Nonlinear Model Predictive Control Algorithm Research Articles

Enhanced gas-lift system operation using LPV nonlinear model predictive control

In this work, we propose a novel Linear Parameter Varying (LPV) Model Predictive Control (MPC) scheme for oil production maximisation in wells operated with gas-lift systems. The control of a gas-lift system poses several engineering challenges, including the nonlinear nature of its behaviour and different kinds of process constraints. Recent studies indicate that MPC strategies stand out as promising solutions to address many of these issues — with results already published for gas-lift applications. However, when nonlinear models are used, the corresponding nonlinear MPC (NMPC) algorithms entail substantial computational costs, potentially complicating the feasibility of (real-time) embedded implementation. Furthermore, certain complexities in standard gas-lift system representations hinder the use of typical NMPC solvers (e.g. CasADi), thus making approximation-based schemes unavoidable. Accordingly, we propose an LPV formulation to describe the gas-lift system that ensures closed-loop stability and recursive feasibility when implemented as a model for MPC. In this regard, we synthesise an LPV MPC scheme and compare it to an NMPC through CasADi. Several realistic nonlinear numerical simulations are presented and our results indicate that the proposed LPV MPC scheme, in addition to being three times faster (in average), achieved an increase in the total amount of produced oil when compared to an NMPC via CasADi. Then, aiming to maximise oil production rate, we introduce a modified version of the LPV MPC approach, resulting in an increase in the total amount of produced oil of approximately 3% in the studied scenario, when compared to the unmodified LPV MPC scheme.

An accurate trajectory tracking method for low-speed unmanned vehicles based on model predictive control

Trajectory tracking on a low-speed vehicle using the model predictive control (MPC) algorithm usually assumes a simple road terrain. This assumption does not correspond to the actual road situation, leading to low tracking accuracy. Therefore, a trajectory tracking method considering road curvature based on MPC is proposed in this paper. In this method, the controller can automatically switch between MPC types. Linear model predictive control (LMPC) is selected for small road curvatures, while nonlinear model predictive control (NMPC) is employed for large road curvatures. In addition, the NMPC algorithm in this work considers the effect of road curvature on tracking accuracy, making it suitable for tracking time-varying curvature roads. To verify the feasibility of the algorithm, simulation comparisons with the basic MPC model were carried out at different testing roads and vehicle longitudinal speeds. The results indicate that the method significantly improves trajectory tracking accuracy, all while ensuring real-time calculations. The intelligent switching capability of control models based on road curvature allows its application to track trajectories on arbitrarily complex roads.

A collision-avoidance decision-making scheme based on artificial potential fields and event-triggered control

In this paper, a collision-avoidance decision-making scheme is proposed based on improved artificial potential field (APF) and event-triggered nonlinear model predictive control. A calculation model is used to calculate the collision avoidance dynamic parameters between ships. In accordance with relevant rules of the International Regulations for Preventing Collisions at Sea (COLREGs), abovementioned collision avoidance parameters are used as the main index and applied to construct the repulsive potential field. Then, an anti-collision decision-making scheme is developed by incorporating event-triggered mechanism and improved APF method into the nonlinear model predictive control algorithm. Based on improved repulsive potential field, heading of the ship and orientation of the target point, the event-triggered conditions are set to save considerable computational resources. Following this approach, optimal collision avoidance actions in line with COLREGs is realised, and the adverse effects of ignoring the manoeuvrability characteristics of ships in the process of preventing collisions are eliminated. Finally, simulation examples verify the effectiveness and rationality of the proposed scheme for multi-ship encounter scenarios.

Nonlinear Model Predictive Control—Cross-Coupling Control with Deep Neural Network Feedforward for Multi-Hydraulic System Synchronization Control

This paper studies a multi-hydraulic system (MHS) synchronization control algorithm. Firstly, a general nonlinear asymmetric MHS state space entirety model is established and subsequently the model form is simplified by nonlinear feedback linearization. Secondly, an entirety model-type solution is proposed, integrating a nonlinear model predictive control (NMPC) algorithm with a cross-coupling control (CCC) algorithm. Furthermore, a novel disturbance compensator based on the system's inverse model is introduced to effectively handle disturbances, encompassing unmodeled errors and noise. The proposed innovative controller, known as nonlinear model predictive control—cross-coupling control with deep neural network feedforward (NMPC-CCC-DNNF), is designed to minimize synchronization errors and counteract the impact of disturbances. The stability of the control system is rigorously demonstrated. Finally, simulation results underscore the efficacy of the NMPC-CCC-DNNF controller, showcasing a remarkable 60.8% reduction in synchronization root mean square error (RMSE) compared to other controllers, reaching up to 91.1% in various simulations. These results affirm the superior control performance achieved by the NMPC-CCC-DNNF controller.

