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# Research (oil and gas)

They are also listed below:

## Physics-Informed Neural Nets for Control of Dynamical Systems

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by Ordinary Differential Equations (ODEs), the conventional PINN has a continuous time input variable and outputs the solution of the corresponding ODE. In their original form, PINNs do not allow control inputs neither can they simulate for long-range intervals without serious degradation in their predictions. In this context, this work presents a new framework called Physics-Informed Neural Nets for Control (PINC), which proposes a novel PINN-based architecture that is amenable to control problems and able to simulate for longer-range time horizons that are not fixed beforehand. The framework has new inputs to account for the initial state of the system and the control action. In PINC, the response over the complete time horizon is split such that each smaller interval constitutes a solution of the ODE conditioned on the fixed values of initial state and control action for that interval. The whole response is formed by feeding back the predictions of the terminal state as the initial state for the next interval. This proposal enables the optimal control of dynamic systems, integrating a priori knowledge from experts and data collected from plants into control applications. We showcase our proposal in the control of two nonlinear dynamic systems: the Van der Pol oscillator and the four-tank system.

**MPC**: Representation of the output prediction in a time instant, where the proposed actions generate a predicted behavior that reduces the distance between the value predicted by the model and a reference trajectory:

The PINC network has initial state y(0) of the dynamic system and control input u as inputs, in addition to continuous time scalar t. Both y(0) and u can be multidimensional. The output y(t) corresponds to the state of the dynamic system as a function of t 2 [0; T], and initial conditions given by y(0) and u. The deep network is fully connected even though not all connections are shown:

Below, modes of operation of the PINC network. (a) PINC net operates in self-loop mode, using its own output prediction as next initial state, after T seconds. This operation mode is used within one iteration of MPC, for trajectory generation until the prediction horizon of MPC completes (predicted output from the first Figure). (b) Block diagram for PINC connected to the plant. One pass through the diagram arrows corresponds to one MPC iteration applying a control input u for Ts timesteps for both plant and PINC network. Note that the initial state of the PINC net is set to the real output of the plant. In practice, in MPC, these two operation modes are executed in an alternated way (optimization in the prediction horizon, and application of control action).

a).

b)

Below, the representation of a trained PINC network evolving through time in self-loop mode (previous Figure a)) for trajectory generation in prediction horizon. The top dashed black curve corresponds to a predicted trajectory y of a hypothetical dynamic system in continuous time. The states y[k] are snapshots of the system in discrete time k positioned at the equidistant vertical lines. Between two vertical lines (during the inner continuous interval between steps k and k + 1), the PINC net learns the solution of an ODE with t \in [0; T], conditioned on a fixed control input u[k] (blue solid line) and initial state y(0) (green thick dashed line). Control action u[k] is changed at the vertical lines and kept fixed for T seconds, and the initial state y(0) in the interval between steps k and k + 1 is updated to the last state of the previous interval k 1 (indicated by the red curved arrow). The PINC net can directly predict the states at the vertical lines without the need to infer intermediate states t < T as numerical simulation does. Here, we assume that T = Ts and, thus, the number of discrete timesteps M is equal to the length of the prediction horizon in MPC.

## ESN-PNMPC: Efficient data-driven model predictive control of unknown nonlinear processes

The **control of nonlinear industrial processes** is a challenging task since the model of the plant may not be completely known a priori. In addition, the application of **nonlinear model predictive control** may be affected by modeling errors and subject to high computational complexity.

In this work, a new efficient **data-driven scheme** is proposed that alleviates some known issues in the so called **Practical Nonlinear Model Predictive Controll**er (PNMPC). In **PNMPC**, the model is only linearized partially: while the free response of the system is kept fully nonlinear, only the forced response is linearized. The general model for PNMPC proposed in this work consists of an **Echo State Network** (**ESN**), a recurrent neural network with very efficient training for system identification.

The benefit of the proposed **ESN-PNMPC** scheme is that it allows:

- fast system identification for nonlinear dynamic systems with arbitrary accuracy;
- analytical computation of derivatives from the ESN model for the forced response.

This last feature assures significantly lower computational complexity for derivative computation when compared to the original finite difference method of PNMPC.

The proposed scheme is also enhanced with a correction filter that provides robustness to unforeseen disturbances during execution time, and compared to an **LSTM** (Long-Short Term Memory) implementation for the model as well as to a PI controller. The universality of the approach is shown by application to the **control of different nonlinear plants**.

Figure from J. Jordanou 2020, et al (submitted).

## Online recurrent neural network learning for control of nonlinear plants in oil and gas production platforms

This research line aims at designing **adaptive controllers** by using **Echo State Networks** (ESN) as a efficient data-driven method for training **recurrent neural networks** capable of controlling complex nonlinear plants, with a focus on **oil and gas production platforms** from *Petrobras*.

The resulting **ESN**-based controllers should learn **inverse models of the controlled plant **in an online fashion by interacting with the industrial plant and observing its dynamical behaviors.

In collaboration with supervised Master Student Jean P. Jordanou.

Well model. Figure by Jahanshahi et al. (2012).

Manifold connecting two oil wells and a riser. Figure by Jordanou.

Scheme of Adaptive ESN-based controller and nonlinear plant. Figure by Jordanou

## Proxy dynamical models of offshore oil production platforms via recurrent neural networks

Process measurements are of vital importance for monitoring and **control of industrial plants**. When we consider **offshore oil production platforms**, wells that require *gas-lift* technology to yield oil production from low pressure oil reservoirs can become unstable under some conditions. This undesirable phenomenon is usually called *slugging flow*, and can be identified by an oscillatory behavior of the downhole pressure measurement.

Given the importance of this measurement and the unreliability of the related sensor, this work aims at designing data-driven **soft-sensors** for **downhole pressure estimation** in two contexts: one for speeding up first-principled model simulation of a vertical riser model; and another for estimating the downhole pressure using real-world data from an oil well from *Petrobras* based only on topside platform measurements. Both tasks are tackled by employing **Echo State Networks (ESNs)** as an efficient technique for training Recurrent Neural Networks.

We show that a single ESN is capable of robustly modeling both the slugging flow behavior and a steady state based only on a square wave input signal representing the production choke opening in the vertical riser. Besides, we compare the performance of a standard network to the performance of a multiple timescale hierarchical architecture in the second task and show that for some periods the latter architecture performs better.