Nonlinear Model Predictive Control Framework Research Articles

Enhanced Traffic Light Guidance for Safe and Energy-Efficient Driving: A Study on Multiple Traffic Light Advisor (MTLA) and 5G Integration

This paper presents Multiple Traffic Light Advisor (MTLA), a novel Green Light Optimal Speed Advisory (GLOSA) system that leverages 5G communication technology. GLOSA systems are emerging as a key component in intelligent transportation systems, thanks to the development of effective communication technologies. At its core, MTLA serves as a guidance system for drivers, providing real-time instructions to adjust vehicle speed to optimize the utilization of current and future states of traffic lights along their route.The work addresses several limitations in the current state-of-the-art approaches, including the use of an overly simplified velocity profile, the omission of potential grip and jerk in problem formulation, and the absence of a detailed description of the algorithm’s implementation aspects. Initially, we comprehensively present an optimization-free implementation of the overall control architecture based on an unconventional speed profile. Subsequently, MTLA is improved within a non-linear Model Predictive Control (MPC) framework which uses the latter nonoptimal solution as an initial guess and considers potential grip and jerk in the problem formulation. The developed systems are numerically tested and compared within a high-fidelity simulation environment using the IPG CarMaker simulator. The results demonstrate promising performance in terms of energy savings, with a significant reduction of 37% in energy usage, as well as improved overall comfort with respect to the case where no guidance is given to the driver. These findings suggest a high potential for future developments in this domain.

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.

A robust nonlinear tracking MPC using qLPV embedding and zonotopic uncertainty propagation

In this paper, we propose a novel Nonlinear Model Predictive Control (NMPC) framework for tracking for piece-wise constant reference signals. The main novelty is the use of quasi-Linear Parameter Varying (qLPV) embeddings in order to describe the nonlinear dynamics. Furthermore, these embeddings are exploited by an extrapolation mechanism, which provides the future behaviour of the scheduling parameters with bounded estimation error. Therefore, the resulting NMPC becomes computationally efficient (comparable to a Quadratic Programming algorithm), since, at each sampling period, the predictions are linear. Benefiting from artificial target variables, the method is also able to avoid feasibility losses due to large set-point variations. Robust constraint satisfaction, closed-loop stability, and recursive feasibility certificates are provided, thanks to uncertainty propagation zonotopes and parameter-dependent terminal ingredients. A benchmark example is used to illustrate the effectiveness of the method, which is compared to state-of-the-art techniques.

Multivariable robust tube-based nonlinear model predictive control of mammalian cell cultures

In this paper, the application of a robust nonlinear model predictive control (NMPC) framework to mammalian cell cultures is proposed, dealing with possible large kinetic parameter uncertainties. Industrial constraints formulated in view of good manufacturing practice and quality-by-design approach are also considered, namely the assurance that all state trajectories are contained within a corridor defined by lower and upper safety bounds. The latter are assimilated to the well-known tube-based paradigm which is used to formulate the corresponding robust NMPC problem. Both classical and tube-based NMPC performances are assessed in numerical simulations where specific key-species are regulated while dealing with an uncertain plant model. The capability of the tube-based method to reduce the impact of the parameter variations on the state trajectories and the violation of the constraints is highlighted, suggesting the transfer of the method on a real pharmaceutical process.

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

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

Perception-Aware Image-Based Visual Servoing of Aggressive Quadrotor UAVs

The maintenance of visual features within the sensor field of view poses a significant challenge for underactuated aerial vehicles such as quadrotors, especially during aggressive maneuvers. However, the existing image-based visual servo (IBVS) control methods rely on strict target visibility assumptions or impose excessive constraints on the quadrotor's agility to meet this requirement. Furthermore, the effectiveness of the visibility constraint defined in prior works remains unverified in aggressive flight tests. To address these issues, we present a robust IBVS scheme for quadrotors to perform aggressive maneuvers while ensuring target visibility. Based on the nonlinear model-predictive control framework, we propose a novel underactuation compensation scheme to eliminate the need for a virtual camera frame, which enables us to formulate the true target visibility constraint. We then introduce a quaternion-based representation of spherical visual features to handle the nonsmooth vector field problem on the 2-sphere and derive its corresponding image kinematics. We validate our method through three challenging visual servo tasks where agile maneuvers are desired: fast landing, aggressive long-distance flight, and dynamic object tracking. Extensive simulation and experiment show that our method consistently achieves a target-visible rate of 100% in all the image frames, even under a maximum pitch of 21.04 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> . The results validate the effectiveness of our visibility constraint under large robot rotations and underscore its importance in enabling robust and aggressive flights.

