Model Predictive Control Framework Research Articles

Optimization of Hybrid Energy Systems Based on MPC-LSTM-KAN: A Case Study of a High-Altitude Wind Energy Work Umbrella Control System

This paper presents an optimization method for hybrid energy systems based on Model Predictive Control (MPC), Long Short-Term Memory (LSTM) networks, and Kolmogorov–Arnold Networks (KANs). The proposed method is applied to a high-altitude wind energy work umbrella control system, where it aims to enhance the stability and efficiency of energy utilization. The work umbrella system integrates wind and solar energy sources, with energy stored in a battery and used to control the umbrella’s operations. The MPC framework is employed to optimize control actions by solving a finite-horizon optimization problem, ensuring the battery State of Charge (SOC) remains within an optimal range. The LSTM network provides accurate predictions of environmental conditions, including wind speed and solar irradiance, which are essential for MPC’s decision-making process. To address complex nonlinearities in the system, the KAN is utilized to model and approximate these dynamics, refining the LSTM predictions. The integration of these advanced control strategies enables the system to handle varying operational conditions and maintain optimal performance. The case study demonstrates the effectiveness of the MPC-LSTM-KAN approach, revealing improvements in the SOC stability, energy efficiency, and operational endurance of the high-altitude wind energy work umbrella system. The results indicate that this hybrid optimization method offers a robust solution for managing hybrid energy systems in dynamic environments.

A Fractional-Order Model Predictive Control Strategy with Takagi–Sugeno Fuzzy Optimization for Vehicle Active Suspension System

Aiming at the problem of system controller performance failure caused by improperly setting the value of each weighting coefficient of the model predictive control (MPC), a fractional-order MPC strategy with Takagi–Sugeno fuzzy optimization (T–SFO MPC) is proposed for a vehicle active suspension system. Firstly, the fractional-order model predictive control framework for active suspension systems is designed based on a 1/4 vehicle model. Then, we analyze the influence of different weighting coefficients on the suspension performance and introduce the Takagi–Sugeno fuzzy optimization theory to adaptively adjust the weighting coefficients of the fractional-order MPC controller. Finally, the system responses of the T–SFO MPC, traditional MPC, linear quadratic regulator (LQR), and passive suspension control are numerically analyzed under various road conditions. Simulation results show that suspension response with the T–SFO MPC is significantly improved compared with passive suspension control, traditional MPC control, and LQR control, and the weight coefficients of the T–SFO MPC can be adaptively adjusted according to the dynamic changes of suspension response. Compared with passive suspension, the root mean square (RMS) value of the vertical acceleration of the T–SFO MPC under various roads decreased by a maximum of 37.97%, and the RMS value of suspension dynamic deflection and tire dynamic load decreased by a maximum of 32.94% and 37.8%, respectively. These results validate that the proposed control method can achieve coordinated optimization of vehicle comfort and handling stability.

Gust load alleviation of a flexible flying wing with linear parameter-varying modeling and model predictive control

This paper presents a practical model predictive control (MPC) framework for gust load alleviation of a flexible flying wing. Both the controller solving and state estimation are based on a reduced-order model, which features a linear parameter-varying (LPV) form, avoiding online linearization and reducing the scale of the corresponding quadratic programming problem. An improved modeling and model reduction process is used to enhance modeling efficiency and ensure that the reduced-order model can accurately capture the rigid-flexible coupled characteristics of the flexible flying wing under arbitrary gusts. By reconstructing the output of the control-oriented model to include both rigid-body motion and flexible vibrations, the rigid-flexible coupled multi-objective control is established as an MPC problem for reference tracking. The online optimization is formulated in a sparse fashion and combined with an iterative algorithm based on predicted trajectories, describing the variation of model dynamics within the prediction horizon more accurately. With a time-varying Kalman estimator for state updating, the closed-loop simulations are performed for gust alleviation performance validation. Additionally, the real-time potential of the proposed MPC framework is demonstrated through Monte Carlo simulations.