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.

Multi-Intersection Ecological Cooperative Control of a Pure Electric Vehicle Platoon with Dual-Motor Dual-Axis Drive

The advent of intelligent transportation system technology has expedited the advancement of eco-driving controls. Research on energy-saving cooperative control of intelligent connected vehicles in intelligent transportation environments is still in need of ongoing refinement. This article proposes a dual-level ecological driving control strategy for a pure electric vehicle platoon with dual-motor dual-axis drive in an urban multi-intersection environment. The upper-level design incorporates optimal platoon speed decision-making based on the nonlinear model predictive control algorithm. The multi-objective optimization function considers three scenarios: energy-optimal, time-optimal, and energy-time-optimal. It also takes into account platoon following control and passing efficiency, ensuring smooth passage through multi-intersections without interruptions. Built on the upper level’s optimal speed design, an energy management strategy is proposed for achieving optimal torque distribution of pure electric vehicles with front and rear independent drives. Finally, the upper and lower levels are jointly simulated in real-time. The results indicate that, compared to the energy-optimal mode, the average passage time decreased by 14.6% and 5.97% in the time-optimal and energy-time-optimal modes, respectively. Under average torque distribution, the time-optimal and energy-time-optimal modes increased the energy consumption of the vehicle platoon by 21.05% and 5.44%, respectively, compared to the energy-optimal mode. Under the optimal torque allocation strategy, the time-optimal and energy-time-optimal modes increased energy consumption by 15.31% and 6.11%, respectively, compared to the energy-optimal mode. In contrast to the average torque allocation strategy, the optimal torque allocation strategy for the dual-motor vehicles reduced energy consumption by 10.18%, 14.44%, and 9.61% in the energy-optimal mode, time-optimal mode and energy-time-optimal mode, respectively.

Nonlinear Model Predictive Control for a Dynamic Positioning Ship Based on the Laguerre Function

In this paper, we present a novel nonlinear model predictive control (NMPC) algorithm based on the Laguerre function for dynamic positioning ships to solve the problems of input saturation, unknown time-varying disturbances, and heavy computation. The nonlinear model of a dynamic positioning ship is presented as a linear model, transformed from a standard affine nonlinear state-space model by precise feedback linearization. The environmental disturbance is overcome using an integrator. The time cost of the proposed nonlinear control algorithm is decreased by inducing the Laguerre function to describe the feedback-linearization system input increments. The Laguerre function reduces the matrix dimensions of the nonlinear optimization problem. The simulation results for a DP supply vessel showed that the novel algorithm maintained the effective control performance of the original nonlinear model predictive control algorithm and had a reduced computation load to satisfy the requirements of real-time operation.

Fast two-layer nonlinear economic predictive control using machine learning for ORC systems with non-Gaussian disturbances

This study proposes a machine learning-based generalized correntropy two-layer nonlinear economic model predictive control (ML-GC-TL-NEMPC) algorithm to improve the computational speed for Organic Rankine Cycle (ORC) systems with non-Gaussian disturbances. In the upper layer, the ratio of the net output power to the total heat transfer area is used as the economic performance index to optimize the optimal reference trajectory. In the lower layer, the generalized correntropy-based MPC (GC-MPC) is used to track the optimal trajectory. To quickly obtain an optimal solution, a Deep Neural Network (DNN) neural network controller is combined with kernel support vector machine (SVM). It learns the possible optimal solution via off-line training. Then it can be quickly implemented on on-line applications, so it can save the optimal calculation time. The proposed ML-GC-TL-NEMPC is applied to ORC. Its computation and performance are faster and better than the traditional two-layer EMPC and single-layer EMPC.

