(295b) Distributed Kalman Filter Approach to Approximate the Arrival Cost in Distributed Moving Horizon Estimation

There has been a rapid increase in the scale, complexity, and level of integration of manufacturing systems/industrial processes [1][2][3]. The traditional centralized paradigm has been insufficient to handle plantwide monitoring and decision-making for these industrial processes. This has highlighted the necessity of using the distributed architecture to develop flexible and scalable decision-making solutions for large-scale industrial systems with tightly integrated physical components. Within a distributed framework, multiple computing agents are deployed to make decisions on process operation through real-time communication. This way, a higher fault tolerance ability, maintenance flexibility, and computational efficiency can be achieved by the distributed framework [4]. As the dual problem of distributed process control, distributed state estimation, in particular distributed moving horizon estimation (DMHE), is has been crucial for the real-time monitoring and control of large-scale industrial processes due to its capability of addressing scalability, nonlinearity, and constraints on variables.

In this work, we study partition-based nonlinear DMHE, which incorporates multiple local estimators that are designed based on decomposed subsystem models. Each estimator calculates to provide estimates of the corresponding subsystem states by solving a partitioned optimization problem every sampling time. There have been some results on partition-based DMHE with iterative executions of the local estimators [5][6], which can provide estimates that can converge to the estimates of the centralized counterpart.

Moving horizon estimation (MHE) convert a state estimation problem into an optimization problem, which minimizes a cost function over a fixed-size moving horizon of sensor measurements. Typically, increasing the length of the estimation horizon can improve the performance of the MHE algorithm, but at the expense of significantly higher computational complexity. A cost-effective means to approximately characterize the effect of past measurements prior to the current estimation window, an additional term called arrival cost can be incorporated into the objective function [7]. A well-designed approximation of the arrival cost can reduce the length of the estimation horizon and thus reduce the complexity of the optimization problem without compromising on performance and stability [8]. However, in most of the studies on partition-based DMHE [6][9][10], the arrival cost is either neglected or designed based on a fixed weighting matrix. In our previous design [10], arrival costs were neglected in two of the local estimators of the proposed DMHE algorithms. This can lead to inadequate approximations of the costs to arrive and poor estimates if the length of the estimation horizon is not sufficiently long. In [6][9], the arrival cost was designed as a weighting 2-norm of the error between the state estimates and the initial guess at the beginning of the estimation horizon. It is worthwhile mentioning that if the weighting matrix is not appropriately tuned, the estimation accuracy may be compromised.

In this work, we shed light on improving the calculation of the arrival costs for the local estimators within a DMHE framework, and propose an iterative partition-based DMHE algorithm. Specifically, the weighting matrices for the arrival costs for the local estimators are updated at every new sampling instant by leveraging distributed Kalman filter. Specifically, first, we propose a partition-based distributed full-information estimation design where the estimators are required to be executed iteratively. Then, in the linear context, full-information estimation formulation is taken advantage of to formulate an iterative DMHE algorithm with adaptive arrival costs for the local estimators. The approximations of the local arrival costs are accounted for by implementing the distributed Kalman filter algorithm. We prove that the calculated arrival costs based on the proposed method amount to the information being disregarded due to the transition from the distributed full-information estimation to DMHE in the linear unconstrained setting. The stability of this DMHE design is conducted for linear systems of interconnected subsystems. Finally, the proposed DMHE algorithm is extended to general nonlinear processes, and its performance is illustrated via the application to wastewater treatment.

References

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