Nonlinear model predictive control for maximum wind energy extraction of semi-submersible floating offshore wind turbine based on simplified dynamics model

The application of floating offshore wind turbines means better exploitation of offshore wind resources. However, the six-degree of freedom motion characteristics of floating platforms bring greater challenges to control system design. Based on the dynamic characteristics of semi-submersible floating offshore wind turbines, this paper establishes a simplified nonlinear dynamic model for control system design. On this basis, a complete framework for nonlinear model predictive control of maximum wind energy extraction for semi-submersible floating offshore wind turbines considering wind and wave disturbances is developed. Based on the previewed wind and wave, a dynamic optimization problem with both state and control constraints is constructed, considering maximum wind energy extraction and torque fluctuation. Then, an improved equilibrium optimizer is proposed to address the nonlinear non-convex dynamic optimization problems, which achieves a better trade-off between exploitation and exploration. Simulation results verify the superiority of the proposed nonlinear model predictive control framework via the improved equilibrium optimizer, and the influences of different control algorithms on the platform motion state, power coefficient, and equivalent wind speed are analyzed.

Data-driven system identification and model predictive control of pneumatic conveying using nonlinear dynamics analysis for optimised energy consumption

Pneumatic conveying systems provide secure transportation of particulate material and a dust-free environment. These systems face high energy consumption, material degradation, and pipeline blockages. This research presents an innovative solution by integrating nonlinear dynamics analysis of electrostatic sensor data, including chaos and recurrence quantification analysis, sparse identification of nonlinear dynamics with control (SINDYc) and model predictive control (MPC). The Lyapunov exponent, approximate entropy and recurrence rate of electrostatic sensor data reveal the chaotic nature of gas-solid flows. MPC framework was tailored for real-time optimisation of a pneumatic conveying system. SINDYc system models were developed using data collected from an open-loop control pneumatic conveying process to conduct MPC simulations and select an appropriate model for real-time control. This research illustrates the potential of integrating nonlinear dynamics analysis, SINDYc integrated and MPC for enhanced system performance, showcased a significant reduction in energy consumption without compromising the system's efficiency or reliability.

Contact-implicit Model Predictive Control: Controlling diverse quadruped motions without pre-planned contact modes or trajectories

This paper presents a contact-implicit model predictive control (MPC) framework for the real-time discovery of multi-contact motions, without predefined contact mode sequences or foothold positions. This approach utilizes the contact-implicit differential dynamic programming (DDP) framework, merging the hard contact model with a linear complementarity constraint. We propose the analytical gradient of the contact impulse based on relaxed complementarity constraints to further the exploration of a variety of contact modes. By leveraging a hard contact model-based simulation and computation of search direction through a smooth gradient, our methodology identifies dynamically feasible state trajectories, control inputs, and contact forces while simultaneously unveiling new contact mode sequences. However, the broadened scope of contact modes does not always ensure real-world applicability. Recognizing this, we implemented differentiable cost terms to guide foot trajectories and make gait patterns. Furthermore, to address the challenge of unstable initial roll-outs in an MPC setting, we employ the multiple shooting variant of DDP. The efficacy of the proposed framework is validated through simulations and real-world demonstrations using a 45 kg HOUND quadruped robot, performing various tasks in simulation and showcasing actual experiments involving a forward trot and a front-leg rearing motion.

Model predictive control for unprotected left-turn based on sequential convex programming

In autonomous driving, an unprotected left turn is a highly challenging scenario. It refers to the situation where there is no dedicated traffic signal controlling the left turns; instead, left-turning vehicles rely on the same traffic signal as the through traffic. This presents a significant challenge, as left-turning vehicles may encounter oncoming traffic with high speeds and pedestrians crossing against red lights. To address this issue, we propose a Model Predictive Control (MPC) framework to predict high-quality future trajectories. In particular, we have adopted the infinity norm to describe the obstacle avoidance for rectangular vehicles. The high degree of non-convexity due to coupling terms in our model makes its optimization challenging. Our way to solve it is to employ Sequential Convex Optimization (SCP) to approximate the original non-convex problem near certain initial solutions. Our method performs well in the comparison with the widely used sampling-based planning methods.

