MPC Methods Research Articles

Longitudinal robust dynamic programming control for driving robot vehicles with performance self-learning

To realise the accurate and stable longitudinal control of the vehicle manipulated by the driving robot (DRV) under different test conditions, a longitudinal robust dynamic programming (RDP) control method for the DRV based on performance self-learning is proposed. Firstly, the dynamics of the driving robot and the vehicle are analysed. Then, the adjoint sensitivity method is used for the DRV to train the neural ordinary differential equation (NODE). The performance of the vehicle under different pedal openings is learned. A RDP controller is designed to solve the nominal target acceleration. Moreover, the unscented Kalman filtering (UKF) method is used to estimate the uncertain external disturbance of the DRV. Furthermore, dynamic compensation is used for the driving robot to track the vehicle's speed. Finally, the stability of the controller is proved. Compared with MPC, LQR, and PID methods, test results show the effectiveness of the proposed method.

A recursive framework of vehicle trajectory planning at mixed‐traffic signalized intersections

AbstractThis study aims to introduce a new strategy for anticipating the behaviour of human‐driven vehicles (HDVs) and designing trajectories for connected and automated vehicles (CAVs) at signalized intersections under mixed traffic scenarios. To tackle the challenge of unreliable HDV trajectory predictions stemming from driving unpredictability, a recursive framework is developed. This framework integrates real‐time tracking data from both traffic detectors and CAVs, continuously updating HDV predictions. The proposed approach employs the updated predictions to formulate optimal control problems recursively to optimize or adjust CAV trajectories, enhancing travel and energy efficiency. Besides, the recomputing of CAV trajectories will only be conducted when the variation in predictions rises to a certain threshold, balancing efficiency and computing consumption, inspired and modified based on MPC methods. The application of the Pontryagin maximum principle aids in finding solutions efficiently by transforming necessary conditions into a system of equations and consolidating elementary unconstrained and constrained arcs. Numerical simulations were carried out to evaluate the performance of the proposed recursive framework, revealing its superiority over the one‐time approach, particularly in isolated intersections with high traffic demands. Additionally, the recursive framework exhibited more robust and effective enhancements throughout the road network.

MPC for the Indoor Climate Control and Energy Optimization of a Building-Integrated Rooftop Greenhouse Systems

In this work, we design a nonlinear model predictive control (NMPC) strategy to optimize energy management in integrated rooftop greenhouses and buildings, aimed at minimizing operational expenses and reducing climate irregularities. This integrated system is tailored to maintain ideal conditions for both plant growth and building occupancy, utilizing the building’s excess heat and air to lower energy consumption and CO2 emissions. The NMPC framework employs dynamic nonlinear models for temperature, humidity, and CO2, enhanced with real-time weather data, to improve control accuracy beyond traditional MPC methods. It manages various systems—including fans, pad cooling, shading devices, heating, ventilation, air conditioning, CO2 injection, and lighting—to precisely control environmental conditions. A case study from a rooftop greenhouse in Brooklyn, New York, demonstrates the NMPC’s efficacy, showing an average energy savings of 15.2%. These results highlight the significant potential of NMPC to advance urban agricultural systems and building management practices.

Enhanced Dual–Vector Model Predictive Control for PMSM Drives Using the Optimal Vector Selection Principle

The Dual–Vector model predictive control (DV–MPC) method can improve the steady–state control performance of motor drives compared to using the single–vector method in one switching cycle. However, this performance enhancement generally increases the computational burden due to the exponential increase in the number of vector selections, lowering the system’s dynamic response. Alternatively, limiting the vector combinations will sacrifice system steady–state performance. To address this issue, this paper proposes an enhanced DV–MPC method that can determine the optimal vector combinations along with their duration time within minimized calculation times. Compared to the existing DV–MPC methods, the proposed enhanced technique can achieve excellent steady–state performance while maintaining a low computational burden. These benefits have been demonstrated in the results from a 2.5k rpm permanent magnet synchronous motor drive.

