@article {332, title = {Physics-Informed Neural Nets for Control of Dynamical Systems}, journal = {Neurocomputing}, volume = {579}, year = {2024}, chapter = {127419}, abstract = {

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 \emph{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.

}, doi = {10.1016/j.neucom.2024.127419}, url = {https://doi.org/10.1016/j.neucom.2017.09.005}, author = {Eric A Antonelo and Eduardo Camponogara and Laio Oriel Seman and Eduardo Rehbein de Souza and Jean Panaioti Jordanou and Jomi Fred H{\"u}bner} } @article {352, title = {Investigation of Proper Orthogonal Decomposition for Echo State Networks}, journal = {Neurocomputing}, year = {2023}, pages = {126395}, abstract = {

Echo State Networks (ESN) are a type of Recurrent Neural Network that yields promising results in representing time series and nonlinear dynamic systems. Although they are equipped with a very efficient training procedure, Reservoir Computing strategies, such as the ESN, require high-order networks, i.e., many neurons, resulting in a large number of states that are magnitudes higher than the number of model inputs and outputs. A large number of states not only makes the time-step computation more costly but also may pose robustness issues, especially when applying ESNs to problems such as Model Predictive Control (MPC) and other optimal control problems. One way to circumvent this complexity issue is through Model Order Reduction strategies such as the Proper Orthogonal Decomposition (POD) and its variants (POD-DEIM), whereby we find an equivalent lower order representation to an already trained high dimension ESN. To this end, this work aims to investigate and analyze the performance of POD methods in Echo State Networks, evaluating their effectiveness through the Memory Capacity (MC) of the POD-reduced network compared to the original (full-order) ESN. We also perform experiments on two numerical case studies: a NARMA10 difference equation and an oil platform containing two wells and one riser. The results show that there is little loss of performance comparing the original ESN to a POD-reduced counterpart and that the performance of a POD-reduced ESN tends to be superior to a normal ESN of the same size. Also, the POD-reduced network achieves speedups of around 80\% compared to the original ESN.

}, keywords = {Echo State Networks., Model Order Reduction, reservoir computing}, issn = {0925-2312}, doi = {https://doi.org/10.1016/j.neucom.2023.126395}, url = {https://www.sciencedirect.com/science/article/pii/S0925231223005180}, author = {Jean Panaioti Jordanou and Eric Aislan Antonelo and Eduardo Camponogara and Eduardo Gildin} } @article {338, title = {Nonlinear Model Predictive Control of Electrical Submersible Pumps based on Echo State Networks }, journal = {Advanced Engineering Informatics}, volume = {52}, year = {2022}, month = {04/2022}, abstract = {

Employed for artificial lifting in oil well production, Electrical Submersible Pumps (ESP) can be operated with Model Predictive Control (MPC) to drive an optimal production, while ensuring a safe operation and respecting system constraints.
\ Due to the nonlinear dynamics of ESPs, Echo State Networks (ESNs), a recurrent neural network with fast training, are employed for efficient system identification of unknown dynamic systems.
Besides the synthesis of highly accurate prediction models, this work contributes by designing two Nonlinear MPC (NMPC) strategies for the control of an ESP-lifted oil well:\  a standard Single-Shooting NMPC that embeds the ESN model completely, and the Practical Nonlinear Model Predictive Controller (PNMPC) that\  approximates the NMPC through fast trajectory-linearization of the ESN model.
Another contribution is the implementation of an error correction filter to reject disturbances and counter modeling errors in both NMPC strategies.
Finally, in computational experiments, both ESN-based NMPC strategies performed well in controlling simulated ESP-lifted oil wells when the model of the plant is unknown. However, PNMPC was more efficient and induced a similar performance to standard NMPC.

}, issn = {1474-0346}, doi = {10.1016/j.aei.2022.101553}, author = {Jean Panaioti Jordanou and Iver Osnes and Sondre B. Hernes and Eduardo Camponogara and Eric Aislan Antonelo and Lars Imsland} } @article {337, title = {Echo State Networks for Practical Nonlinear Model Predictive Control of Unknown Dynamic Systems}, journal = {IEEE Transactions on Neural Networks and Learning Systems}, year = {2021}, pages = {1-15}, abstract = {

Nonlinear model predictive control (NMPC) of industrial processes is changeling in part because the model of the plant may not be completely known but also for being computationally demanding. This work proposes an extremely efficient reservoir computing (RC)-based control framework that speeds up the NMPC of processes. In this framework, while an echo state network (ESN) serves as the dynamic RC-based system model of a process, the practical nonlinear model predictive controller (PNMPC) simplifies NMPC by splitting the forced and the free responses of the trained ESN, yielding the so-called ESN-PNMPC architecture. While the free response is generated by the forward simulation of the ESN model, the forced response is obtained by a fast and recursive calculation of the input-output sensitivities from the ESN. The efficiency not only results from the fast training inherited by RC but also from a computationally cheap control action given by the aforementioned novel recursive formulation and the computation in the reduced dimension space of input and output signals. The resulting architecture, equipped with a correction filter, is robust to unforeseen disturbances. The potential of the ESN-PNMPC is shown by application to the control of the four-tank system and an oil production platform, outperforming the predictive approach with a long-short term memory (LSTM) model, two standard linear control algorithms, and approximate predictive control.