A robust data-driven model predictive thermal control for rack-based data center

Optimizing and controlling of air-cooled data centers cooling systems are essential for reducing energy consumption. However, traditional cooling system control strategies have been proven inadequate due to the thermodynamic processess complexity and the challenge for accuratly modeling the thermal behavior of data center (DC). Therefore, a data-driven control method whithout explicit modeling process is urgently needed. In this paper, a robust data-driven model predictive control (MPC) method for air-cooled rack-based DCs, based on Willems fundamental lemma, is proposed. The methodology is executed in three phases: Firstly, we show that the system is approximately linear time-invariant (LTI) by zonal model method and experiment. Secondly, we propose a data-driven MPC framework for air-cooled rack-based DC. Thirdly, considering the uncertainties caused by disturbances and the nonlinear dynamics, the data-driven MPC approach is tailored as a robust one. Finally, the proposed approach is verified by computational fluid dynamics simulation experiments. This approach ensures the rack-based DC cold aisle temperature to the reference temperature as well as within acceptable limits. The experiment shows that the steady-state error is guaranteed to be less than 2%, with a control accuracy increased by 2.4% compared with the regular MPC. Thus, this method provides an alternative solution for maintaining the reference temperature in air-cooled rack-based DCs by utilizing only input–output data.

Differential-algebraic equation-based model predictive control for trajectory tracking of spacecraft-mounted continuum manipulators

Spacecraft-mounted continuum manipulators (SMCMs) exhibit great potential for performing dexterous operations in unstructured environments due to their inherent compliance and dexterity. However, the dynamic model of the rigid-flexible coupling SMCM is highly nonlinear and typically formulated as a set of implicit differential-algebraic equations (DAEs), posing significant challenges for precise trajectory tracking control. This paper proposes a novel model predictive control (MPC) framework specifically designed for generic DAEs to achieve precise trajectory tracking of the SMCM under uncertain disturbances and input limitations. The DAE model of the SMCM is discretized into a set of nonlinear algebraic equations. By performing implicit differentiation of these equations with respect to the system state, the state transition matrix (STM) for the DAE model is derived. The optimal control action for the SMCM can be further determined based on the derived STM. Additionally, nonlinear complementary functions are introduced to address the issue of input limitations, allowing the problem of determining the optimal control sequence to be equivalently transformed into a set of nonlinear algebraic equations for solving. Numerical simulations demonstrate that the proposed approach can achieve precise trajectory tracking of the SMCM while strictly adhering to input limitations.

Bi-Layer Model Predictive Control strategy for techno-economic operation of grid-connected microgrids

Effective management of renewable energy sources (RESs) alongside energy storage systems is crucial for maintaining stability and enhancing the economic performance of a grid-connected microgrid (MG). To address shortcomings in existing energy management strategies, which often overlook essential elements such as voltage support, battery degradation management, and uncertainties in load demand and solar generation, this study proposes a Bi-Layer Strategy for optimizing the operation of Battery Energy Storage Systems (BESS) within grid-connected MGs. The proposed approach maximizes economic returns, minimizes battery degradation, and provides reactive power support to maintain voltage stability. The method consists of the Energy Management Layer (EML) and the Control Layer (CL). The EML adopts a Model Predictive Control (MPC) framework to optimize the BESS power output over a 24-h rolling horizon based on forecasted solar generation, load demand, and electricity prices. The CL translates the optimized hourly setpoints from the EML into real-time operational commands, ensuring that the BESS adapts to actual grid conditions and maintains stable operation. Simulations conducted on a test MG, comprising 150 households, 500 kW rooftop solar PV, and a 300 kWh Li-Ion BESS demonstrate the strategy’s effectiveness under both fixed-rate and Time-of-Use (ToU) pricing schemes. The strategy reduces costs, mitigates battery degradation, and enhances voltage stability by optimizing BESS operations. Compared to a similar method in the literature, it reduces battery degradation by 24%, leading to net savings of $10,000 AUD, while the compared strategy resulted in a $5000 AUD loss. Real-time validation using the OPAL-RT platform further confirms the strategy’s effectiveness in optimizing BESS operations under real-world conditions.

