(137b) Distributed Moving Horizon Estimation for Nonlinear Systems With Bounded Uncertainties
Driven by the considerable economic efficiency that a complex and interactive process design can offer, large-scale complex chemical processes increasingly appear in the modern process industry. Such a large-scale complex chemical process ususally consists of several unit operations (subsystems), which are connected together through material and energy flows. Because of the increased process scale and the significant interactions between different subsystems, it poses great challenges in the design of automatic control systems for such large-scale complex chemical processes which are desired to fulfill the fundamental safety, environmental sustainability and profitability requirements. In recent years, distributed model predictive control (DMPC) has emerged as an attractive control approach to handle the scale and interactions of large-scale complex chemical processes. In a DMPC approach, different model predictive controllers communicate through a communication network to cooperate their actions in order to achieve optimal performance in a timely fashion. However, almost all of the existing DMPC designs are developed under the assumption that the state measurements of subsystems or the whole system are available. This assumption does not hold in many applications and we need to consider the design of state observers for DMPC systems.
One obvious approach is to design a centralized observer for a DMPC system, but this does not align with the goal of DMPC. Another approach is to design distributed state estimation systems for DMPC designs. The existing distributed state estimation (DSE) studies are primarily on distributed Kalman filtering. However, these approaches were developed in the context of linear systems. In recent years, distributed moving horizon estimation (DMHE) approaches have been proposed based on consensus algorithms which can handle nonlinearities explicitly and can account for constraints and optimality considerations. However, the existing DMHE approaches require good approximation of the arrival cost (which is in general difficult to obtain when constrained nonlinear systems are considered) and can not in general used for control purpose because the boundedness of the estimation error is not established. The above observations motivate the development of DMHE for nonlinear systems with provable bounded estimation errors when the uncertainties are bounded and tunable convergence rate.
In the present work, we present a robust DMHE design for nonlinear systems with bounded uncertainties. Specifically, we consider a class of nonlinear systems that are composed of several subsystems. Based on the assumption that there exists a local nonlinear deterministic observer for each subsystem that is able to track the nominal subsystem state when the interactions between the subsystems are zero (i.e., the local observers are designed without consider the interactions between the subsystems), the robust DMHE is designed. First, a systematic approach is developed to account for the interactions between the subsystems. Subsequently, based on the local observers and the interaction model, the DMHE is designed. In the design of the DMHE, the local observers and the interaction model are taken advantage of to calculate a confidence region for the actual system state. The DMHE is only allowed to optimize the state estimate within the confidence region. The proposed DMHE is proved to give bounded estimation errors when the uncertainties are bounded. The convergence rate of the DMHE to the actual system state can also be tuned to be any large value as long as the sampling time of the DMHE is sufficiently small. This gives an effective separation principle between the observer and controller designs. The applicability and effectiveness of the proposed DMHE are illustrated via the application to a reactor-separator process example.
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