Physics-Informed Neural Nets for Control of Dynamical Systems

Antonelo, Eric Aislan; Camponogara, Eduardo; Seman, Laio Oriel; Souza, Eduardo Rehbein de; Jordanou, Jean Panaioti; Hübner, Jomi Fred

doi:10.48550/arxiv.2104.02556

Cited by 3 publications

(3 citation statements)

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“…Perhaps their most renowned use is in predicting fluid fields [25,26], but other notable uses include electronics applications [27,28]. Notably, there have been a few attempts to use the PINN-based method to learn and predict nonlinear dynamical systems and chaos [29][30][31][32], with a notable good attempt by Antonelo et al [33] to modify PINN to adjust systematic controls based on the predictions of PINN. Furthermore, PINN has been used to learn controls for a series of optimal planar orbit transfer problems [34].…”

Section: Introductionmentioning

confidence: 99%

Controlling Chaos in Van Der Pol Dynamics Using Signal-Encoded Deep Learning

Zhai

Sands

2022

Mathematics

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Controlling nonlinear dynamics is a long-standing problem in engineering. Harnessing known physical information to accelerate or constrain stochastic learning pursues a new paradigm of scientific machine learning. By linearizing nonlinear systems, traditional control methods cannot learn nonlinear features from chaotic data for use in control. Here, we introduce Physics-Informed Deep Operator Control (PIDOC), and by encoding the control signal and initial position into the losses of a physics-informed neural network (PINN), the nonlinear system is forced to exhibit the desired trajectory given the control signal. PIDOC receives signals as physics commands and learns from the chaotic data output from the nonlinear van der Pol system, where the output of the PINN is the control. Applied to a benchmark problem, PIDOC successfully implements control with a higher stochasticity for higher-order terms. PIDOC has also been proven to be capable of converging to different desired trajectories based on case studies. Initial positions slightly affect the control accuracy at the beginning stage yet do not change the overall control quality. For highly nonlinear systems, PIDOC is not able to execute control with a high accuracy compared with the benchmark problem. The depth and width of the neural network structure do not greatly change the convergence of PIDOC based on case studies of van der Pol systems with low and high nonlinearities. Surprisingly, enlarging the control signal does not help to improve the control quality. The proposed framework can potentially be applied to many nonlinear systems for nonlinear controls.

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Section: Introductionmentioning

confidence: 99%

Controlling Chaos in Van Der Pol Dynamics Using Signal-Encoded Deep Learning

Zhai

Sands

2022

Mathematics

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“…However, the study on this matter in the engineering area is currently still at the stage of using ordinary DNN [25][26] and time series forecasting models such as LSTM [27]. On the other hand, all existing data-driven methods for CODES are based on PINN and therefore cannot handle parametric CODES [6,28,29]. Following the concept of PINO, we aim to propose a physicsinformed neural operator PINO-MBD for CODES in MBD.…”

Section: Machine Learning-based Pde Solversmentioning

confidence: 99%

PINO-MBD: Physics-informed Neural Operator for Solving Coupled ODEs in Multi-body Dynamics

Ding

Tong

et al. 2022

Preprint

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In multi-body dynamics, the motion of a complicated physical object is described as a coupled ordinary differential equation system with multiple unknown solutions. Engineers need to constantly adjust the object to meet requirements at the design stage, where a highly efficient solver is needed. The rise of machine learning-based partial differential equation solvers can meet this need. These solvers can be classified into two categories: approximating the solution function (Physics-informed neural network) and learning the solution operator (Neural operator). The recently proposed physics-informed neural operator (PINO) gains advantages from both categories by embedding physics equations into the loss function of a neural operator. Following this state-of-art concept, we propose the physics-informed neural operator for coupled ODEs in multi-body dynamics (PINO-MBD), which learns the mapping between parameter spaces and solution spaces. Once PINO-MBD is trained, only one forward pass of the network is required to obtain the solutions for a new instance with different parameters. To handle the difficulty that coupled ODEs contain multiple solutions (instead of only one in normal PDE problems), two new physics embedding methods are also proposed. The experimental results on classic vehicle-track coupled dynamics problem show state-of-art performance not only on solutions but also the first and second derivatives of solutions.

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“…However to solve an MPC, we require addition of control variables u. In this work, we add provision for using the control variable u, and a time variable t, to be fed to the neural network, as separate signals, similar to [31]. Substituting the continuous variables, with φ from Eqn.…”

Section: Physics-informed Neural Networkmentioning

confidence: 99%

RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Network

Sanyal¹,

Roy²

2022

Preprint

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Model Predictive Control (MPC) is a state-of-theart (SOTA) control technique which requires solving hard constrained optimization problems iteratively. For uncertain dynamics, analytical model based robust MPC imposes additional constraints, increasing the hardness of the problem. The problem exacerbates in performance-critical applications, when more compute is required in lesser time. Data-driven regression methods such as Neural Networks have been proposed in the past to approximate system dynamics. However, such models rely on high volumes of labeled data, in the absence of symbolic analytical priors. This incurs non-trivial training overheads. Physics-informed Neural Networks (PINNs) have gained traction for approximating non-linear system of ordinary differential equations (ODEs), with reasonable accuracy. In this work, we propose a Robust Adaptive MPC framework via PINNs (RAMP-Net), which uses a neural network trained partly from simple ODEs and partly from data. A physics loss is used to learn simple ODEs representing ideal dynamics. Having access to analytical functions inside the loss function acts as a regularizer, enforcing robust behavior for parametric uncertainties. On the other hand, a regular data loss is used for adapting to residual disturbances (non-parametric uncertainties), unaccounted during mathematical modelling. Experiments are performed in a simulated environment for trajectory tracking of a quadrotor. We report 7.8% to 43.2% and 8.04% to 61.5% reduction in tracking errors for speeds ranging from 0.5 to 1.75 m/s compared to two SOTA regression based MPC methods.

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Physics-Informed Neural Nets for Control of Dynamical Systems

Cited by 3 publications

References 0 publications

Controlling Chaos in Van Der Pol Dynamics Using Signal-Encoded Deep Learning

Controlling Chaos in Van Der Pol Dynamics Using Signal-Encoded Deep Learning

PINO-MBD: Physics-informed Neural Operator for Solving Coupled ODEs in Multi-body Dynamics

RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Network

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