Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Nonlinear models”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models

Abstract. Strongly coupled nonlinear phenomena such as those described by Earth system models (ESMs) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESMs is to remap or interpolate component solution fields defined on their computational mesh to another mesh with a different combinatorial structure and decomposition, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESMs. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations is conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid (Hill et al., 2004), TempestRemap (Ullrich and Taylor, 2015), generalized moving least squares (GMLS) (Trask and Kuberry, 2020) with post-processing filters, and WLS-ENOR (Li et al., 2020). By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless GMLS and hybrid mesh-based WLS-ENOR schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh-invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations, thereby allowing for a more complete analysis of production-ready remapping packages.

58 GEOSCIENCES↗
DOE OSTI2021

Heuristic Dispatch Based on Price Signals for Behind-the-Meter PV-Battery Systems in the System Advisor Model

The economic potential of a behind-the-meter (BTM) PV-battery system depends greatly on how the battery is dispatched. Different utility rates, system sizes, generation and load profiles can all require different dispatch strategies. This paper presents price signals dispatch, a new algorithm for automated economic dispatch of BTM PV-battery systems, which utilizes 24-hour PV and load forecasts, degradation data, and utility rates. The algorithm is integrated with the System Advisor Model (SAM) tool and is tested with a nonlinear generic electrochemical battery model. Price signals dispatch outperforms SAM's existing algorithms in cases requiring a balance between demand charge management and energy arbitrage, and in cases where battery degradation imposes a significant cost.

batteries↗
DOE OSTI2024

A Bayesian Multi-fidelity Neural Network to Predict Nonlinear Frequency Backbone Curves

The use of structural mechanics models during the design process often leads to the development of models of varying fidelity. Often low-fidelity models are efficient to simulate but lack accuracy, while the high-fidelity counterparts are accurate with less efficiency. Here, this paper presents a multi-fidelity surrogate modeling approach that combines the accuracy of a high-fidelity finite element model with the efficiency of a low-fidelity model to train an even faster surrogate model that parameterizes the design space of interest. The objective of these models is to predict the nonlinear frequency backbone curves of the Tribomechadynamics Research Challenge benchmark structure which exhibits simultaneous nonlinearities from frictional contact and geometric nonlinearity. The surrogate model consists of an ensemble of neural networks that learn the mapping between low and high-fidelity data through nonlinear transformations. Bayesian neural networks are used to assess the surrogate model's uncertainty. Once trained, the multi-fidelity neural network is used to perform sensitivity analysis to assess the influence of the design parameters on the predicted backbone curves. Additionally, Bayesian calibration is performed to update the input parameter distributions to correlate the model parameters to the collection of experimentally measured backbone curves.

42 ENGINEERING↗
DOE OSTI2023

Multi-mode quasi-static excitation for systems with nonlinear joints

Finite element models can be used to model and predict the hysteresis and energy dissipation exhibited by nonlinear joints in structures. As a result of the nonlinearity, the frequency and damping of a mode is dependent on excitation amplitude, and when the modes remain uncoupled, quasi-static modal analysis has been shown to efficiently predict this behavior. However, in some cases the modes have been observed to couple such that the frequency and damping of one mode is dependent on the amplitude of other modes. To model the interactions between modes, one must integrate the dynamic equations in time, which is several orders of magnitude more expensive than quasi-static analysis. This work explores an alternative where quasi-static forces are applied in the shapes of two or more modes of vibration simultaneously, and the resulting load–displacement curves are used to deduce the effect of other modes on the effective frequency and damping of the mode in question. This methodology is demonstrated on a simple 2D cantilever beam structure with a single bolted joint which exhibits micro-slip nonlinearity over a range of vibration amplitudes. The predicted frequency and damping are compared with those extracted from a few expensive dynamic simulations of the structure, showing that the quasi-static approach produces reasonable albeit highly conservative bounds on the observed dynamics. This framework is also demonstrated on a 3D structure where dynamic simulations are infeasible.

