Learning-based Nonlinear Model Research Articles

Optimization of energy efficiency for offshore wind farms via wake modeling-free NMPC

This paper presents an energy efficiency improvement scheme for offshore wind farms. This scheme uses learning-based nonlinear model predictive control (NMPC) and does not require wake modeling. The main feature is that each wind turbine can independently complete all optimal control, without the need for wind farm wake model calculation and iterative optimization. Specifically, this paper studies the critical factors for increasing the active power of wind farms and reducing the structural load of wind turbines, and reconstructs the optimal control objectives of wind turbines. Furthermore, combined with the nonlinear model of wind turbines containing uncertainty, a nonlinear model predictive control algorithm based on deep neural networks was designed, which can achieve multi-objective optimal control at the wind turbine level. The simulation results show that the uncertainty estimation method can effectively improve the nonlinear control performance, achieve an increase in the active power of the wind farm without wake iterative optimization, and at the same time suppress the structural loads of all wind turbines.

Real-time Learning-based Nonlinear Model Predictive Control of a virtual motorcycle employing grey-box modeling through Gaussian processes

Virtual prototyping tools simulations are nowadays largely adopted methods in the automotive industry. However, to achieve effective simulative tests for two-wheeled vehicles, a virtual rider, i.e. a controller for virtual motorcycles, is typically needed due to the inherent instability of the system. Different control strategies have been employed to deal with this control task, and promising results have been obtained using Nonlinear Model Predictive Control (NMPC). Yet, performance of NMPC highly relies on the plant characterization, that can be highly complex to obtain analytically for 2-wheel vehicles. To improve it, learning dynamics approaches can be used within a Learning-based Nonlinear Model Predictive Control (LbNMPC) framework, exploiting the combination of data-driven techniques and NMPC strategy. In this manuscript, we present a tailored real-time capable LbNMPC for a virtual motorcycle that relies on a continuous grey-box model based on Gaussian Processes (GPs), method that has proven to be effective for 4-wheel vehicle applications. To cope with the real-time requirement, a feature selection procedure and sparse GP approximations have been adopted. A comparison with a physics-based model NMPC implementation taken from the literature has been carried out, analyzing the impact of different sparse GP representations. Remarkable improvements in both model accuracy and tracking performance have been obtained, and the generalization properties of the grey-box model have been assessed.

Learning-based nonlinear model order reduction for image reconstruction

Learning-based nonlinear model order reduction for image reconstruction

Neural Network-Based Hammerstein Model Identification of a Lab-Scale Batch Reactor.

This paper focuses on two types of neural network-based Hammerstein model identification methods for the acrylamide polymerization reaction of a batch reactor process. The first neural-based identification type formulates the weights of the multilayer network directly as parameters of the nonlinear static and linear dynamic blocks of the Hammerstein model and trains the weights using a gradient-based backpropagation algorithm. In the second identification type, the nonlinear static block of the Hammerstein model is framed as a single hidden-layer feedforward network and both nonlinear and linear block parameters are trained using an extreme learning machine, where the training procedure is exempted from gradient calculation. The primary focus of the paper is neural-based model identification of a complex nonlinear system, which facilitates ease of linear/nonlinear controller design with good learning speed and less computations. A future work toward the machine learning-based nonlinear model predictive controller implementation using the Jetson Orin Nano board is also described.

A Learning-Based Nonlinear Model Predictive Control Approach for Autonomous Driving

This paper introduces a learning-based Nonlinear Model Predictive Control (NMPC) method that combines NMPC with a Reinforcement Learning (RL) algorithm to achieve automatic parameter tuning of the NMPC optimizer, resulting in better control performance. In this study, two learning-based models were designed based on the tabular Q-learning algorithm but with different definitions of state and action spaces. To test the effectiveness of the proposed model, we conducted two kinds of experiments in which the models were applied to optimize the lane-keeping performance of an autonomous driving system. The case study results from simulations showed that the agent could match a proper parameter matrix for the NMPC within one minute. In real-world experiments, we extended the proposed control scheme to practical driving tasks using a 1:8 scale Audi model car in a specific experimental field. The model exhibited acceptable robustness in the face of relatively large deviations from the sensors and other real-time interference. These results demonstrate that the proposed learning-based NMPC method is a promising direction for solving real-time control problems.

