(308d) Distributed Moving Horizon State Estimation of Two-Time-Scale Nonlinear Systems

In recent years, there is significant attention on the development of distributed predictive control schemes for plant-wide control of large-scale complex chemical processes. In these distributed schemes, different controllers communicate with each other to coordinate their actions to achieve improved control performance over decentralized control schemes. It has been demonstrated that these distributed schemes are particularly useful for large-scale integrated process networks such that the coupling between different operating units cannot be neglected. However, almost all of these distributed predictive control schemes are dependent on the availability of the state measurements of the entire system. It is desirable to develop state estimation schemes in the distributed framework.

Motivated by the lack of distributed state estimation schemes that are suitable for output feedback control, an observer-enhanced distributed moving horizon state estimation (DMHE) scheme to estimate the state of large-scale systems in a distributed manner was developed in our previous work [1]. It has been shown that the DMHE scheme gives ensured ultimate boundedness of the estimation error.  Along this line,  in [2], an approach was developed to handle time-varying delays in the communication network of DMHE schemes and was extended in [3] to handle simultaneously communication delays and data losses.

In this work, we continue our efforts in the development of DMHE and consider DMHE design for a class of two-time-scale nonlinear systems (which are common occurrences in chemical processes) that are described in the framework of singularly perturbed systems with bounded uncertainties. Firstly, based on the time-scale separation property, the studied singularly perturbed nonlinear system is decomposed into a reduced-order fast system and a slow system, the latter of which is further divided into several interconnected subsystems for better adaptability. Secondly, an auxiliary nonlinear observer is developed for each subsystem to calculate a confidence region, within which the designed local estimator calculates and gives optimal state estimates for each of the decomposed slow subsystems and the fast system. In the proposed DMHE scheme, only the slow subsystems are required to send out information to other subsystems. The reduced-order fast system does not send out any information to other slow subsystems.  The developed DMHE is proved separately to give bounded estimation errors for both slow subsystems and the reduced-order fast system. Finally, the effectiveness and adaptability of the proposed DMHE are illustrated via the application to a complex chemical process.

[1] Zhang, J. & Liu, J. Distributed Moving Horizon Estimation for Nonlinear Systems with Bounded Uncertainties. Journal of Process Control, 2013, 23, 1281-1295.

[2] Zhang, J. & Liu, J. Observer-Enhanced Distributed Moving Horizon State Estimation subject to Communication Delays. Journal of Process Control, 2014, 24, 672-686.

[3] Zeng, J. & Liu, J. Distributed Moving Horizon State Estimation: Simultaneously Handling Communication Delays and Data Losses. Systems & Control Letters, 2015, 75, 56-68.