42 ENGINEERING↗
DOE OSTI2020

Intensity measure adequacy assessment for nonlinear site response using Information Theory

Nonlinear site response modeling is a crucial aspect of Probabilistic Seismic Hazard Analysis. Site amplification models routinely rely on a rock intensity measure to characterize the strength of the bedrock motion. However, the adequacy of such intensity measures towards predicting amplifications across the oscillator period range has not been investigated in the literature. This paper analyzes the adequacy of rock intensity measures using state of the art criterion established in Performance-Based Earthquake Engineering and techniques from Information Theory. The efficiency and the sufficiency of several rock intensity measure are assessed. It was found that spectral accelerations at low periods usually are adequate for predicting amplifications across the period range. This supports the current practice of using Peak Ground Acceleration in Ground Motion Models. However, for extremely soft sites, which demonstrate nonlinear effects well into the period range, it is better practice to ensure that amplification and spectral acceleration share the same oscillator period. Lastly, for predicting the peak shear strain (an important parameter that controls nonlinearity of site response), Peak Ground Velocity is generally adequate, and this conclusion is in line with the definition of proxy shear strain.

42 ENGINEERING↗
DOE OSTI2023

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators: correcting the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction–diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Nonlinear manifold-based reduced order model

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physicsinformed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LSROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers’ equations. A speedup of up to 2.6 for 1D Burgers’ and a speedup of 11.7 for 2D Burgers’ equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Finally, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Engineering-scale Modeling of High-Temperature Creep and Creep Crack Growth in Alloy 316H

This document demonstrates completion of the goals described in the technical narrative of the Department of Energy’s Industry Funding Opportunity Announcement (iFOA) project entitled “Modeling and Simulation Development Pathways to Accelerating KP-FHR Licensing,” which relates to the development and demonstration of capabilities for conducting engineering-scale simulations of Alloy 316H components under high-temperature conditions. This work encompassed two major aspects: integrating and testing constitutive models for the creep response of 316H at high temperatures, and developing tools for modeling creep crack growth (CCG) in 316H. Two classes of constitutive models were used in this effort: phenomenological models based on behavior observed at the engineering scale, and reduced-order models (ROMs) that represent the nonlinear response of mesoscale models that capture the sensitivity to material microstructure and processing. Likewise, the approaches employed for CCG modeling considered both simplified engineering approaches and detailed simulations of creep and damage ahead of the crack tip. These developments, which were performed by utilizing the Grizzly code as well as the open-source libraries it depends on, strengthen Grizzly’s ability to support licensing and safety analyses of high-temperature reactor components.

316H↗
DOE OSTI2022

A Julia Framework for Graph-Structured Nonlinear Optimization

Graph theory provides a convenient framework for modeling and solving structured optimization problems. Under this framework, the modeler can arrange/assemble the components of an optimization model (variables, constraints, objective functions, and data) within nodes and edges of a graph, and this representation can be used to visualize, manipulate, and solve the problem. In this work, we present a Julia framework for modeling and solving graph-structured nonlinear optimization problems. Our framework integrates the modeling package Plasmo.jl (which facilitates the construction and manipulation of graph models) and the nonlinear optimization solver MadNLP.jl (which provides capabilities for exploiting graph structures to accelerate solution). We illustrate with a simple example how model construction and manipulation can be performed in an intuitive manner using Plasmo.jl and how the model structure can be exploited by MadNLP.jl. We also demonstrate the scalability of the framework by targeting a large-scale, stochastic gas network problem that contains over 1.7 million variables.

