Nonlinear Model Predictive Control Research Articles

Real-Time Co-optimization of Gear Shifting and Engine Torque for Predictive Cruise Control of Heavy-Duty Trucks

Fuel consumption is one of the main concerns for heavy-duty trucks. Predictive cruise control (PCC) provides an intriguing opportunity to reduce fuel consumption by using the upcoming road information. In this study, a real-time implementable PCC, which simultaneously optimizes engine torque and gear shifting, is proposed for heavy-duty trucks. To minimize fuel consumption, the problem of the PCC is formulated as a nonlinear model predictive control (MPC), in which the upcoming road elevation information is used. Finding the solution of the nonlinear MPC is time consuming; thus, a real-time implementable solver is developed based on Pontryagin’s maximum principle and indirect shooting method. Dynamic programming (DP) algorithm, as a global optimization algorithm, is used as a performance benchmark for the proposed solver. Simulation, hardware-in-the-loop and real-truck experiments are conducted to verify the performance of the proposed controller. The results demonstrate that the MPC-based solution performs nearly as well as the DP-based solution, with less than 1% deviation for testing roads. Moreover, the proposed co-optimization controller is implementable in a real-truck, and the proposed MPC-based PCC algorithm achieves a fuel-saving rate of 7.9% without compromising the truck’s travel time.

Learning Lyapunov terminal costs from data for complexity reduction in nonlinear model predictive control

AbstractA classic way to design a nonlinear model predictive control (NMPC) scheme with guaranteed stability is to incorporate a terminal cost and a terminal constraint into the problem formulation. While a long prediction horizon is often desirable to obtain a large domain of attraction and good closed‐loop performance, the related computational burden can hinder its real‐time deployment. In this article, we propose an NMPC scheme with prediction horizon and no terminal constraint to drastically decrease the numerical complexity without significantly impacting closed‐loop stability and performance. This is attained by constructing a suitable terminal cost from data that estimates the cost‐to‐go of a given NMPC scheme with long prediction horizon. We demonstrate the advantages of the proposed control scheme in two benchmark control problems.

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.

Continuous adaptive nonlinear model predictive control using spiking neural networks and real-time learning

Model predictive control (MPC) is a prominent control paradigm providing accurate state prediction and subsequent control actions for intricate dynamical systems with applications ranging from autonomous driving to star tracking. However, there is an apparent discrepancy between the model’s mathematical description and its behavior in real-world conditions, affecting its performance in real-time. In this work, we propose a novel neuromorphic (brain-inspired) spiking neural network for continuous adaptive non-linear MPC. Utilizing real-time learning, our design significantly reduces dynamic error and augments model accuracy, while simultaneously addressing unforeseen situations. We evaluated our framework using real-world scenarios in autonomous driving, implemented in a physics-driven simulation. We tested our design with various vehicles (from a Tesla Model 3 to an Ambulance) experiencing malfunctioning and swift steering scenarios. We demonstrate significant improvements in dynamic error rate compared with traditional MPC implementation with up to 89.15% median prediction error reduction with 5 spiking neurons and up to 96.08% with 5,000 neurons. Our results may pave the way for novel applications in real-time control and stimulate further studies in the adaptive control realm with spiking neural networks.

Hybrid control strategy for efficiency enhancement of a raft-type wave energy converter

To improve the wave energy capture performance of a raft-type wave energy converter, a novel hybrid control strategy consisting of a passive control strategy and an active control strategy is proposed. In the passive control strategy, a nonlinear stiffness mechanism is introduced to generate a nonlinear passive control force. The passive control strategy has the advantage of broadening the capture width, whereas the active control strategy, which uses nonlinear model predictive control, is mainly utilized to improve the capture efficiency. Considering the high dimensions of the dynamic model, a dimension reduction strategy is given. Moreover, a mechanism for selecting the initial value is proposed to avoid the local optimum. Then, a dimension reduction nonlinear model predictive control controller is proposed to obtain the optimal active control force. Finally, the wave energy capture performance is evaluated for both regular and irregular waves. Numerical simulation results show that the wave energy capture performance can be improved using the novel hybrid control strategy.

