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.

}, url = {https://arxiv.org/abs/2104.02556}, 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 {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} }