Nonlinear Model Predictive Control Approach Research Articles

A Non-Linear Offset-Free Model Predictive Control Design Approach

This paper presents a non-linear model predictive control approach for offset-free tracking and the rejection of piece-wise constant disturbances. The approach involves augmenting the system’s state vector with the integral of the tracking error, enabling the design of a non-linear model predictive controller for this augmented system. Nominal closed-loop stability is enforced thanks to a terminal equality constraint and proven by a Lyapunov argument. Compared to the existing offset-free approaches in the literature, our method offers greater simplicity, as it does not rely on linear approximations of the system to control. Furthermore, it eliminates the need to estimate disturbances, a task that is especially challenging with non-linear systems. Comprehensive simulations and experimental tests are conducted according to a non-linear, coupled, two-tank laboratory experiment, demonstrating the robustness and effectiveness of the proposed approach.

An Advanced Control Method for Aircraft Carrier Landing of UAV Based on CAPF–NMPC

This paper investigates a carrier landing controller for unmanned aerial vehicles (UAVs), and a nonlinear model predictive control (NMPC) approach is proposed considering a precise motion control required under dynamic landing platform and environment disturbances. The NMPC controller adopts constraint aware particle filtering (CAPF) to predict deck positions for disturbance compensation and to solve the nonlinear optimization problem, based on a model establishment of carrier motion and wind field. CAPF leverages Monte Carlo sampling to optimally estimate control variables for improved optimization, while utilizing constraint barrier functions to keep particles within a feasible domain. The controller considers constraints such as fuel optimization, control saturation, and flight safety to achieve trajectory control. The advanced control method enhances the solution, estimating optimal control sequences of UAV and forecasting deck positions within a moving visual field, with effective trajectory tracing and higher control accuracy than traditional methods, while significantly reducing single-step computation time. The simulation is carried out using UAV “Silver Fox”, considering several scenarios of different wind scales compared with traditional CAPF–NMPC and the nlmpc method. The results show that the proposed NMPC approach can effectively reduce control chattering, with a landing error in rough marine environments of around 0.08 m, and demonstrate improvements in trajectory tracking capability, constraint performance and computational efficiency.

Real-time coordination of integrated transmission and distribution systems: Flexibility modeling and distributed NMPC scheduling

This paper proposes a real-time distributed operational architecture to coordinate integrated transmission and distribution systems (ITD). At the distribution system level, the distribution system operator (DSO) calculates the aggregated flexibility of all controllable devices by power-energy envelopes and provides them to the transmission system operator (TSO). At the transmission system level, a distributed nonlinear model predictive control (nmpc) approach is proposed to coordinate the economic dispatch of multiple TSOs, considering the aggregated flexibility of all distribution systems. The subproblems of the proposed approach are associated with different TSOs and individual time periods. In addition, the aggregated flexibility of controllable devices in distribution networks is encapsulated, re-calculated, and communicated through the power-energy envelopes, facilitating a reduction in computational complexity and eliminating redundant information exchanges between TSOs and DSOs, thereby enhancing privacy and security. The framework’s effectiveness and applicability in real-world scenarios are validated through simulated operational scenarios on a summer day in Germany, highlighting its robustness in the face of significant prediction mismatches due to severe weather conditions.

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.

NMPC in Haptic Shared Control Steering:Optimizing Vehicle Motion

As vehicles become more automated in the pursuit of comfort and safety, the human-machine interface must adapt to accommodate the intent of both driver and automation. The concept of haptic shared control steering allows lateral control of the vehicle to be continuously shared between driver and automation via the steering wheel. The automation imparts a torque on the steering wheel which serves to both guide the vehicle and inform the driver of the automation's intent without impairing the driver's ability to steer the vehicle. The combination of haptic feedback and seamless transition of vehicle control makes the use of automation more intuitive. This paper describes a Nonlinear Model Predictive Control (NMPC) approach for controlling the strength of the automation torque with the aim of optimizing vehicle motion. NMPC allows for intuitive tuning and customization of the vehicle steering performance through the NMPC parameterization. Results on a vehicle in real driving scenarios show that the proposed control is able to decrease the lateral jerk, a common measure of passenger comfort, compared to the current state of the art by up to 50% while maintaining the same or similar levels of path tracking performance.