Dynamic Optimal Obstacle Avoidance Control of AUV Formation Based on MLoTFWA Algorithm

In addressing the optimal formation obstacle avoidance control problem for Autonomous Underwater Vehicles (AUVs) in environments with unknown and moving obstacles, this paper employs the Modified Fireworks Algorithm based on a Loser Elimination Mechanism (MLoTFWA) and constructs a Distributed Model Predictive Control (DMPC) framework to achieve obstacle avoidance for AUV formations. Initially, a prediction model is established, followed by feedback compensation to mitigate the effects of unknown perturbations. An appropriate fitness function is then formulated, and enhancements such as the loser elimination rule are introduced to optimize the fireworks algorithm. Additionally, the concept of an adaptive DMPC prediction window is proposed to conserve resources. The local and global stability of the DMPC formation control framework is theoretically proven. Simulations verify that the control system based on the DMPC framework ensures safe obstacle avoidance for the formation, maintains formation consistency, and achieves the shortest and smoothest path. The improved fireworks algorithm demonstrates superior performance compared with the original fireworks algorithm and other optimization algorithms. In testing, the improved fireworks algorithm exhibits better adaptability, higher average fitness, and best fitness, along with a significantly faster convergence speed. Compared with the ordinary fireworks algorithm, the convergence speed is reduced by 30%.

Automatic Overtaking Path Planning and Trajectory Tracking Control Based on Critical Safety Distance

The overtaking process for autonomous vehicles must prioritize both efficiency and safety, with safe distance being a crucial parameter. To address this, we propose an automatic overtaking path planning method based on minimal safe distance, ensuring both maneuvering efficiency and safety. This method combines the steady movement and comfort of the constant velocity offset model with the smoothness of the sine function model, creating a mixed-function model that is effective for planning lateral motion. For precise longitudinal motion planning, the overtaking process is divided into five stages, with each stage’s velocity and travel time calculated. To enhance the control system, the model predictive control (MPC) algorithm is applied, establishing a robust trajectory tracking control system for overtaking. Numerical simulation results demonstrate that the proposed overtaking path planning method can generate smooth and continuous paths. Under the MPC framework, the autonomous vehicle efficiently and safely performs automatic overtaking maneuvers, showcasing the method’s potential to improve the performance and reliability of autonomous driving systems.

Nonlinear scenario‐based model predictive control for quadrotors with bidirectional thrust

AbstractThe control of quadrotor vehicles under state and parameter uncertainty is a well studied problem that is vitally important to the deployment of these systems under real world conditions. In this article, we propose a linearization‐based extension to nonlinear systems of the existing scenario model predictive control (MPC) framework, which quantifies the impact of uncertainty on the vehicle dynamics through repeated sampling of the uncertainty space. Given the computational costs of such an approach, we also propose two simplifications of the scenario MPC algorithm that are significantly more tractable. In order to evaluate the performance of the algorithms, the specific problem of the control of a bidirectionally actuated quadrotor vehicle is considered. Simulations are carried out for each scenario MPC scheme as well as for a reference deterministic MPC scheme. When a sufficiently large sample count is considered, each of the scenario MPC algorithms achieves safer performance than the deterministic formulation without sacrificing any optimality. Additionally, the approximate solution techniques conclusively outperform the original nonlinear scenario MPC formulation for the same computational cost.