}, keywords = {Echo State Networks, Model Predictive Control, reservoir computing}, doi = {10.1109/TNNLS.2021.3136357}, url = {https://ieeexplore.ieee.org/abstract/document/9664461}, author = {Jordanou, Jean Panaioti and Antonelo, Eric Aislan and Camponogara, Eduardo} } @article {309, title = {Online Learning Control with Echo State Networks of an Oil Production Platform}, journal = {Engineering Applications of Artificial Intelligence}, volume = {85}, year = {2019}, pages = {214-228}, abstract = {

The design of a control algorithm is exceptionally hard when models are unavailable, the physics are varying in time, or structural uncertainties are involved. One such case is an oil production platform in which reservoir conditions and the composition of the multiphase flow are not known precisely. Today, with streams of data being generated from sensors, black-box adaptive control emerged as an alternative to the control of such systems. In this work, an online adaptive controller based on Echo State Networks (ESNs) is employed in diverse scenarios of controlling an oil production platform. The ESN learns an inverse model of the plant from which a control law is derived to attain set-point tracking of a simulated model. The analysis considers high steady-state gains, potentially unstable conditions, and a multi-variate control structure. All in all, this work contributes to the literature by demonstrating that online-learning control can be effective in highly complex dynamic systems (oil production platforms) devoid of suitable models, and with multiple inputs and outputs.

}, doi = {10.1016/j.engappai.2019.06.011}, url = {https://www.sciencedirect.com/science/article/pii/S0952197619301502?dgcid=author}, author = {Jean P. Jordanou and Eric A. Antonelo and Eduardo Camponogara} } @article {304, title = {Nonlinear Model Predictive Control of an Oil Well with Echo State Networks}, journal = {IFAC-PapersOnLine (3rd IFAC Workshop on Automatic Control in Offshore Oil and Gas Production OOGP 2018)}, volume = {51}, year = {2018}, pages = {13 - 18}, abstract = {

In oil production platforms, processes are nonlinear and prone to modeling errors, as the flowregime and components are not entirely known and can bring about structural uncertainties,making designing predictive control algorithms for this type of system a challenge. In thiswork, an efficient data-driven framework for Model Predictive Control (MPC) using Echo StateNetworks (ESN) as prediction model is proposed. Differently from previous work, the ESN model for MPC is only linearized partially: while the free response of the system is kept fullynonlinear, only the forced response is linearized. This MPC framework is known in the literatureas the Practical Nonlinear Model Predictive Controller (PNMPC). In this work, by using theanalytically computed gradient from the ESN model, no finite difference method to compute derivatives is needed as in PNMPC. The proposed method, called PNMPC-ESN, is applied tocontrol a simplified model of a gas lifted oil well, managing to successfully control the plant,obeying the established constraints while maintaining setpoint tracking.

}, keywords = {Echo State Networks, Gas, Model Predictive Control, Oil, System Identification}, issn = {2405-8963}, doi = {https://doi.org/10.1016/j.ifacol.2018.06.348}, url = {http://www.sciencedirect.com/science/article/pii/S2405896318306785}, author = {Jean Panaioti Jordanou and Eduardo Camponogara and Eric A. Antonelo and Marco Aurelio S. de Aguiar} } @proceedings {302, title = {Recurrent Neural Network based control of an Oil Well}, journal = {XIII Brazilian Symposium on Intelligent Automation (SBAI)}, year = {2017}, pages = {924-931}, abstract = {

Echo State Networks (ESN) are dynamical learning models composed of two parts: a recurrent network (reservoir) with fixed weights and a linear adaptive readout output layer. The output layer\’s weights are learned for the ESN to reproduce temporal patterns usually by solving a least-squares problem. Such recurrent networks have shown promising results in previous applications to dynamic system identification and closed-loop control. This work applies an echo state network to control the bottom hole pressure of an oil well, whereby the opening of the production choke is manipulated. The controller utilizes a network to learn the plant inverse model, whose model input is the plant output and the vice-versa, and another network to compute the control action that induces a desired plant behavior. Despite the nonlinearities of the well model, the ESN effectively learned the inverse model and achieved near global setpoint tracking and disturbance rejection, with little setpoint deviation in the latter case. These results show that echo state networks are a viable tool for the control of complex dynamic systems by means of online inverse-model learning.

}, url = {https://www.ufrgs.br/sbai17/papers/paper_269.pdf}, author = {Jean Panaioti Jordanou and Eric A Antonelo and Eduardo Camponogara and Marco Aurelio S. de Aguiar} }