(105b) Online Data-Gathering Lyapunov-Based Economic Model Predictive Control for Model Selection and Verification

Several techniques have been proposed in the literature regarding process data collection for developing model-based control designs such as model predictive control (MPC) (e.g., [1, 2, 3, 4, 5]). Particularly, the model must be sufficiently accurate to have state predictions representative of the process and allow the controller to compute proper control actions based on the expected future states. However, if the process model used by the controller does not capture the plant dynamics (e.g., due to process dynamics changes over the time of operation), it must be revised and updated to achieve the desired closed-loop performance and safe operation. The task to update the process model can be more challenging when a process is operated at steady-state operation, which may not provide as much data useful for the model identification as might be desired. Moreover, data recorded offline may not carry relevant information to reidentify the process model during online operation. A control-assisted selection of the process model that allows the system to be excited out of steady-state may be used to aid in online data collection for model updates.

In this context, an MPC formulation in which experiment design is included as an auxiliary constraint has been proposed that applies control signals to excite the process and obtain relevant operational data for online identification [1]. In a similar vein, MPC based on requiring persistently exciting control actions to the process has been studied which may be used for closed-loop system identification [2, 3]. Another MPC alternative has been proposed with dual features (i.e., the control actions are computed to both control and explore the process) [4] and performs parameter identification only when there is high uncertainty in the model parameters. In addition to model/parameter identification, the selection of an appropriate model structure with a physics-based portion can play an important role in data-driven modeling techniques (e.g., structured hybrid modeling [6]) and verification for safety purposes. However, the development or selection of a physics-based model may add important challenges to the aforementioned methods, which may include the consideration of time-varying complex nonlinearities, closed-loop stability issues, and profit loss. In light of this, a type of model-based controller that incorporates a free form objective function and closed-loop stability constraints known as Lyapunov-based economic model predictive control (LEMPC) [7, 8] may be utilized to design control-assisted frameworks that could gather informative data online while accounting for time-varying process dynamics and operation, process safety, and profitability. This may also be directed to address limitations in MPC for safe learning as many learning-based control techniques cannot ensure that safety/physical constraints are satisfied during learning iterations [9].

Motivated by the above, this work investigates an online data gathering-based LEMPC for model selection and verification purposes. In particular, we propose an LEMPC design that automatically chooses and collects the information that leads to the most suitable model candidate among a predefined set of models available, which could potentially contain data-driven/first-principles model structures, while ensuring closed-loop stability in a safe region of state-space. Specifically, we formalize a flexible control method in which the objective function includes a soft constraint on the deviation of state predictions from the various potential models from one another. Assuming that the stability regions for the different potential models are nested and that a sufficiently accurate model is contained within the set of potential models, closed-loop stability can be maintained (in the sense that the closed-loop state is maintained within a bounded region of operation throughout the time of operation) even as data is gathered to discern which of the model candidates is most appropriate to utilize in the controller. Models are discarded from the set utilized by the controller when, at the end of a sampling period, state predictions from a given model and state measurements over the last sampling period are determined not to be sufficiently close to one another. We discuss methods for reducing the complexity of the proposed technique compared to a case in which state predictions from all models are subjected to Lyapunov-based stability constraints, and compare this type of strategy for probing for model fidelity with other strategies for determining desired information that could lead to the development of more physics-based process models from on-line operating data, such as the strategy in [10] or strategies which attempt to develop multiple steady-states in state-space which LEMPC’s might drive the closed-loop state toward to attempt to gather data along specific trajectories. We discuss different techniques for triggering that type of probing for data, including techniques which only attempt to gather the data if the profit is not significantly impacted over the subsequent sampling period. For the data-gathering scheme based on discerning an adequate model from a set of models, we discuss techniques for selecting the appropriate model. A chemical process example consisting of a continuous stirred tank reactor for the case that there are several candidate models, including the first-principles model and its linearization around the operating steady-state, is used to illustrate the proposed data gathering-based control scheme based on model discernment.

References:

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9. Hewing, L., Wabersich, K. P., Menner, M., & Zeilinger, M. N. (2020). Learning-based model predictive control: Toward safe learning in control. Annual Review of Control, Robotics, and Autonomous Systems, 3, 269-296.

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