Adaptive model predictive control of a heat pump-assisted solar water heating system

Full electrification of building energy systems makes that the electricity-driven heat pump and solar heat become the most promising heating sources for hot water production in the future. The heat pump assisted solar water heater will be a good solution to jointly use these two heating sources. The system has large potential in demand response because of large capacity thermal storage tank which requires reasonable optimal control. In this context, this paper presents an adaptive model predictive control (AMPC) to achieve demand response with adaptive boundary and linear time-varying heat pump efficiency. Using adaptive parameters, the controller improves the adaptability and achieves optimal control under various disturbance conditions. The results demonstrated the AMPC realize 20% cost saving and 12% energy saving compared with PID, which are 7% reduction in costs and a 3% decrease in energy consumption compared to conventional MPC methods. Furthermore, a detailed analysis research was conducted on the controller parameters and disturbances, considering equipment parameters, electricity pricing models, weather conditions, and load types. Notably, the MPC exhibited even greater performance improvements in scenarios involving real-time pricing, concentrated loads, and low heat pump capacity.

Research on the High-Speed Collision Avoidance Method of Distributed Drive Electric Vehicles

High-speed autonomous emergency collision avoidance for intelligent vehicles is a challenging task. Many existing studies have not considered the effect of the road adhesion coefficient in the vehicle high-speed collision avoidance planning layer. Additionally, in lateral control, the effect of strong coupling of vehicle motion on the system model is not considered. This effect increases the uncertainty in the collision avoidance process and correlates with driving safety. In this regard, this paper conducted relevant studies. First, a distributed drive electric vehicle (DDEV) with controlled longitudinal speed was selected as the research platform and derived the transformed square-root cubature Kalman filter (T-SCKF) algorithm with cubature point sampling rule transformation to estimate the road adhesion coefficient. Second, the road adhesion coefficient information was used to calibrate the following vehicle safety distance model and the lane change collision avoidance lateral acceleration information was used to determine the vehicle autonomous emergency collision avoidance trajectory and to optimize the planning decision of the vehicle collision avoidance process. Last, the DDEV was laterally controlled to complete the tracking of the high-speed emergency collision avoidance trajectory by the adaptive model predictive control (Adaptive MPC) method with real-time updating of the system model. The relevant validation shows that the T-SCKF algorithm proposed in this paper can effectively estimate the road adhesion coefficient. The tracking control of the high-speed collision avoidance trajectory by the adaptive MPC method has better tracking accuracy and stability than traditional MPC and linear quadratic regulator (LQR) methods.

Three-Dimensional Prescribed Performance Tracking Control of UUV via PMPC and RBFNN-FTTSMC

To address the search-and-docking problem in multi-stage prescribed performance switching (MPPS) scenarios, this paper presents a novel compound control method for three-dimensional (3D) underwater trajectory tracking control of unmanned underwater vehicles (UUVs) subjected to unknown disturbances. The proposed control framework can be divided into two parts: kinematics control and dynamics control. In the kinematics control loop, a novel parallel model predictive control (PMPC) law is proposed, which is composed of a soft-constrained model predictive controller (SMPC) and hard-constrained model predictive controller (HMPC), and utilizes a weight allocator to enable switching between soft and hard constraints based on task goals, thus achieving global optimal control in MPPS scenarios. In the dynamics control loop, a finite-time terminal sliding mode control (FTTSMC) method combining a finite-time radial basis function neural network adaptive disturbance observer (RBFNN-FTTSMC) is proposed to achieve disturbance estimation and fast convergence of velocity tracking errors. The simulation results demonstrate that the proposed PMPC-FTTSMC approach achieved an average improvement of 33% and 80% in the number of iterations compared with MPC with sliding mode control (MPC-SMC) and traditional MPC methods, respectively. Furthermore, the approach improved the speed of response by 35% and 44%, respectively, while accurately achieving disturbance observation and enhancing the system robustness.

NN-Based Parallel Model Predictive Control for a Quadrotor UAV

A novel neural network (NN)-based parallel model predictive control (PMPC) method is proposed to deal with the tracking problem of the quadrotor unmanned aerial vehicles (Q-UAVs) system in this article. It is well known that the dynamics of Q-UAVs are changeable while the system is operating in some specific environments. In this case, traditional NN-based MPC methods are not applicable because their model networks are pre-trained and kept constant throughout the process. To solve this problem, we propose the PMPC algorithm, which introduces parallel control structure and experience pool replay technology into the MPC method. In this algorithm, an NN-based artificial system runs in parallel with the UAV system to reconstruct its dynamics model. Furthermore, the experience replay technology is used to maintain the accuracy of the reconstructed model, so as to ensure the effectiveness of the model prediction algorithm. Furthermore, a convergence proof of the artificial system is also given in this paper. Finally, numerical results and analysis are given to demonstrate the effectiveness of the PMPC algorithm.