Autonomous Underwater Vehicle (AUV) Motion Design: Integrated Path Planning and Trajectory Tracking Based on Model Predictive Control (MPC)

This paper attempts to develop a unified model predictive control (MPC) method for integrated path planning and trajectory tracking of autonomous underwater vehicles (AUVs). To deal with the computational burden of online path planning, an event-triggered model predictive control (EMPC) method is introduced by using the environmental change as a triggering mechanism. A collision hazard function utilizing the changing rate of hazard as a triggering threshold is proposed to guarantee safety. We further give an illustration of how to calculate this threshold. Then, a Lyapunov-based model predictive control (LMPC) framework is developed for the AUV to solve the trajectory tracking problem. Leveraging a nonlinear integral sliding mode control strategy, we construct the contraction constraint within the formulated LMPC framework, thereby theoretically ensuring closed-loop stability. We derive the necessary and sufficient conditions for recursive feasibility, which are subsequently used to prove the closed-loop stability of the system. In the simulations, the proposed path planning and tracking control are verified separately and integrated and combined with static and dynamic obstacles.

Collaborative energy management of interconnected regional integrated energy systems considering spatio-temporal characteristics

Multi-regional integrated energy systems (MRIES), which encompass renewable distributed generation (RDG) and electric vehicles (EV) dispersed across multiple regions, are pivotal for promoting low-carbon energy supplies, offering both economic and environmental benefits. However, the complexity introduced by diverse energy conversions and spatiotemporal coupling in MRIES poses significant challenges for energy management. This paper introduces a novel low-carbon energy management framework (EMF) for multi-regional IES, based on spatiotemporal correlations and considering three-dimensional (3D) integrated demand-side response (IDR). The proposed framework employs a novel Cross-Gated Spatio-Temporal Graph Convolutional Network (CGSTG) to achieve high-precision joint power forecasting separately for the RDG and multi-type loads. In the day-ahead stage, 3D IDR involving flexible loads, e.g., EVs, is considered with multi-regional IES sharing electricity and heat. By engaging in IDR across the temporal (horizontal), spatial (depth), and energy conversion (vertical) dimensions, each IES can enhance its coordinated scheduling capability and operational economy. During the intra-day stage, rolling optimization is performed based on the model predictive control (MPC) framework, incorporating a ladder-type carbon trading mechanism (CTM). Comparative experiments demonstrate that the proposed method can effectively reduce operational costs and carbon emissions with significant improvement of coordinated scheduling capability, leading to economic and environmental benefits of MRIES.

An adaptive distributed architecture for multi-agent state estimation and control of complex process systems

A multi-agent integrated distributed moving horizon estimation (DMHE) and model predictive control (DMPC) framework is developed for complex process networks. This framework utilizes an adaptive spectral community detection-based decomposition approach for a weighted graph representation of the state space model of the system to identify the optimal communities for distributed estimation and control. As the operating conditions of the process network change, the system decomposition adjusts, and the estimation and control agents are reassigned accordingly. These adjustments enable optimizing the integrated DMHE and DMPC architecture, enhancing robustness and closed-loop system performance. The effectiveness of the proposed adaptive distributed multi-agent estimation and control framework is demonstrated through a benchmark benzene alkylation process under various operating conditions. Simulation results show that the proposed multi-agent approach enhances closed-loop performance and computational efficiency compared to traditional system decomposition methods using unweighted hierarchical community detection.

Robust Stochastic Model Predictive Control for Autonomous Vehicle Motion Planning

This work presents a Robust Stochastic Model Predictive Control (RSMPC) framework for real-time motion planning autonomous vehicles, addressing the complex multi-modal vehicle interactions. The proposed framework involves adding expert policy from observations to the dataset and applying the Data Aggregation (DAgger) method to filter unsafe demonstrations and resolve expert conflicts. A Dual-Stage Attention-based Recurrent Neural Network (DA-RNN) model is integrated to predict dual class variables from the dataset, producing a set containing constraints collision-avoidance predicted to be active. The RSMPC framework enhances formulation optimization by eliminating irrelevant collision avoidance constraints, resulting in faster control signals. The framework is applied iteratively, continuously updating observations and solving the RSMPC optimization formulation in real-time. Evaluation of the DA-RNN model achieved a recall value of 0.97 and a high accuracy rate of 98.1% in predicting dual interactions, with a minimal false negative rate of 0.026, highlighting its effectiveness in capturing interaction intricacies. Validated through simulations of interactive traffic intersections, the proposed framework demonstrably excels, showing high feasibility of 99.84% and a 15-fold increase in response speed compared to the baseline. This approach ensures autonomous vehicles navigate safely and efficiently in complex traffic scenarios, paving the way for more reliable and scalable autonomous driving solutions.