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.

Real-time and hardware in the loop validation of electric vehicle performance: Robust nonlinear predictive speed and currents control based on space vector modulation for PMSM

The transport industry's environmental impact has prompted various stakeholders to focus more on electric vehicles as a potential solution. Extensive research on electric vehicle motor control reveals their complexity, highlighting the crucial role of the traction motor control mechanism being one of their essential subsystems. This study presents a novel approach to control the drive system of an electric vehicle's permanent magnet synchronous motor, using a robust non-linear model predictive control in a cascaded structure combined with a space vector modulation technique. The formulation of the robust non-linear model predictive control law involves optimizing a new cost function with the inclusion of an integral action in the controller to ensure zero steady-state error. An important aspect of this control approach is its ability to enhance robustness without needing information about external perturbations and parameter uncertainties. Moreover, the space vector modulation technique is designed to address the issue of current harmonic distortion by carefully selecting appropriate switching vectors. The appropriate selection for space voltage vectors for every sampling period maintains a consistent switching frequency. As a result, the SVM can enhance torque-rippled regulation and accomplish effective flux and torque control. The performance of the proposed control system is evaluated through a series of numerical simulations using MATLAB/Simulink. The simulation results are analyzed and compared to assess the effectiveness of the proposed control system in terms of tracking accuracy, disturbance rejection, robustness against parameter uncertainties, reduction of torque, and current ripples. To further validate the numerical simulation results, a hardware-in-the-loop (HIL) setup is established using the OPAL-RT platform. Furthermore, experimental validation on a PMSM utilizing the dSPACE DS1202 board is carried out, demonstrating the efficacy of the proposed control system. These findings validate the suggested control technique's robustness and efficiency.