Towards Black-Box Dynamics Modelling within Learning-based Nonlinear Model Predictive Control for Virtual Motorcycles

Towards Black-Box Dynamics Modelling within Learning-based Nonlinear Model Predictive Control for Virtual Motorcycles

Learning-Based Nonlinear Model Predictive Controller for Hydraulic Cylinder Control of Ship Steering System

The steering mechanism of ship steering gear is generally driven by a hydraulic system. The precise control of the hydraulic cylinder in the steering mechanism can be achieved by the target rudder angle. However, hydraulic systems are often described as nonlinear systems with uncertainties. Since the system parameters are uncertain and system performances are influenced by disturbances and noises, the robustness cannot be satisfied by approximating the nonlinear theory by a linear theory. In this paper, a learning-based model predictive controller (LB-MPC) is designed for the position control of an electro-hydraulic cylinder system. In order to reduce the influence of uncertainty of the hydraulic system caused by the model mismatch, the Gaussian process (GP) is adopted, and also the real-time input and output data are used to improve the model. A comparative simulation of GP-MPC and MPC is performed assuming that the interference and uncertainty terms are bounded. Consequently, the proposed control strategy can effectively improve the piston position quickly and precisely with multiple constraint conditions.

Deep learning-based nonlinear model predictive control of the attitude manoeuvre of a barbell electric sail through voltage regulation

An electric solar wind sail (electric sail or E-sail) is a new type of propulsion system that does not require propellant. This paper proposes a nonlinear model predictive control law based on deep learning to control the attitude of a barbell electric sail. A barbell E-sail is composed of two tip satellites connected via long conductive tethers to a central insulated confluence point. The two tethers are insulated from each other at the confluence point such that the voltages of the two tethers can be independently controlled. The attitude dynamics of the system is modelled using a nonsingular description of tether orientation. To reduce online computation loads, the proposed control scheme has a two-stage design, namely, an offline stage and an online stage. In the offline stage, a large amount of data is generated using the nonlinear model predictive control law and then taken as a dataset to train a deep neural network. In the online stage, feedback control of the system attitude is achieved with extremely low computational cost by performing real-time mapping from the system state to the control output using the trained deep neural network. Finally, the efficacy and performance of the proposed deep learning-based control law are demonstrated via numerical case studies.

Learning-based nonlinear model predictive control with accurate uncertainty compensation

A learning-based nonlinear model predictive control (LBNMPC) method is proposed in this paper for general nonlinear systems under system uncertainties and subject to state and input constraints. The proposed LBNMPC strategy decouples the robustness and performance requirements by employing an additional learned model and introducing it into the MPC framework along with the nominal model. The nominal model helps to ensure the closed-loop system’s safety and stability, and the learned model aims to improve the tracking behaviors. As a core of the learned model construction, an online parameter estimator is designed to deal with system uncertainties. This estimation process effectively evaluates both the current and historical effects of uncertainties, leading to superior estimating performance compared with conventional methods. By constructing an invariant terminal constraint set, we prove that the LBNMPC is recursively feasible and robustly asymptotically stable. Numerical verifications for a two-link manipulator are conducted to validate the effectiveness and robustness of the proposed control scheme.

High precision control and deep learning-based corn stand counting algorithms for agricultural robot

This paper presents high precision control and deep learning-based corn stand counting algorithms for a low-cost, ultra-compact 3D printed and autonomous field robot for agricultural operations. Currently, plant traits, such as emergence rate, biomass, vigor, and stand counting, are measured manually. This is highly labor-intensive and prone to errors. The robot, termed TerraSentia, is designed to automate the measurement of plant traits for efficient phenotyping as an alternative to manual measurements. In this paper, we formulate a Nonlinear Moving Horizon Estimator (NMHE) that identifies key terrain parameters using onboard robot sensors and a learning-based Nonlinear Model Predictive Control (NMPC) that ensures high precision path tracking in the presence of unknown wheel-terrain interaction. Moreover, we develop a machine vision algorithm designed to enable an ultra-compact ground robot to count corn stands by driving through the fields autonomously. The algorithm leverages a deep network to detect corn plants in images, and a visual tracking model to re-identify detected objects at different time steps. We collected data from 53 corn plots in various fields for corn plants around 14 days after emergence (stage V3 - V4). The robot predictions have agreed well with the ground truth with $C_{robot}=1.02 \times C_{human}-0.86$ and a correlation coefficient $R=0.96$. The mean relative error given by the algorithm is $-3.78\%$, and the standard deviation is $6.76\%$. These results indicate a first and significant step towards autonomous robot-based real-time phenotyping using low-cost, ultra-compact ground robots for corn and potentially other crops.

Extreme learning‐based non‐linear model predictive controller for an autonomous underwater vehicle: simulation and experimental results

In this study, an extreme learning-based non-linear model predictive controller (NMPC) is proposed for path following planning of an autonomous underwater vehicle (AUV) using horizontal way-points. The proposed controller comprises a kinematic controller and a dynamic controller. The kinematic controller is designed by using back-stepping approach whilst the dynamic controller is designed by employing the NMPC approach. The dynamics of the AUV is identified in real-time by employing an extreme learning machine (ELM) structure. In view of achieving improved performance of the ELM structure, its hidden layer parameters are optimally determined by applying Jaya optimisation algorithm. The resulting ELM model is then used to design a NMPC considering the constraint on rudder planes. The tracking performance of the proposed controller is compared with that of two recently reported control algorithms namely, $H_\infty $ H ∞ state feedback controller and inverse optimal self-tuning proportional–integral–derivative (PID) controller. The proposed controller is implemented using MATLAB and then in real-time on a prototype AUV developed in the authors’ laboratory. From both the simulation and experimental results obtained, it is observed that the proposed controller exhibits superior tracking performance compared to both $H_\infty $ H ∞ state feedback controller and inverse optimal self-tuning PID controller.