Developing a resilient and sustainable non-linear closed-loop supply chain management framework for the automotive sector industry using a gaussian fuzzy optimization based non-linear model predictive control approach

ABSTRACT Efforts to merge sustainability and resilience within the automotive industry’s supply chain models have proven challenging. This paper proposes a novel non-linear closed-loop supply chain management framework tailored to the tire industry supply chain from the automotive sector to address the issue of exploring interrelationships. Framework employs trapezoidal linguistic cubic fuzzy Z-score technique for order of preference by similarity to the ideal solution ranking approach to prioritize resilience strategies to maintain sustainability performance during sudden disturbances. Furthermore, Gaussian fuzzy optimization-based non-linear model predictive control acts as a feedback controller to integrate sustainability and resilience by providing a stable output based on the objective function related to sustainability dimensions. An experimental study assesses the impact of resilience strategies on total supply chain costs, highlighting significant cost savings. Adopting strategies like multiple sourcing, information sharing, and improved design quality of the supply chain keeps total expected costs optimal for various sustainability levels.

A non-linear model predictive control strategy to minimise mechanical degradation effects of lithium-ion battery

Mechanical stresses are not only developed inside the active material of the composite electrode, but also in the solid electrolyte interface layer (SEI) due to the graphite expansion. Due to diffusion induced stress (DIS) phenomena, stresses in the negative electrode are generated during charging and discharging cycles. This article presents the proposed optimal charging profile explicitly incorporating the effects of mechanical degradation. Non-linear model predictive control approach along with Gauss pseudo-spectral method is used to optimise charging trajectories. It is assumed that active material is not the weakest material but system is modelled based on SEI break and repair effect. The dynamics of battery is represented by a single particle model. The simulated results are compared with benchmark constant current constant voltage (CCCV) strategy. Furthermore, proposed methodology is compared with optimal CCCV using cycle life ageing experimental scenario. It is estimated that stress amplitude decreased by 7% and nominal capacity increased by 11% using the proposed optimal charging profile.

Trajectory planning and control for autonomous vehicles: a “fast” data-aided NMPC approach

A huge research effort is being spent worldwide by automotive companies and academic institutions for developing vehicles with high levels of autonomy, ranging from advanced driving-assisted systems to fully automated vehicles. Nonlinear Model Predictive Control (NMPC) has the potential to become a key technology in this context, thanks to its capability to deal with linear and nonlinear systems, manage physical constraints and satisfy multi-objective performance criteria. However, NMPC is based on the on-line solution of a nonconvex optimization problem and this operation may require a high computational cost, compromising its real-time implementation. In this paper, a “fast” data-aided NMPC approach is developed, aimed at trajectory planning and control for autonomous vehicles. In particular, a Set Membership approximation method is used to derive from data tight bounds on the optimal NMPC control law. These bounds are used to restrict the search domain of the underlying NMPC optimization process, allowing a significant reduction of the computation time. The proposed NMPC trajectory planning and control approach is tested in simulation and compared with other state-of-the-art methods, considering different road scenarios.

A Hybrid Deep Reinforcement Learning and Optimal Control Architecture for Autonomous Highway Driving

