Jean Panaioti Jordanou

Jean Panaioti Jordanou, Eric Aislan Antonelo, Eduardo Camponogara et al.

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.

Jean Panaioti Jordanou, Eduardo Camponogara, Eduardo Gildin

Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven identification of such systems, the literature is quite scarce in terms of works that tackle the identification of LPV models for large-scale systems. Since large-scale systems are ubiquitous in practice, this work develops a methodology for the local and global identification of large-scale LPV systems based on nonintrusive reduced-order modeling. The developed method is coined as DMD-LPV for being inspired in the Dynamic Mode Decomposition (DMD). To validate the proposed identification method, we identify a system described by a discretized linear diffusion equation, with the diffusion gain defined by a polynomial over a parameter. The experiments show that the proposed method can easily identify a reduced-order LPV model of a given large-scale system without the need to perform identification in the full-order dimension, and with almost no performance decay over performing a reduction, given that the model structure is well-established.

Eric Aislan Antonelo, Eduardo Camponogara, Laio Oriel Seman et al.

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 variable 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, making it a very flexible framework when compared to traditional PINNs. Furthermore, this long-range time simulation of differential equations is faster than numerical methods since it relies only on signal propagation through the network, making it less computationally costly and, thus, a better alternative for simulation of models in Model Predictive Control. We showcase our proposal in the control of two nonlinear dynamic systems: the Van der Pol oscillator and the four-tank system.