Robust tube-based NMPC for dynamic systems with discrete degrees of freedom

We present a robust nonlinear model predictive control (NMPC) algorithm for dynamic systems with mixed degrees of freedom, i.e., continuous and discrete manipulated variables. The discrete variables are often excluded from the NMPC layer and determined at a supervisory layer, which typically leads to suboptimal solutions. In contrast, the proposed controller optimizes both classes of degrees of freedom within the NMPC layer, thereby enhancing the closed-loop performance. Our approach relies on a computationally efficient relaxation and integrality restoration strategy. Initially, a nominal controller computes relaxed central reference trajectories for the states and the input variables. These trajectories are then tracked by an ancillary NMPC controller before the integrality of the discrete variables is restored. The role of the ancillary controller is to ensure robustness against the integer restoration error as well as other disturbances based on a nonlinear Tube MPC approach. Furthermore, we provide sufficient conditions to establish recursive feasibility and guarantee robust closed-loop stability. Finally, the effectiveness of the approach is demonstrated through two nonlinear simulation examples, affirming its viability and robustness.

Trajectory Tracking and Obstacle Avoidance of Robotic Fish Based on Nonlinear Model Predictive Control.

The attainment of accurate motion control for robotic fish inside intricate underwater environments continues to be a substantial obstacle within the realm of underwater robotics. This paper presents a proposed algorithm for trajectory tracking and obstacle avoidance planning in robotic fish, utilizing nonlinear model predictive control (NMPC). This methodology facilitates the implementation of optimization-based control in real-time, utilizing the present state and environmental data to effectively regulate the movements of the robotic fish with a high degree of agility. To begin with, a dynamic model of the robotic fish, incorporating accelerations, is formulated inside the framework of the world coordinate system. The last step involves providing a detailed explanation of the NMPC algorithm and developing obstacle avoidance and objective functions for the fish in water. This will enable the design of an NMPC controller that incorporates control restrictions. In order to assess the efficacy of the proposed approach, a comparative analysis is conducted between the NMPC algorithm and the pure pursuit (PP) algorithm in terms of trajectory tracking. This comparison serves to affirm the accuracy of the NMPC algorithm in effectively tracking trajectories. Moreover, a comparative analysis between the NMPC algorithm and the dynamic window approach (DWA) method in the context of obstacle avoidance planning highlights the superior resilience of the NMPC algorithm in this domain. The proposed strategy, which utilizes NMPC, demonstrates a viable alternative for achieving precise trajectory tracking and efficient obstacle avoidance planning in the context of robotic fish motion control within intricate surroundings. This method exhibits considerable potential for practical implementation and future application.

Comparison of Advanced Control Strategies Applied to a Multiple-Degrees-of-Freedom Wave Energy Converter: Nonlinear Model Predictive Controller versus Reinforcement Learning

Achieving energy maximizing control of a Wave Energy Converter (WEC) not only needs a comprehensive dynamic model of the system—including nonlinear hydrodynamic effects and nonlinear characteristics of Power Take-Off (PTO)—but to treat the entire system using an integrated approach, i.e., as a cyber–physical system considering the WEC dynamics, control strategy, and communication interface. The resulting energy-maximizing optimization formulation leads to a non-quadratic and nonstandard cost function. This article compares the (1) Nonlinear Model Predictive Controller (NMPC) and (2) Reinforcement Learning (RL) techniques as applied to a class of multiple-degrees-of-freedom nonlinear WEC–PTO systems subjected to linear as well as nonlinear hydrodynamic conditions in simulation, using the WEC-Sim™ toolbox. The results show that with an optimal choice of RL agent and hyperparameters, as well as suitable training conditions, the RL algorithm is more robust under more stringent operating requirements, for which the NMPC algorithm fails to converge. Further, RL agents are computationally efficient on real-time target machines with a significantly reduced Task Execution Time (TET).

Nonlinear Closed-Loop Predictive Control of Heart Rate and Blood Pressure Using Vagus Nerve Stimulation: An In Silico Study.

We propose a nonlinear model-based control technique for regulating the heart rate and blood pressure using vagus nerve neuromodulation. The closed-loop framework is based on an in silico model of the rat cardiovascular system for the simulation of the hemodynamic response to multi-location vagal nerve stimulation. The in silico model is derived by compartmentalizing the various physiological components involved in the closed-loop cardiovascular system with intrinsic baroreflex regulation to virtually generate nominal and hypertension-related heart dynamics of rats in rest and exercise states. The controller, using a reduced cycle-averaged model, monitors the outputs from the in silico model, estimates the current state of the reduced model, and computes the optimum stimulation locations and the corresponding parameters using a nonlinear model predictive control algorithm. The results demonstrate that the proposed control strategy is robust with respect to its ability to handle setpoint tracking and disturbance rejection in different simulation scenarios.