Autonomous vehicles in highway driving scenarios are expected to become a reality in the next few years. Decision-making and motion planning algorithms, which allow autonomous vehicles to predict and tackle unpredictable road traffic situations, play a crucial role. Indeed, finding the optimal driving decision in all the different driving scenarios is a challenging task due to the large and complex variability of highway traffic scenarios. In this context, the aim of this work is to design an effective hybrid two-layer path planning architecture that, by exploiting the powerful tools offered by the emerging Deep Reinforcement Learning (DRL) in combination with model-based approaches, lets the autonomous vehicles properly behave in different highway traffic conditions and, accordingly, to determine the lateral and longitudinal control commands. Specifically, the DRL-based high-level planner is responsible for training the vehicle to choose tactical behaviors according to the surrounding environment, while the low-level control converts these choices into the lateral and longitudinal vehicle control actions to be imposed through an optimization problem based on Nonlinear Model Predictive Control (NMPC) approach, thus enforcing continuous constraints. The effectiveness of the proposed hierarchical architecture is hence evaluated via an integrated vehicular platform that combines the MATLAB environment with the SUMO (Simulation of Urban MObility) traffic simulator. The exhaustive simulation analysis, carried out on different non-trivial highway traffic scenarios, confirms the capability of the proposed strategy in driving the autonomous vehicles in different traffic scenarios.

Influence of Estimators and Numerical Approaches on the Implementation of NMPCs

Advanced control strategies, together with state-estimation methods, are frequently applied to nonlinear and complex systems. It is crucial to understand which of these are the most efficient methods for the best use of these approaches in a chemical process. In the current work, nonlinear model predictive control (NMPC) approaches were developed that considered three numerical methods: single shooting (SS), multiple shooting (MS), and orthogonal collocation (OC). Their performance was compared against the Van de Vusse reactor benchmark while considering set-point changes, unreachable set-point, disturbances, and mismatches. The results showed that the NMPC based on OC presented less computational cost than the other approaches. The extended Kalman filter (EKF), constrained extended Kalman filter (CEKF), and the moving horizon estimator (MHE) were also developed. The estimators’ performance was compared for the same benchmark by considering the computational cost and the mean squared error (MSE) for the estimated variables, thereby verifying the CEKF as the best option. Finally, the performance of the nine combinations of estimators and control approaches was compared to consider the Van de Vusse reactor and the same scenarios, thereby verifying the best performance of the CEKF with the OC. The present work can help with choosing the numerical method and the estimator for controlling chemical processes.

Plant-Inspired Soft Growing Robots: A Control Approach Using Nonlinear Model Predictive Techniques

Soft growing robots, which mimic the biological growth of plants, have demonstrated excellent performance in navigating tight and distant environments due to their flexibility and extendable lengths of several tens of meters. However, controlling the position of the tip of these robots can be challenging due to the lack of precise methods for measuring the robots’ Cartesian position in their working environments. Moreover, classical control techniques are not suitable for these robots because they involve the irreversible addition of materials, which introduces process constraints. In this paper, we propose two optimization-based approaches, combining Moving Horizon Estimation (MHE) with Nonlinear Model Predictive Control (NMPC), to achieve superior performance in point stabilization, trajectory tracking, and obstacle avoidance for these robots. MHE is used to estimate the entire state of the robot, including its unknown Cartesian position, based on available configuration measurements. The proposed NMPC approach considers process constraints by relying on the estimated state to ensure optimal performance. We perform numerical simulations using the nonlinear kinematic model of a vine-like robot, one of the newly introduced plant-inspired growing robots, and achieve satisfactory results in terms of reduced computation times and tracking error.

Optimal control of a fourth generation district heating network using an integrated non-linear model predictive controller

District heating (DH) can help increasing the share of renewable and residual energy sources in the heating sector. Usually a rule-based controller (RBC) is used for controlling these networks while more advanced control strategies like model predictive control (MPC) can support the transition to a decarbonised heating sector. In this paper, an integrated non-linear MPC approach for the control of DH networks is presented. The main novelties are the consideration of the system as a whole (including the heat demand side) and the inclusion of important non-linearities and all types of flexibility in the controller model of the MPC. A simulation-based methodology and dedicated solver are used in which the MPC is applied to an existing fourth generation DH network. The results of a three-day simulation in both a winter and spring period show that the MPC outperforms the currently used RBC: the thermal discomfort is lower in the winter period and comparable in the spring period while the electrical energy use of the DH system is reduced by 3% and 17%, respectively. The MPC achieves these results by lowering the network temperatures, using its anticipatory ability, and exploiting the flexibility of the building thermal inertia.