Learning-based Nonlinear Model Predictive Control

Spanish MINECO Grant PRX15-00300 and projects DPI2013-48243-C2-2-R and DPI2016-76493-C3-1-R. UK Engineering and Physical Research Council, grant no.EP/J012300/1.

Learning-based Nonlinear Model Predictive Control

This paper presents stabilizing Model Predictive Controllers (MPC) in which prediction models are inferred from experimental data of the inputs and outputs of the plant. Using a nonparametric machine learning technique called LACKI, the estimated (possibly nonlinear) model function together with an estimation of Holder constant is provided. Based on these, a number of predictive controllers with stability guaranteed by design are proposed. Firstly, the case when the prediction model is estimated offline is considered and robust stability and recursive feasibility is ensured by using tightened constraints in the optimisation problem. This controller has been extended to the more interesting and complex case: the online learning of the model, where the new data collected from feedback is added to enhance the prediction model. An on-line learning MPC based on a double sequence of predictions is proposed.

Robust Constrained Learning-based NMPC enabling reliable mobile robot path tracking

This paper presents a Robust Constrained Learning-based Nonlinear Model Predictive Control (RC-LB-NMPC) algorithm for path-tracking in off-road terrain. For mobile robots, constraints may represent solid obstacles or localization limits. As a result, constraint satisfaction is required for safety. Constraint satisfaction is typically guaranteed through the use of accurate, a priori models or robust control. However, accurate models are generally not available for off-road operation. Furthermore, robust controllers are often conservative, since model uncertainty is not updated online. In this work our goal is to use learning to generate low-uncertainty, non-parametric models in situ. Based on these models, the predictive controller computes both linear and angular velocities in real-time, such that the robot drives at or near its capabilities while respecting path and localization constraints. Localization for the controller is provided by an on-board, vision-based mapping and navigation system enabling operation in large-scale, off-road environments. The paper presents experimental results, including over 5 km of travel by a 900 kg skid-steered robot at speeds of up to 2.0 m/s. The result is a robust, learning controller that provides safe, conservative control during initial trials when model uncertainty is high and converges to high-performance, optimal control during later trials when model uncertainty is reduced with experience.

Learning-based Nonlinear Model Predictive Control to Improve Vision-based Mobile Robot Path Tracking

This paper presents a Learning-based Nonlinear Model Predictive Control (LB-NMPC) algorithm to achieve high-performance path tracking in challenging off-road terrain through learning. The LB-NMPC algorithm uses a simple a priori vehicle model and a learned disturbance model. Disturbances are modeled as a Gaussian process (GP) as a function of system state, input, and other relevant variables. The GP is updated based on experience collected during previous trials. Localization for the controller is provided by an onboard, vision-based mapping and navigation system enabling operation in large-scale, GPS-denied environments. The paper presents experimental results including over 3 km of travel by three significantly different robot platforms with masses ranging from 50 to 600 kg and at speeds ranging from 0.35 to 1.2 m/s (associated video at http://tiny.cc/RoverLearnsDisturbances). Planned speeds are generated by a novel experience-based speed scheduler that balances overall travel time, path-tracking errors, and localization reliability. The results show that the controller can start from a generic a priori vehicle model and subsequently learn to reduce vehicle- and trajectory-specific path-tracking errors based on experience.

Control of Copolymer Properties in a Semibatch Methyl Methacrylate/Methyl Acrylate Copolymerization Reactor by Using a Learning-Based Nonlinear Model Predictive Controller

This paper is concerned with the production of copolymers with uniform copolymer composition and desired weight-average molecular weight by using a learning-based nonlinear model predictive control (NLMPC). For an effective control in a semibatch copolymerization system, the successive linearization method used in NLMPC is modified. The nonlinear model for the copolymerization system is linearized by using the previous batch data within the prediction horizon in such a way that the linear time-varying model is obtained as a function of the increment of the inputs between the two consecutive batches. The learning algorithm is incorporated into the controller by virtue of the model structure, and the effectiveness of the proposed controller is shown by comparison with a conventional nonlinear model predictive controller as well as a linear model-based learning controller. Through the implementation of the controller to a semibatch methyl methacrylate/methyl acrylate copolymerization reactor, it is proven that copolymers with desired properties are produced effectively using the algorithm proposed in this study.