EMPMR berthing scheme: A novel event-triggered motion planning and motion replanning scheme for unmanned surface vessels

In this study, the issues related to approaching and berthing of unmanned surface vessels (USVs) are investigated. The automatic berthing task is divided into motion planning and motion replanning. First, a smooth path from the initial position to the berth is planned using A* algorithm and B-spline. Then, the segmented interpolation method is employed to let the USV velocities converge slowly to zero at the berth, and an initial berthing trajectory is obtained. Moreover, considering the kinetic constraints of the USV, the nonlinear model predictive control (NMPC) algorithm is employed in the offline motion planning and online motion replanning scheme. In this scheme, novel static, and COLREGs-based dynamic obstacle avoidance functions are proposed based on Gaussian functions. Furthermore, the event-triggered mechanism is adopted to improve the real-time performance of the NMPC algorithm. The proposed event-triggered motion planning and motion replanning (EMPMR) scheme and Han et al.’s scheme are tested in six scenarios. Simulation results show that the proposed EMPMR scheme can accomplish USV’s approaching and automatic berthing of USVs and has better obstacle avoidance and computational performance.

A COLREGs-Compliant Ship Collision Avoidance Decision-Making Support Scheme Based on Improved APF and NMPC

In this paper, combined with the improved artificial potential field (IAPF) method and the nonlinear model predictive control (NMPC) algorithm, a collision avoidance decision-making support scheme considering ship maneuverability and the International Regulations for Preventing Collisions at Sea (COLREGs) is proposed. First, to comply with the requirements of COLREGs, an improved repulsive potential field is presented for different encounter scenarios when the ship detects the risk of collision, and the coordinated ship domain is applied to provide safety criteria for collision avoidance. Then, by transforming the MMG model to a discrete-time nonlinear system, the NMPC is utilized to predict the future state of the ship according to the current state, and the IAPF method is incorporated to calculate the potential field in each future state as the objective function. Following this approach, the action taken to avoid collision is more effective, the ship motion in avoiding collision is more accurate, and the collision avoidance decision making is more reasonable. Finally, two simulation examples of multi-ship encounter scenarios are applied to illustrate the merits and effectiveness of the proposed collision avoidance decision-making support scheme.

Event-trigger NMPC for 3-D trajectory tracking of UUV with external disturbances

In this paper, a novel Three-Dimensional (3-D) trajectory tracking method based on Event-triggered Nonlinear Model Predictive Control (ENMPC) is designed for an Underwater Unmanned Vehicle (UUV) with external disturbances. Firstly, the 5-Degrees of Freedom (5-DoF) model of UUV is represented by both kinematics and dynamics. After that, a Nonlinear Model Predictive Control (NMPC) algorithm is designed for the 3-D trajectory tracking of UUV, and the feasibility of the control method and the stability of the closed-loop system are proved, which are further verified by simulation experiments. Then, an event-triggered mechanism is introduced on the basis of NMPC algorithm, which reduces the amount of calculation iterations without affecting the 3-D trajectory tracking performance. Finally, the simulation results verify the feasibility and effectiveness of the proposed algorithm. Compared with the Traditional Model Predictive Control (TMPC) and NMPC algorithm, the ENMPC strategy can effectively reduce the amount of calculation iterations and improve the tracking efficiency.

NMPC-based UAV-USV cooperative tracking and landing

The study aims to solve the problem of real time tracking and precise landing of unmanned aerial vehicle (UAV) during unmanned surface vehicle (USV) navigation. In this paper, a UAV-USV cooperative tracking and landing control strategy based on nonlinear model predictive control (NMPC) is proposed. Firstly, the UAV-USV heterogeneous intelligent body collaborative system is constructed based on the mathematical model of UAV and USV; secondly, the tracking controller is designed based on NMPC algorithm to ensure that the UAV can track the USV in real time; finally, a UAV-USV cooperative landing control strategy is proposed to realize the heave motion of the USV to the peak vertex, thus, the UAV completes the precise landing with the minimum impact. As the simulation experimental results show, the UAV-USV cooperative tracking and landing control scheme proposed in this paper can provide effective solution against real time tracking and accurate landing of UAV during the navigation of USV.