Nonlinear Model Predictive Control Framework for Cooperative Three-Agent Target Defense Game

Nonlinear Model Predictive Control Framework for Cooperative Three-Agent Target Defense Game

NMPC-based visual path following control with variable perception horizon

AbstractFor greater autonomy of visual control-based solutions, especially applied to mobile robots, it is necessary to consider the existence of unevenness in the navigation surface, an intrinsic characteristic of several real applications. In general, depth information is essential for navigating three-dimensional environments and for the consistent parameter calibration of the visual models. This work proposes a new solution, including depth information in the visual path-following (VPF) problem, which allows the variation of the perception horizon at runtime while forcing the coupling between optical and geometric quantities. A new NMPC (nonlinear model predictive control) framework considering the addition of a new input to an original solution for the constrained VPF-NMPC allows the maintenance of low computational complexity. Experimental results in an outdoor environment with a medium-sized commercial robot demonstrate the correctness of the proposal.

Nonlinear Hierarchical MPC With Application to Aircraft Fuel Thermal Management Systems

A nonlinear hierarchical model predictive control (MPC) framework is proposed and applied to maximize the thermal endurance of aircraft. Effectively controlling the fuel temperatures in a nonlinear multitimescale aircraft fuel thermal management system (FTMS) requires controllers capable of long-term planning and fast update rates. In this article, a two-level hierarchical MPC controller is formulated using successive linearization (SL) that directly accounts for the multitimescale and nonlinear system dynamics to achieve accurate predictive capabilities and computational efficiency. Detailed simulation results show that the proposed hierarchical structure can increase aircraft thermal endurance by at least 21% compared to a centralized approach while significantly reducing the computational cost. The results also show that SL provides a valuable framework for efficiently accounting for nonlinear system dynamics within both levels of the hierarchical MPC formulation.

BiConMP: A Nonlinear Model Predictive Control Framework for Whole Body Motion Planning

Online planning of whole-body motions for legged robots is challenging due to the inherent nonlinearity in the robot dynamics. In this work, we propose a nonlinear model predictive control (MPC) framework, the BiConMP which can generate whole body trajectories online by efficiently exploiting the structure of the robot dynamics. BiConMP is used to generate various cyclic gaits on a real quadruped robot and its performance is evaluated on different terrain, countering unforeseen pushes, and transitioning online between different gaits. Furthermore, the ability of BiConMP to generate nontrivial acyclic whole-body dynamic motions on the robot is presented. The same approach is also used to generate various dynamic motions in MPC on a humanoid robot (Talos) and another quadruped robot (AnYmal) in simulation. Finally, an extensive empirical analysis on the effects of planning horizon and frequency on the nonlinear MPC framework is reported and discussed.

Homing tracking control of autonomous underwater vehicle based on adaptive integral event-triggered nonlinear model predictive control

The homing problem of autonomous underwater vehicle with constraints and bounded disturbances is studied in this paper. More specifically, a nonlinear model predictive control (NMPC) framework based on adaptive integral event-triggered (AIET) mechanism is designed for AUV tracking mobile docking station (DS). Firstly, according to the characteristics of AUV homing, a guidance system based on mobile DS is designed, which can provide a feasible reference trajectory for the subsequent AUV tracking independent of the vehicle model. Then, in the framework of AIET-NMPC control, the designed tracking controller can reduce the computational cost while guaranteeing the control accuracy. The proposed AIET mechanism can dynamically adjust the trigger threshold according to the integral error between the real state and the optimal state of the system. In addition, by designing exponential robust constraints in the NMPC optimization problem, the system stability margin is increased. Finally, it strictly proves the Zeno free behavior, the feasibility of the algorithm, and the stability of the system. Simulation results demonstrate that the proposed control approach yields better effects in terms of tracking control performance and computational performance compared to other methods.

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.