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Purpose To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1 are often used in the joints of a robotic manipulator. This results into an actuator with large mechanical impedance (also known as nonback-drivable actuator). This in turn generates high contact forces when collision of the robotic mechanism occur and can cause humans’ injury. Another disadvantage of electric actuators is that they can exhibit overheating when constant torques have to be provided. Comparing to electric actuators, pneumatic actuators have promising properties for robotic applications, due to their low weight, simple mechanical design, low cost and good power-to-weight ratio. Electropneumatically actuated robots usually have better friction properties. Moreover, because of low mechanical impedance, pneumatic robots can provide moderate interaction forces which is important for robotic surgery and rehabilitation tasks. Pneumatic actuators are also well suited for exoskeleton robots. Actuation in exoskeletons should have a fast and accurate response. While electric motors come against high mechanical impedance and the risk of causing injuries, pneumatic actuators exhibit forces and torques which stay within moderate variation ranges. Besides, unlike direct current electric motors, pneumatic actuators have an improved weight-to-power ratio and avoid overheating problems. Design/methodology/approach The aim of this paper is to analyze a nonlinear optimal control method for electropneumatically actuated robots. A two-link robotic exoskeleton with electropneumatic actuators is considered as a case study. The associated nonlinear and multivariable state-space model is formulated and its differential flatness properties are proven. The dynamic model of the electropneumatic robot is linearized at each sampling instance with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Within each sampling period, the time-varying linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. An H-infinity controller is designed for the linearized model of the robot aiming at solving the related optimal control problem under model uncertainties and external perturbations. An algebraic Riccati equation is solved at each time-step of the control method to obtain the stabilizing feedback gains of the H-infinity controller. Through Lyapunov stability analysis, it is proven that the robot’s control scheme satisfies the H-infinity tracking performance conditions which indicate the robustness properties of the control method. Moreover, global asymptotic stability is proven for the control loop. The method achieves fast convergence of the robot’s state variables to the associated reference trajectories, and despite strong nonlinearities in the robot’s dynamics, it keeps moderate the variations of the control inputs. Findings In this paper, a novel solution has been proposed for the nonlinear optimal control problem of robotic exoskeletons with electropneumatic actuators. As a case study, the dynamic model of a two-link lower-limb robotic exoskeleton with electropneumatic actuators has been considered. The dynamic model of this robotic system undergoes first approximate linearization at each iteration of the control algorithm around a temporary operating point. Within each sampling period, this linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modeling error which is due to the truncation of higher-order terms from the Taylor series is considered to be a perturbation which is asymptotically compensated by the robustness of the control algorithm. To stabilize the dynamics of the electropneumatically actuated robot and to achieve precise tracking of reference setpoints, an H-infinity (optimal) feedback controller is designed. Actually, the proposed H-infinity controller for the model of the two-link electropneumatically actuated exoskeleton achieves the solution of the associated optimal control problem under model uncertainty and external disturbances. This controller implements a min-max differential game taking place between: (i) the control inputs which try to minimize a cost function which comprises a quadratic term of the state vector’s tracking error and (ii) the model uncertainty and perturbation inputs which try to maximize this cost function. To select the stabilizing feedback gains of this H-infinity controller, an algebraic Riccati equation is being repetitively solved at each time-step of the control method. The global stability properties of the H-infinity control scheme are proven through Lyapunov analysis. Research limitations/implications Pneumatic actuators are characterized by high nonlinearities which are due to air compressibility, thermodynamics and valves behavior and thus pneumatic robots require elaborated nonlinear control schemes to ensure their fast and precise positioning. Among the control methods which have been applied to pneumatic robots, one can distinguish differential geometric approaches (Lie algebra-based control, differential flatness theory-based control, nonlinear model predictive control [NMPC], sliding-mode control, backstepping control and multiple models-based fuzzy control). Treating nonlinearities and fault tolerance issues in the control problem of robotic manipulators with electropneumatic actuators has been a nontrivial task. Practical implications The novelty of the proposed control method is outlined as follows: preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics. These results considered that the control inputs gain matrix is not dependent on the values of the system’s state vector. Moreover, in these approaches the linearization was performed around points of the desirable trajectory, whereas in the present paper’s control method the linearization points are related with the value of the state vector at each sampling instance as well as with the last sampled value of the control inputs vector. The Riccati equation which has been proposed for computing the feedback gains of the controller is novel, so is the presented global stability proof through Lyapunov analysis. This paper’s scientific contribution is summarized as follows: (i) the presented nonlinear optimal control method has improved or equally satisfactory performance when compared against other nonlinear control schemes that one can consider for the dynamic model of robots with electropneumatic actuators (such as Lie algebra-based control, differential flatness theory-based control, nonlinear model-based predictive control, sliding-mode control and backstepping control), (ii) it achieves fast and accurate tracking of all reference setpoints, (iii) despite strong nonlinearities in the dynamic model of the robot, it keeps moderate the variations of the control inputs and (iv) unlike the aforementioned alternative control approaches, this paper’s method is the only one that achieves solution of the optimal control problem for electropneumatic robots. Social implications The use of electropneumatic actuation in robots exhibits certain advantages. These can be the improved weight-to-power ratio, the lower mechanical impedance and the avoidance of overheating. At the same time, precise positioning and accurate execution of tasks by electropneumatic robots requires the application of elaborated nonlinear control methods. In this paper, a new nonlinear optimal control method has been developed for electropneumatically actuated robots and has been specifically applied to the dynamic model of a two-link robotic exoskeleton. The benefit from using this paper’s results in industrial and biomedical applications is apparent. Originality/value A comparison of the proposed nonlinear optimal (H-infinity) control method against other linear and nonlinear control schemes for electropneumatically actuated robots shows the following: (1) Unlike global linearization-based control approaches, such as Lie algebra-based control and differential flatness theory-based control, the optimal control approach does not rely on complicated transformations (diffeomorphisms) of the system’s state variables. Besides, the computed control inputs are applied directly on the initial nonlinear model of the electropneumatic robot and not on its linearized equivalent. The inverse transformations which are met in global linearization-based control are avoided and consequently one does not come against the related singularity problems. (2) Unlike model predictive control (MPC) and NMPC, the proposed control method is of proven global stability. It is known that MPC is a linear control approach that if applied to the nonlinear dynamics of the electropneumatic robot, the stability of the control loop will be lost. Besides, in NMPC the convergence of its iterative search for an optimum depends on initialization and parameter values selection and consequently the global stability of this control method cannot be always assured. (3) Unlike sliding-mode control and backstepping control, the proposed optimal control method does not require the state-space description of the system to be found in a specific form. About sliding-mode control, it is known that when the controlled system is not found in the input-output linearized form the definition of the sliding surface can be an intuitive procedure. About backstepping control, it is known that it cannot be directly applied to a dynamical system if the related state-space model is not found in the triangular (backstepping integral) form. (4) Unlike PID control, the proposed nonlinear optimal control method is of proven global stability, the selection of the controller’s parameters does not rely on a heuristic tuning procedure, and the stability of the control loop is assured in the case of changes of operating points. (5) Unlike multiple local models-based control, the nonlinear optimal control method uses only one linearization point and needs the solution of only one Riccati equation so as to compute the stabilizing feedback gains of the controller. Consequently, in terms of computation load the proposed control method for the electropneumatic actuator’s dynamics is much more efficient.