Cole, David↗
DOE OSTI2020

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Joint analysis of Dark Energy Survey Year 3 data and CMB lensing from SPT and P l a n c k . II. Cross-correlation measurements and cosmological constraints

Cross-correlations of galaxy positions and galaxy shears with maps of gravitational lensing of the cosmic microwave background (CMB) are sensitive to the distribution of large-scale structure in the Universe. Such cross-correlations are also expected to be immune to some of the systematic effects that complicate correlation measurements internal to galaxy surveys. We present measurements and modeling of the cross-correlations between galaxy positions and galaxy lensing measured in the first three years of data from the Dark Energy Survey with CMB lensing maps derived from a combination of data from the 2500 deg 2 SPT-SZ survey conducted with the South Pole Telescope and full-sky data from the Planck satellite. The CMB lensing maps used in this analysis have been constructed in a way that minimizes biases from the thermal Sunyaev Zel’dovich effect, making them well suited for cross-correlation studies. The total signal-to-noise of the cross-correlation measurements is 23.9 (25.7) when using a choice of angular scales optimized for a linear (nonlinear) galaxy bias model. Here we use the cross-correlation measurements to obtain constraints on cosmological parameters. For our fiducial galaxy sample, which consist of four bins of magnitude-selected galaxies, we find constraints of Ω m =0.272$^{+0.032}_{-0.052}$ and S 8 ≡σ8$\sqrt{Ω_m/0.3}$=0.736$^{+0.032}_{-0.028}$ (Ω m =0.245$^{+0.026}_{-0.044}$ and S 8 =0.734$^{+0.035}_{-0.028}$) when assuming linear (nonlinear) galaxy bias in our modeling. Considering only the cross-correlation of galaxy shear with CMB lensing, we find Ω m =0.270$^{+0.043}_{-0.061}$ and S 8 =0.740$^{+0.034}_{-0.029}$. Our constraints on S8 are consistent with recent cosmic shear measurements, but lower than the values preferred by primary CMB measurements from Planck.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Learning Optimal Power Flow Solutions using Linearized Models in Power Distribution Systems

Solving nonlinear optimal power flow (OPF) problem is computationally expensive, and poses scalability challenges for power distribution networks. An alternative to solving the original nonlinear OPF is the linear approximated OPF models. Although, these linear approximated OPF models are fast, the resulting solutions may result in significant optimality gap. Lately, the application of machine learning (ML) methods in successfully solving the nonlinear OPF has been reported. These methods learn and estimate the nonlinear control policies using a purely data-driven approach. In this paper, we propose an approach to complements the ML based approach to solving OPF using solutions from known linearized OPF model. Specifically, we use supervised learning to map the solutions of linear OPF to nonlinear control variables. Unlike, the traditional ML based methods for OPF that approximate the full distribution feeder model using function approximation, our approach uses a two-node approximation of radial networks. The proposed approach is validated using IEEE 123 bus test system for OPF solutions obtained using the nonlinear OPF models.

optimal power flow, power distribution systems, su↗
DOE OSTI2020

Nonlinear sparse Bayesian learning for physics-based models

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. Here, a semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence is considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Theoretical Control-Centric Modeling for Precision Model-Based Sliding Mode Control of a Hydraulic Artificial Muscle Actuator

Artificial muscles (AMs) typically rely on pneumatic sources of fluid power. The use of hydraulics can increase the power and force to weight and volume ratios of AM actuators. This paper develops a control-centric third-order single-input single-output (SISO) lumped-parameter dynamic model and sliding mode position controller based on Filippov's principle of equivalent dynamics for a braided hydraulic artificial muscle (HAM) actuator. The model predicts the nonlinear behavior of the HAM free contraction and captures the fluid and actuator nonlinear dynamic interactions in addition to the braid deformation. Model simulations are compared to experimental results for quasi-static pressurization, isometric pressurization, and open-loop square wave commands at 0.25, 0.5, and 1 Hz. Experiments of sine wave tracking at 0.25, 0.5, and 1 Hz and continuous square wave tracking at 0.067 Hz are conducted using a sliding mode controller (SMC) derived from the model. The SMC achieves a steady-state error of 6 μm at multiple setpoints within the actuator's 17 mm stroke. Compared to a proportional-integral-derivative (PID) controller, the SMC root-mean-square (RMS) error, mean error, and absolute maximum error are reduced on average by 53%, 61%, and 44%, respectively, demonstrating the benefit of model-based approaches for controlling HAMs.

