sets. Furthermore, we also consider systems with time-delays and investigate how the delays affect the minimal number of steps required to compute the final value. These results find applications in minimal-time network consensus problems with minimal and uncertain (e.g., noisy) information.