Real-time nonlinear model predictive control for optimizing the ammonia coverage ratio of an SCR system based on TC-QPSO

SCR systems with complex chemical reaction dynamics are important components of emission aftertreatment systems. Their contradictory emission requirements of higher NOx conversion efficiency and lower NH3 slip can be simultaneously achieved by optimizing the ammonia coverage ratio, which can be accomplished with a nonlinear model predictive control (NMPC) framework. However, how to find a reasonable NMPC approach for optimizing the ammonia coverage ratio and utilize an appropriate method to solve it remain a formidable challenge. In this paper, a two-layer hierarchical control framework for an SCR system is developed to decouple the optimization and tracking control of the ammonia coverage ratio. In the upper layer, an NMPC controller with a long prediction horizon is designed to account for the emission objectives and constraints and generate optimal trajectories for the ammonia coverage ratio. In the lower layer, a robust observing and tracking controller with a short horizon is employed which takes the planned trajectories as the tracking target. Moreover, an improved thermonuclear-initiation and cross-boundary quantum-behaved particle swarm optimization (TC-QPSO) method for optimizing the ammonia coverage ratio based on its dynamic characteristics is proposed to solve the NMPC problem. The simulation results show that the proposed TC-QPSO emission optimization effects of NOx and NH3 are closest to those of the SQP method (the benchmark controller) with a slight computation time penalty. The experimental results under the three transient cycles show that the average NOx conversion efficiency of the proposed two-layer hierarchical control framework with the TC-QPSO algorithm can reach more than 98% with an average NH3 slip of less than 11 ppm, which is able to satisfy emission requirements, and that compared to the traditional QPSO algorithm, the average NH3 slip of the proposed TC-QPSO algorithm is improved by 45.6% with an average NOx conversion efficiency penalty of 1.09% and its emission optimization effects have better robustness for uncertainties in transient cycles.

Nonlinear Model Predictive Control: an Optimal Search Domain Reduction

Nonlinear Model Predictive Control (NMPC) is a powerful control method, used in many industrial contexts. NMPC is based on the online solution of a suitable Optimal Control Problem (OCP) but this operation may require high computational costs, which may compromise its implementation in “fast” real-time applications. In this paper, we propose a novel NMPC approach, aiming to improve the numerical efficiency of the underlying optimization process. In particular, a Set Membership approximation method is applied to derive from data tight bounds on the optimal NMPC control law. These bounds are used to restrict the search domain of the OCP, allowing a significant reduction of the computation time. The effectiveness of the proposed NMPC strategy is demonstrated in simulation, considering an overtaking maneuver in a realistic autonomous vehicle scenario.

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.

Data-driven Model Predictive Control for pH regulation in Raceway Reactors*

The industrial production of microalgae is a highly sustainable and attractive process due to its variety of applications, especially when it is combined with wastewater treatment. From a control point of view, the optimization of the process requires a considerable effort regarding the culture conditions. The biological nature of the process renders its characterization considerably difficult, as well as the acquisition of models describing its dynamics. In this work, a complete methodology for pH control in raceway photobioreactors based on the Practical Nonlinear Model Predictive Control (PNMPC) approach is proposed. Models based on artificial Neural Networks (ANN) of the system have been obtained and validated, and a PNMPC controller based on these data-driven models has been developed and tested in a real raceway reactor. The results demonstrate the reliability of this type of models, and justify the possibility of combining them with predictive control algorithms in highly nonlinear systems.