42 ENGINEERING↗
DOE OSTI2025

High harmonic generation in Haldane model quantum dots

We study theoretically the nonlinear electron dynamics of Haldane model quantum dots placed in the field of an ultrashort optical pulse. One of the tuning parameters of the Haldane model is the phase accumulated by an electron during its transfer between the next nearest neighbor sites. We study how this parameter affect the nonlinear electron dynamics and the generation of high optical harmonics. With increasing the phase from its zero value to 90°, the low-energy electron states in the conduction and valence bands become more localized near the edges of the quantum dot resulting in suppression of the band gap, enhancement of the dipole inter-band coupling, and strong suppression of the average low-energy electron density of the states. As a result, the nonlinear response of the electron system of a Haldane model quantum dot is the strongest at intermediate values of the phase, ≈ 30− 40°. At these values of the phase, the electron dynamics is irreversible and a few first high-order harmonics have the largest intensities. Here, when the phase approaches 90° value the generation of high harmonics is strongly suppressed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Development of a Filtered CFD-DEM Drag Model with Multiscale Markers Using an Artificial Neural Network and Nonlinear Regression

Here, the accuracy of coarse-grained Euler-Lagrangian simulations of fluidized beds heavily depends on the mesoscale drag models to account for the influences of the unresolved sub-grid structures. Traditional filtered drag models are regressed with mesoscale markers such as voidage and slip velocities. In this research, a filtered drag was regressed with both mesoscale and macro-scale markers using fine grid Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) simulations. The traditional non-linear regression method was compared with machine learning regression using an Artificial Neural Network (ANN) implemented in PyTorch and coupled with MFiX. The new drag showed higher accuracy than the Wen-Yu drag and another filtered drag derived from the two-fluid model. The nonlinear regression shows slightly better results than ANN regression in cases with similar R 2 values. The utilization of the gas inlet velocity as an additional macro-scale marker reduced the errors by up to 55.3% in the tested cases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗
DOE OSTI2022

Development of a Control Co-Design Modeling Tool for Marine Hydrokinetic Turbines: Preprint

This report describes the ongoing and planned development of the software package CT-Opt (Current/Tidal Optimization), a control co-design modeling tool for marine hydrokinetic turbines. The commercialization of these turbines has faced significant challenges due to the complex, multidisciplinary nature of their design and the extreme environmental conditions of their operation. This project aims to create a modeling tool that will enable the efficient design of robust, cost-competitive hydrokinetic turbine systems. Rather than using traditional optimization methods, CT-Opt combines multiple models across a range of fidelities to enable coupled optimization of the system design and system controller via a control co-design approach. With this method, the parameters that affect system performance are considered more comprehensively at every stage of the design process. The lowest-fidelity, frequency-domain model called by CT-Opt is RAFT (Response Amplitudes of Floating Turbines), which was originally developed by the National Renewable Energy Laboratory (NREL) to model response amplitudes of floating offshore wind turbines. The highest-fidelity, time-domain model is OpenFAST, which was developed by NREL for land-based and offshore wind turbines. As part of the CT-Opt project, new functionalities will be added to RAFT and OpenFAST to enable the accurate simulation of fixed and floating marine hydrokinetic turbines. In addition to expanding the capabilities of RAFT and OpenFAST, new midfidelity models will be developed. These models will be based on RAFT and OpenFAST and will consist of linearized, state-space models derived from the fully coupled, nonlinear OpenFAST equations and derivative function surrogate models that approximate the nonlinear system behavior. Each model will be coupled with controllers to allow control co-design methods to be applied both within models and across fidelity levels, enabling efficient system optimization.

control co-design↗