Neural critic learning with accelerated value iteration for nonlinear model predictive control

In practical industrial processes, the receding optimization solution of nonlinear model predictive control (NMPC) is always a very knotty problem. Based on adaptive dynamic programming, the accelerated value iteration predictive control (AVI-PC) algorithm is developed in this paper. Integrating iteration learning with the receding horizon mechanism of NMPC, a novel receding optimization solution pattern is exploited to resolve the optimal control law in each prediction horizon. Besides, the basic architecture and the specific form of the AVI-PC algorithm are demonstrated, including the relationship among the iterative learning process, the prediction process, and the control process. On this basis, the convergence and admissibility conditions are established, and the relevant properties are comprehensively analyzed when the accelerated factor satisfies the established conditions. Furthermore, the accelerated value iterative function is approximated through the single critic network constructed by utilizing the multiple linear regression method. Finally, the plentiful simulation experiments are conducted from various perspectives to verify the effectiveness and progressiveness of the AVI-PC algorithm.

Planar curved path following controller for a small fixed-wing unmanned aerial vehicle with constrained parameters optimized by nonlinear model predictive control

Path following presents a pivotal challenge within the realm of small fixed-wing unmanned aerial vehicles. Firstly, a Lyapunov-stable path guidance law was formulated to follow specific planar curved paths. To ensure differentiability of the guidance law, a modified, smooth saturation function was derived. Secondly, an analysis was conducted to ascertain the interrelationship between control parameters and input constraints, thereby identifying the relevant parameter domains. Thirdly, the nonlinear model predictive control technique was harnessed to optimize both guidance law parameters, enhancing the unmanned aerial vehicle’s capacity to achieve optimal performance in both straight-line and circular path following, hereafter referred to as PFC_NMPC. By leveraging Lyapunov stability arguments for switched systems, the stability of the corresponding nonlinear switched system was guaranteed. In this study, square and circular paths were generated to assess the path-following control of a simulated fixed-wing unmanned aerial vehicle. The performance of various guidance laws, including those with fixed parameters (PFC), those with parameters tuned using fuzzy logic (PFC_FL), PFC_NMPC, vector field, and pure pursuit with line-of-sight, was compared. Notably, the proposed PFC_NMPC method exhibited the ability to expedite the unmanned aerial vehicle’s convergence to the desired path while maximizing the effective flight path length.

Modeling and Nonlinear Predictive Control of Solar Thermal Systems in District Heating

This study presents data-driven modeling and nonlinear model predictive control of solar thermal plants in district heating, for the purpose of operation optimization. The study considers the efficient operation of a solar thermal plant in Hillerød, Denmark. A dynamic model is estimated as a system of stochastic differential equations using grey-box modeling and real-world data. The presented nonlinear model predictive controller design is based on repeated trajectory linearization and the dynamic model. Several objective designs are considered, e.g., maximizing energy or temperature. The study provides simulations for analyzing the model fitness and controller performances. The model is shown to fit the daytime operation of the plant. The designed controllers are shown to improve efficiency, increasing the transported energy up to 28%.

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.