Nonlinear Model Predictive Control of Vagal Nerve Stimulation to regulate hemodynamic variables

Various pre-clinical investigations indicate that the electrical stimulation of the cervical branch of the vagus that innervates the heart has therapeutic value in the management of various cardiac diseases. In theory, the design of a closed-loop control mechanism that automatically adjusts vagal nerve stimulation (VNS) parameters based on real-time physiological feedback can eliminate intra-patient variability in VNS outcomes and therefore represents a major step towards patient-specific therapy. This study develops a nonlinear model predictive control (NMPC) approach for VNS of a pulsatile, human cardio-baroreflex system. The manipulated variables are the frequency and amplitude of a charge-balanced biphasic current. The effects of these variables on hemodynamic quantities such as heart rate, blood pressure, heart contractility e.t.c. are estimated under the assumption that the desired activation of efferent vagal nerve fibers within the vagosympathetic complex can not be realistically isolated from the off-target activation of afferent fibers. An approximate, cycle-averaged cardiovascular model is derived to eliminate pulsatility and is used for prediction in the controller. The feasibility of this NMPC scheme is explored with a set-point tracking example.

Toward transactive control of coupled electric power and district heating networks

Although electric power networks and district heating networks are physically coupled, they are not operated in a coordinated manner. With increasing penetration of renewable energy sources, a coordinated market-based operation of the two networks can yield significant advantages, as reduced need for grid reinforcements, by optimizing the power flows in the coupled systems. Transactive control has been developed as a promising approach based on market and control mechanisms to coordinate supply and demand in energy systems, which when applied to power systems is being referred to as transactive energy. However, this approach has not been fully investigated in the context of market-based operation of coupled electric power and district heating networks. Therefore, this paper proposes a transactive control approach to coordinate flexible producers and consumers while taking into account the operational aspects of both networks, for the benefit of all participants and considering their privacy. A nonlinear model predictive control approach is applied in this work to maximize the social welfare of both networks, taking into account system operational limits, while reducing losses and considering system dynamics and forecasted power supply and demand of inflexible producers and consumers. A subtle approximation of the operational optimization problem is used to enable the practical application of the proposed approach in real time. The presented technique is implemented, tested, and demonstrated in a realistic test system, illustrating its benefits.

Analysis of the Impact of Variable Speed Limits on Environmental Sustainability and Traffic Performance in Urban Networks

This work focuses on evaluating the potential of variable speed limits (VSLs) in a synthetic urban network to improve both environmental sustainability and traffic performance. The traffic system is modeled using the microscopic traffic simulator SUMO, and a physical fuel consumption and NOx emission model is used to assess the vehicles’ energy efficiency. Speed limits are controlled through a nonlinear model predictive control (NMPC) approach, in which the traffic evolution and fuel consumption are respectively predicted with a macroscopic traffic model, namely the cell transmission model (CTM), and a pre-calibrated artificial neural network (ANN). The results reveal that in transient phases between different levels of congestion, the proposed eco-VSL controller is faster to decongest the network, resulting in an improvement of the environmental sustainability and the traffic performance both in the controlled network, and at its boundary roads.

A new fast nonlinear model predictive control of parallel manipulators: Design and experiments

High-speed parallel manipulators are characterized by fast sampling rates and challenges owing to the presence of constraints, high nonlinearities, uncertainties, and fast dynamics. The development of a reliable nonlinear model predictive control (NMPC) approach for this type of robotic systems is challenging because of the complex dynamics that involves high computational burden. To address this control problem, this paper proposes a new fast NMPC strategy applied to high-speed parallel robots. Based on (i) a parameterization technique, (ii) a fast gradient solver, (iii) a proportional integral derivative (PID) control term, (iv) a nonlinear dynamic model, and (v) an artificial neural network (ANN) model, two fast NMPC frameworks were developed to reduce the computational cost of the classical NMPC and address online implementation. In this study, we focus on improving the performance of the standard predictive control strategy outside of the range of its classical applicability by developing a fast NMPC controller for high-speed parallel kinematic manipulators (PKMs). Numerical simulations and real-time experimental results were presented and discussed to validate the relevance of the proposed controllers. Experiments were conducted on a four-degree-of-freedom (4-DOF) PKM called VELOCE developed in our laboratory. The results show that the proposed solution outperforms the original scheme in terms of real-time tracking performance.