NMPC-Based Cooperative Strategy to Lure Two Attackers Into Collision by Two Targets

This letter presents a cooperative target defense strategy using nonlinear model-predictive control (NMPC) framework for a two–target two–attacker (2T2A) problem. Each attacker needs to capture a designated target individually. The objective of the two targets is to cooperate such that they lure the two attackers into a collision. We assume that the targets do not have perfect knowledge of the attacker states, and hence they estimate the attacker states using EKF. The NMPC scheme computes closed-loop optimal control commands for the targets while satisfying state and control constraints. Theoretical analysis is carried out to determine escape regions that will lead to the targets’ survival or capture. Numerical simulations are carried out to evaluate the performance of the proposed NMPC-based strategy for different scenarios validating the theoretical results.

Sustainable building climate control with renewable energy sources using nonlinear model predictive control

Sustainable energy sources are promising solutions for reducing carbon footprint and environmental impacts within the building sectors. Reducing energy consumption while ensuring thermal comfort for occupants is now an essential task in building climate control. Two possible ways to cut down building energy consumption are implementing renewable and sustainable energy sources, such as solar energy and geothermal energy, and adopting the model predictive control method. In this study, we develop a novel nonlinear model predictive control (NMPC) framework for climate control of buildings with renewable energy systems to minimize electricity costs. A nonlinear dynamic model of the building climate and renewable energy systems, including temperature, humidity, thermal comfort, geothermal heat pump, and solar panels, is first constructed based on mass and energy balance equations. The nonlinear dynamic model is then integrated into the proposed NMPC framework, which iteratively solves a nonlinear programming problem to generate the optimal control inputs which minimize energy consumption and carbon footprints for sustainability. A simulation case study on controlling a building located on the Cornell University campus is conducted to demonstrate the capability of renewable energy sources to reduce building energy consumption using the proposed NMPC framework. The results show the NMPC framework could efficiently minimize total electricity cost and constraint violation for thermal comfort to 12.9% with no more than 0.2 of violation on predicted mean value index in different seasons. Implementing an electricity storage component could reduce the electricity cost by 19%. The results indicate better sustainability for the smart building using sustainable energy sources and the NMPC framework.

Constrained tracking control of stochastic multivariable nonlinear systems via Gaussian process predictions

To overcome the difficulty of propagating the stochastic uncertainties through a nonlinear model for successful online implementation of the stochastic nonlinear model predictive control (SNMPC) framework, this paper proposes the utilisation of Gaussian processes (GPs) in the context of SNMPC for the stochastic multivariable nonlinear systems to track a given trajectory in the presence of stochastic uncertainties and system constraints. Taking advantage of the GP regression which not only provides predictions, but also uncertainty quantification in the function estimation, the proposed GP-SNMPC architecture exploits the probability distribution of stochastic uncertainties and utilises the predictions provided by the GPs to formulate the model cost and constraint functions, which yields a tractable framework for handling nonlinear constrained control problems with Gaussian parametric uncertainties. By employing a cancellation strategy, the control law consists of two components, that is, tracking control law and disturbance rejection control law. Theoretical results regarding the performance bounds of the closed-loop system are derived. Numerical examples are provided to verify the effectiveness of the proposed GP-SNMPC scheme.

Distributed dynamic rendezvous control of the AUV-USV joint system with practical disturbance compensations using model predictive control

This paper addresses the distributed dynamic rendezvous control problem of the AUV-USV heterogeneous joint system in the presence of unknown external disturbances using nonlinear model predictive control. By utilizing the nonlinear model predictive control framework, the rendezvous problem can be solved without constructing explicit error dynamics of the heterogeneous system. The inputs and states constraints such as spatial and velocity constraints can also be considered simultaneously in an intuitive way. To facilitate distributed implementations, distributed optimization problems with incorporated moving suppression are then constructed to guarantee nominal stability. Considering unknown external disturbances, a practical disturbance compensating method is finally proposed, ensuring the satisfaction of state constraints. The nominal recursive feasibility and stability are proved in this paper. Compared with existing works, the proposed scheme improves the applicability and robustness against external disturbances for dynamic rendezvous between two heterogeneous robots. Simulations and comparisons are conducted to demonstrate the effectiveness and advantages of the proposed method.

Novel enhancement of energy management in fuel cell hybrid electric vehicle by an advanced dynamic model predictive control

In this paper, an Advanced Dynamic Model Predictive Control (AMPC) based on a Nonlinear Model Predictive Control (NMPC) framework with a multi-objective cost function driven by dynamic weights is proposed to improve the energy performance of fuel cell hybrid electric vehicles whilst prolonging their component lifetime. By the use of dynamic weights, the cost function is effectively formulated as the combination of fuel consumption, rate of change of fuel cell power, battery power, the fuel cell efficiency, state of charge of the battery, and their temperatures. In order to enhance the adaptability of the AMPC, a Fuzzy Cognitive Map (FCM) is then newly designed to regulate online the dynamic weights to adjust the importance of each cost component according to the conditions prevailing during driving. A comparative study between the proposed AMPC, a constant weight based NMPC and a conventional NMPC having cost function with fewer objectives has been carried out by means of simulation using a FCHEV model from the simulation tool ADVISOR to illustrate the efficacy of the proposed AMPC.