Approximate Dynamic Programming for Control of Wave Energy Converters With Implementation and Validation on a Point Absorber Prototype

It is recognized that the application of constrained optimal control for wave energy converters (WECs), represented by model predictive control (MPC), is hindered by its computation burden resulting from online optimization, especially when the model contains nonlinearities. In this article, a novel control solution based on approximate dynamic programming (ADP) is proposed, in which an explicit controller is solved by model sampling and neural network training. In this way, the major computation load is moved offline to enable fast online execution, and the need for wave prediction is eliminated. The effectiveness of ADP is verified by a simulation case study based on a nonlinear WEC system. Using nonlinear MPC as the performance benchmark, over 90% energy efficiency is achieved by ADP under various sea states with constraint satisfaction and dramatically faster computation. The ADP controller is further experimentally validated on a newly constructed WEC prototype through wave tank testing, where successful implementation and satisfactory performance are demonstrated.

Decarbonization through smart energy management: Climate control in building-integrated rooftop greenhouses for urban agriculture across various climate conditions

This paper investigates the potential benefits of integrating rooftop greenhouses (RTGs) with buildings to reduce energy and CO2 costs, contributing to urban decarbonization efforts. This integration not only advances sustainable urban agriculture but also aligns with the United Nations Sustainable Development Goal 7 (SDG7) - Affordable and Clean Energy, and Sustainable Development Goal 11 (SDG11) - Sustainable Cities and Communities, through its energy-efficient, low-carbon approach. We hypothesize that this integration can significantly lower energy use in integrated RTGs (i-RTGs) and set out to validate this through dynamic models for both building and i-RTG climates, focusing on CO2 concentration, humidity, and temperature. Central to our approach is the implementation of a nonlinear model predictive control (NMPC) framework, which utilizes these dynamic models to make control decisions aimed at minimizing total control costs. This framework operates in a receding horizon procedure, regulating climate factors within the i-RTG and building using various actuators. We validate our approach by simulating an i-RTG atop a building in eleven different cities, demonstrating interactions such as energy, moisture, and CO2 exchange. Significantly, our study reveals that integrating i-RTG with buildings under the NMPC framework leads to a 15.2% reduction in control costs. Additionally, we find that the i-RTG model is adaptable to different climates, with colder regions showing greater cost reduction potential. Our study underscores the viability and advantages of integrating i-RTGs with buildings, offering a sustainable, decarbonizing solution for urban agriculture and building management that contributes to the fulfillment of SDG7 and SDG11.

Explicit flatness-based MPC design for indoor nano-quadcopter position tracking

Due to the nonlinearities and operational constraints of quadcopters, Model Predictive Control (MPC) encounters the requirement of high computational power. This problem may prove impractical, especially for hardware-limited setups. By removing the need for online solvers, Explicit MPC (ExMPC) stands out as a strong candidate. Yet, the formulation was usually hindered by the system's nonlinearity and dimensionality. In this paper, we propose an ExMPC solution for quadcopter position stabilisation. With the former issue, the system is exactly linearised into a concatenation of three double integrators. For the latter, with a suitable characterisation of the new convoluted constraints, the stabilising ExMPC can be computed for each double integrator separately. The controller is validated via simulations and experiments on a nanodrone platform. The proposed scheme provides similar performance and theoretical guarantees to the up-to-date nonlinear MPC solutions but with notably less computational effort, allowing scalability in a centralised manner.

Learning model predictive controller for wheeled mobile robot with less time delay

The weak spots have been examined, a solution has been suggested, the solution has been applied, and a comparison between the simulation and experimental test results has been given in this work. In order to do this, a nonlinear model predictive controller and a linear quadratic regulator controller have been utilized to control a four-wheel mobile robot during modeling and implementation. But the combination of these classic and modern controllers with machine learning can greatly help to make these controllers work more accurately; As a result, in order to increase the accuracy of the performance of these controllers, by training neural networks of multilayer perceptrons, the controllers have been made intelligent. Controllers with cost function have coefficients as weighting to the matrix of system state variables and control input, which are greatly affected by changing these two weighting matrices of problem solving and optimization. For this reason, it is necessary to extract these two matrices for each separate path in order to improve the performance of the controller by trial and error. But by applying the proposed network which is trained with a new algorithm, not only the performance accuracy has increased, but the network extracts these two matrices without the need to spend human energy. Additionally, by training additional neural networks to optimally extract the benefit of the forecast horizon, fewer calculations and faster solution times have been achieved, helping to reduce the current time delays, particularly in the implementation of the nonlinear controller on the robot in the experimental mode. In the hardware section, the solution time has been shortened by looking at and utilizing operators like the U2D2 interface and the pixy camera, which are quicker than the standard procedure. The information indicates that the proposed intelligence technology reacts 40%–50% quicker than the NMPC standard procedure. The suggested algorithm has also minimized the path tracking error since it extracts the optimal gain at each stage. Moreover, a hardware mode solving speed comparison between the recommended and conventional methods is given. In this domain, a 33% increase in solving speed has been noted.