A nonlinear model predictive control based control method to quadrotor landing on moving platform

AbstractTo address the problems that the UAV (Unmanned Aerial Vehicle) is vulnerable to distance limitation and environmental interference when tracking and landing on a moving platform autonomously, the accuracy of position estimation relying only on visual odometry in the point‐featureless environment is insufficient, and the traditional linear path planning solvers and controllers cannot meet the fast and safe requirements under the non‐linear strong coupling characteristics of the cooperative landing system, an nonlinear model predictive control (NMPC)‐based multi‐sensor fusion method for autonomous landing of UAVs on motion platforms is proposed. The UAV combines the position information obtained by the RTK‐GPS and the image information obtained by the camera and uses the special identification codes placed in the landing area of the UAV to carry out cooperative planning and navigation while using UKF (Unscented Kalman Filter) to estimate the position of the moving platform and using the interference‐resistant NMPC algorithm to optimise the UAV tracking trajectory based on the precise positioning of the two platforms to achieve the autonomous landing control of the UAV. The simulation and practical experimental results show the feasibility and effectiveness of the proposed algorithm and the autonomous landing control method and provide an effective solution for the autonomous landing of quadrotors on arbitrarily moving platforms.

Precision Post-Stall Landing Using NMPC With Learned Aerodynamics

In this paper, we present an approach for achieving precision post-stall landings with medium-sized Group 1 Unmanned Aerial Systems (UAS). To do this, we employ an aggressive dive-and-stall maneuver to significantly reduce maneuver distance, time, and touchdown speed. Our approach relies on a nonlinear model predictive control (NMPC) algorithm and learned aerodynamic coefficients to achieve accuracy and reliability in the presence of wind disturbances. We demonstrate our approach in hardware with a 60-inch wingspan, 4.2 kg fixed-wing UAS, and show the ability to land with low speed and high accuracy using minimal throttle.

Autonomous overtaking control considering the velocity change of obstacle vehicles on two-lane highways

Aiming at the speed change of obstacle vehicles in the process of autonomous ground vehicle (AGV) overtaking on two-lane highways, an overtaking control method including trajectory planning and trajectory control is proposed. First, the reference overtaking trajectory of the AGV is planned in stages (lane changing, passing and merging) using fifth order polynomials satisfying stability and comfort constraints. The initial planning trajectory may be unsafe due to the speed change of obstacle vehicles. So a collision prediction algorithm is built to predict two kinds of dangerous situations in real time: AGV collides with the leading vehicle during lane changing, and AGV collides with the oncoming vehicle during merging. Secondly, the potential field of the obstacle vehicles embedded with the relative speed is established and combined with the road potential field as the risk indicator. Then, combining the nonlinear model predictive control algorithm and risk index, the overtaking trajectory is replanned in real time with the initial trajectory as reference. Finally, a lateral path tracking controller based on model predictive control and a longitudinal speed tracking controller based on sliding mode control are established to track the planned trajectory rapidly and stably. To verify the performance of the proposed method, overtaking in three cases is simulated, and vehicle responding curves are obtained. The results show that the proposed control method can achieve safe and stable overtaking.

Practical Nonlinear Model Predictive Control for Improving Two-Wheel Vehicle Energy Consumption

Increasing the range of electric vehicles (EVs) is possible with the help of eco-driving techniques, which are algorithms that consider internal and external factors, like performance limits and environmental conditions, such as weather. However, these constraints must include critical variables in energy consumption, such as driver preferences and external vehicle conditions. In this article, a reasonable energy-efficient non-linear model predictive control (NMPC) is built for an electric two-wheeler vehicle, considering the Paris-Brussels route with different driving profiles and driver preferences. Here, NMPC is successfully implemented in a test bed, showing how to obtain the different parameters of the optimization problem and the estimation of the energy for the closed-loop system from a practical point of view. The efficiency of the brushless DC motor (BLCD) is also included for this test bed. In addition, this document shows that the proposal increases the chance of traveling the given route with a distance accuracy of approximately 1.5% while simultaneously boosting the vehicle autonomy by almost 20%. The practical result indicates that the strategy based on an NMPC algorithm can significantly boost the driver’s chance of completing the journey. If the vehicle energy is insufficient to succeed in the trip, the algorithm can guide the minimal State of Charge (SOC) required to complete the journey to reduce the driver energy-related uncertainty to a minimum.