Safety-Preserving Lyapunov-Based Model Predictive Rendezvous Control for Heterogeneous Marine Vehicles Subject to External Disturbances.

This article investigates the cooperative rendezvous control problem for perturbed heterogeneous marine systems composed of an autonomous underwater vehicle (AUV) and an autonomous surface vehicle (ASV). A novel Lyapunov-based model predictive control (LMPC) framework is presented to accomplish safe and precise rendezvous under input limitations and external disturbances. First, by incorporating the prescribed performance control (PPC) technique into the LMPC framework, we transform the original ascending state of the AUV into a self-constrained state, which serves as the decision variable of the model predictive control (MPC) optimization problem. Then, PPC-aided auxiliary control laws based on disturbance observers (DOBs) are designed to establish a robust contractive constraint to provide stability margins. Combining the LMPC with the PPC technique makes the original state-constrained problem an equivalent state-constraint-free problem. By addressing the MPC problem for the equivalent unconstrained system, the proposed method preserves the rendezvous safety. With the robust contractive constraint, the proposed safety-preserving LMPC (SP-LMPC) controller can inherit robustness and stability from the robust auxiliary control laws. Furthermore, theoretical analyses are conducted to assess recursive feasibility and closed-loop stability. With comprehensive theoretical support, the proposed method provides a new framework to simultaneously address state constraints and disturbances for highly nonlinear marine systems. Finally, simulations and comparisons are conducted to demonstrate the effectiveness and advantages of the proposed algorithm.

Model predictive complex system control from observational and interventional data

Complex systems, characterized by intricate interactions among numerous entities, give rise to emergent behaviors whose data-driven modeling and control are of utmost significance, especially when there is abundant observational data but the intervention cost is high. Traditional methods rely on precise dynamical models or require extensive intervention data, often falling short in real-world applications. To bridge this gap, we consider a specific setting of the complex systems control problem: how to control complex systems through a few online interactions on some intervenable nodes when abundant observational data from natural evolution is available. We introduce a two-stage model predictive complex system control framework, comprising an offline pre-training phase that leverages rich observational data to capture spontaneous evolutionary dynamics and an online fine-tuning phase that uses a variant of model predictive control to implement intervention actions. To address the high-dimensional nature of the state-action space in complex systems, we propose a novel approach employing action-extended graph neural networks to model the Markov decision process of complex systems and design a hierarchical action space for learning intervention actions. This approach performs well in three complex system control environments: Boids, Kuramoto, and Susceptible-Infectious-Susceptible (SIS) metapopulation. It offers accelerated convergence, robust generalization, and reduced intervention costs compared to the baseline algorithm. This work provides valuable insights into controlling complex systems with high-dimensional state-action spaces and limited intervention data, presenting promising applications for real-world challenges.

Analytic optimal control for multi-satellite assembly using linearized twistor-based model

This paper presents Guidance and Control (G&C) systems for multi-satellite assembly in proximity operations. The systems utilize the twistor model, which is linearized through Taylor’s series. Decentralized control laws, designed using Linear Quadratic Regulator (LQR) and Model Predictive Control (MPC), are employed to track an energy-optimal trajectory generated using the Hamiltonian approach. Data exchange between satellites and their neighbors is represented using graph theory. The decentralized MPC framework is implemented using the CasADi package. To ensure collision avoidance between the satellites, a repulsive control law is designed, considering symmetric input saturation in the actuators. The proposed G&C systems are tested using a high-fidelity nonlinear satellite relative motion model that incorporates orbital perturbations. Numerical simulations are performed in a MATLAB® environment, and the results are visualized using STK®. Furthermore, a comparative study is conducted to evaluate tracking performance and fuel consumption between the two control methods. The results demonstrate that the use of an optimal trajectory reduces fuel consumption for both control algorithms.