A Multi-Source Braking Force Control Method for Electric Vehicles Considering Energy Economy

Advancements in electric vehicle technology have promoted the development trend of smart and low-carbon environmental protection. The design and optimization of electric vehicle braking systems faces multiple challenges, including the reasonable allocation and control of braking torque to improve energy economy and braking performance. In this paper, a multi-source braking force system and its control strategy are proposed with the aim of enhancing braking strength, safety, and energy economy during the braking process. Firstly, an ENMPC (explicit nonlinear model predictive control)-based braking force control strategy is proposed to replace the traditional ABS strategy in order to improve braking strength and safety while providing a foundation for the participation of the drive motor in ABS (anti-lock braking system) regulation. Secondly, a grey wolf algorithm is used to rationally allocate mechanical and electrical braking forces, with power consumption as the fitness function, to obtain the optimal allocation method and provide potential for EMB (electro–mechanical brake) optimization. Finally, simulation tests verify that the proposed method can improve braking strength, safety, and energy economy for different road conditions, and compared to other methods, it shows good performance.

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 implementation of nonlinear model predictive control for high angle of attack Maneuvers in fighter aircrafts using deep learning

ABSTRACT Nonlinear model predictive control (NMPC) provides a nice framework for accounting for multivariable nonlinear dynamics subject to constraints; however, the cost of implementing NMPC is high due to the need to solve a large-scale nonlinear program to optimality in real-time. This research is focussed on the design of real-time solution to NMPC (low computations) for fast dynamic systems. In this work, a comprehensive and innovative solution based on a deep learning-based approximate NMPC scheme has been proposed to overcome these computational challenges. The main idea is to learn a deep neural network followed by the symbolic simplification of the NMPC law, whose evaluation cost and memory footprint can be optimized offline. Since not all the states of the system are measured, we also combine the deep learning based NMPC approach with an unscented Kalman filter (UKF) as well as show how this scheme can be easily modified to be offset-free (i.e. remove steady-state error due to persistent disturbances and modelling error). The proposed approach is implemented on a highly fast dynamic system (i.e. F-16 fighter aircraft to perform a high angle of attack maneuver) to check the controller efficiency. Fighter aircraft need to be able to make fast and complex maneuvers (that exploit strongly nonlinear dynamics) to be able to maintain air superiority. However, such aggressive maneuvers require strong coordination between the actions to avoid destabilizing the system. A quantitative analysis from comparison with the standard MPC approach shows the practical utility of the proposed approach.

Three-dimensional variable center of mass height biped walking using a new model and nonlinear model predictive control

This paper presents a trajectory generation algorithm for a three-dimensional (3D) biped robot that can adjust the center of mass (CoM) according to the environment. We adopt a new abstract model that supports vertical motion and rotation. Differing from traditional abstract models, the proposed full centroid dynamics inverted pendulum model fully considers the robot’s movement and rotation. Unlike the zero moment point (ZMP), which only ensures the feet do not flip over, we also propose a new additional stability criterion, named zero frictional moment point (ZFMP), guaranteeing no yaw rotation while walking. Next, a nonlinear model predictive control is designed to generate the CoM trajectory, torso rotational angle, and adaptive footholds to induce various biped gaits. A full-dynamics 3D humanoid robot is simulated to test the proposed method while steering, walking underneath a low door, and walking with disturbances.