Intelligent control and energy optimization in controlled environment agriculture via nonlinear model predictive control of semi-closed greenhouse

Greenhouse climate is a highly complex system that contains nonlinearity and dependencies between each system state. This paper proposes a novel nonlinear model predictive control (NMPC) framework for greenhouse climate control to minimize the total control cost mainly coming from energy use. A nonlinear dynamic model of the greenhouse climate, including temperature, humidity, CO2 level, and light intensity, is first constructed based on developed mass balances and energy transport phenomena. Real-world greenhouse climate data and outdoor weather data are gathered to systematically identify the system parameters for the nonlinear greenhouse climate model. The nonlinear dynamic model is then integrated into the proposed NMPC framework which iteratively solves a nonlinear programming problem to obtain the optimal control inputs of fan airflow rate, pad cooling air velocity, heating pipe flow rate, CO2 injection rate, fogging rate, supplemental light intensity, and shade curtain coverage. The stability and feasibility issues of the proposed NMPC framework on a semi-closed greenhouse are explicitly discussed in this work. Case studies on controlling a greenhouse located in Cornell University campus are simulated to demonstrate the performance of the proposed NMPC framework. The results show the NMPC framework could efficiently minimize total control cost and constraint violation. Humidity, CO2 level, and light intensity can be controlled with nearly no violation on the predetermined constraints over different seasons and climate conditions. As for temperature, it is almost always maintained within the acceptable region in winter and spring. On extreme days of summer, there are some temperature violations due to the limited cooling capacity.

Constrained tracking control of stochastic multivariable nonlinear systems using unscented Kalman filter

To overcome the challenges, including propagation of the stochastic uncertainties through a nonlinear model and full determination of the states over the prediction horizon for successful online implementation of the stochastic nonlinear model predictive control (SNMPC) framework, this paper proposes the utilisation of unscented Kalman filter (UKF) in the context of SNMPC for the stochastic multivariable nonlinear systems to track a given trajectory in the presence of stochastic uncertainties and system constraints. Taking advantage of the UKF which estimates and propagates the entire conditional distribution of the states along the time horizon by taking into account errors due to external disturbances and measurement noises as well as errors introduced due to the imperfect knowledge of the states through the state estimation, the proposed UKF-SNMPC framework utilises the conditional mean and conditional covariance of the states to reformulate the model cost and constraint functions, which yields a tractable framework for handling nonlinear chance-constrained tracking control problems. By employing a cancellation strategy, the control law consists of two components, that is, a tracking control law is designed to follow the desired trajectory and an uncertainty compensation control law designed to accommodate the nonlinearities in the plant. The concept of ‘robust horizon’ is introduced as the terminal constraint to prevent the covariance from the explosion and guarantee the convergence of the UKF-SNMPC framework. Performance bounds of the closed-loop system are theoretically analysed. Comparative studies on numerical examples are carried out to verify the effectiveness of the proposed UKF-SNMPC scheme.

Approximate two‐loop robust nonlinear model predictive control with real‐time execution and closed‐loop guarantee

AbstractIn this article, a robust nonlinear model predictive control (NMPC) scheme with two control loops is considered and its real‐time execution is guaranteed for a predefined sampling time. Robustness of the NMPC scheme against bounded input uncertainty is achieved by assuming Lipschitz continuity of the inner‐loop dynamic function. The NMPC control law is approximated using piecewise affine linear functions over hyper‐rectangle regions generated by k‐d tree partitioning algorithm. Additionally, error bound on the approximation of the optimal solution function is obtained by assuming bounds on the subgradient of the optimal solution function. Consequently, the robust stability and recursive feasibility of the closed‐loop system for the proposed approximate NMPC framework are proven, and at the same time, real‐time execution of the proposed scheme for a predefined sampling time is guaranteed. Simulation results, on a nonlinear benchmark problem, are used to better illustrate the proposed approach and to compare it with some other methods.