Predicting the future state of disturbed LTI systems: A solution based on high-order observers

Abstract

Predicting the state of a system in a relatively near future time instant is often needed for control purposes. However, when the system is affected by external disturbances, its future state is dependent on the forthcoming disturbance; which is-in most of the cases-unknown and impossible to measure. In this scenario, making predictions of the future system-state is not straightforward and-indeed-there are scarce contributions provided to this issue. This paper treats the following problem: given a LTI system affected by continuously differentiable unknown disturbances, how its future state can be predicted in a sufficiently small time-horizon by high-order observers. Observer design methodologies in order to reduce the prediction errors are given. Comparisons with other solutions are also established.

Novel Strategies to design Controllers and State Predictors based on Disturbance Observers

“…DOBFD (Wang et al 1996;Han et al 2018;Bernardi et al 2020); and to make predictions of the future system-state i.e. DOBP (Sanz et al 2016b;Castillo et al 2020b). In reference to this, during the last decades an important number of DOB algorithms have been developed.…”

“…DOBCs (Han 2009;Shim et al 2009;She et al 2008;Li et al 2012;Castillo et al 2018;Khlebnikov 2016); ii) Prediction of the future system-state i.e. DOBPs (Sanz et al 2016b;Castillo et al 2020b); and iii) Failure Detection i.e. DOBFDs (Wang et al 1996;Han et al 2018;Bernardi et al 2020).…”

“…After these results, we come to the conclusion that some parts of the technical developments employed to solve the feedback-design problem for DOBCs could be also applied to the prediction problem. This permitted to publish the work (Castillo et al 2020b), summarizing the main results on DOBPs.…”

“…Concretely, the results of Chapter 4 are mainly the ones in Castillo et al 2019b being also related with the work Castillo et al 2017. The content of Chapter 5 is published in Castillo et al 2020b. Chapter 3 has been sent for publication and it is under editorial review in Castillo et al 2020c.…”

“…The ESOs are, nowadays, one of the most popular algorithms to estimate in real-time the system and disturbance states due to their simplicity e.g. (Castillo et al 2018;Chen et al 2016;Chang 2006;Castillo et al 2020b). Let us show how they could be employed under this novel feedback design.…”