Modulated Model Predictive Control of Modular Multilevel Converters Operating in a Wide Frequency Range

The finite control set model predictive control (FCS-MPC), which considers corresponding instantaneous power in the cost function, becomes a promising solution that allows modular multilevel converters (MMCs) to operate in a wide frequency range due to its ability to balance the internal energy. However, FCS-MPC usually suffers from a heavy computational burden. The modulated MPC, which combines modulation techniques with MPC methods, is usually employed to overcome such a challenge. In this paper, we propose an exhaustive active-set method to implement the modulated MPC scheme enabling the MMC to operate over a wide frequency range. With the proposed method, the optimal solution can be obtained by enumerating all possible active sets rather than iterating, so the worst-case computational burden (or calculation time) can be determined. Finally, a comparative study of our proposed method with conventional modulated MPC methods and FCS-MPC has been conducted to demonstrate the effectiveness of the proposed method.

A Novel Continuous Control Set Model Predictive Control for LC-Filtered Three-Phase Four-Wire Three-Level Voltage-Source Inverter

In this article, a novel continuous control set model predictive control (CCS–MPC) is proposed for an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -filtered three-phase three-level four-wire voltage-source inverter (3P-4W-3L-VSI). The proposed MPC algorithm provides independent control of each phase of the 3P-4W-3L-VSI under various unbalanced load conditions, which shows superior performance under unbalanced loads. Furthermore, different from conventional MPC methods, the CCS–MPC achieves fixed switching frequency, hence simplifying the design of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> filters. In addition, dc offsets are introduced to the proposed modulation to effectively balance the neutral-point voltage of the 3P-4W-3L-VSI. Experimental results are presented to verify the effectiveness of the proposed MPC algorithm.

Spatiotemporal learning-based stochastic MPC with applications in aero-engine control

To deal with the issue of model uncertainty, extensive stochastic MPC methods have been investigated, where the uncertainties are typically assumed to follow given statistical distributions. However, in practical scenarios, the statistical properties of model uncertainties may depend on certain hyperparameters varying both temporally and spatially. For instance, in the applications of aero-engine control, different types of uncertainties may occur under different operational conditions, such as flight altitudes and Mach numbers, which are dynamically changing. Traditionally, the stochastic MPC methods may not be able to handle these types of uncertainties directly. Therefore, we propose a spatiotemporal learning-based stochastic model predictive control algorithm to study the stochastic optimal control problem with dynamically changing uncertainties, by constructing spatiotemporal Gaussian processes (GPs) to approximate the uncertainties based on measurement data. Since the spatiotemporal GPs may be difficult to evaluate with long processing time series, we present a state–space representation of GPs to employ computationally efficient Kalman filtering. Then, we derive a computationally tractable control strategy by parameterizing the controller and reformulating the cost and chance constraints, and analyze the corresponding recursive feasibility and closed-loop stability. Finally, the proposed algorithm is applied to the compressor control of the aero-engine, and the comparisons with other MPC controllers are demonstrated to show the effectiveness of our methods.

Deep reinforcement learning for real-time economic energy management of microgrid system considering uncertainties

The electric power grid is changing from a traditional power system to a modern, smart, and integrated power system. Microgrids (MGs) play a vital role in combining distributed renewable energy resources (RESs) with traditional electric power systems. Intermittency, randomness, and volatility constitute the disadvantages of distributed RESs. MGs with high penetrations of renewable energy and random load demand cannot ignore these uncertainties, making it difficult to operate them effectively and economically. To realize the optimal scheduling of MGs, a real-time economic energy management strategy based on deep reinforcement learning (DRL) is proposed in this paper. Different from traditional model-based approaches, this strategy is learning based, and it has no requirements for an explicit model of uncertainty. Taking into account the uncertainties in RESs, load demand, and electricity prices, we formulate a Markov decision process for the real-time economic energy management problem of MGs. The objective is to minimize the daily operating cost of the system by scheduling controllable distributed generators and energy storage systems. In this paper, a deep deterministic policy gradient (DDPG) is introduced as a method for resolving the Markov decision process. The DDPG is a novel policy-based DRL approach with continuous state and action spaces. The DDPG is trained to learn the characteristics of uncertainties of the load, RES output, and electricity price using historical data from real power systems. The effectiveness of the proposed approach is validated through the designed simulation experiments. In the second experiment of our designed simulation, the proposed DRL method is compared to DQN, SAC, PPO, and MPC methods, and it is able to reduce the operating costs by 29.59%, 17.39%, 6.36%, and 9.55% on the June test set and 30.96%, 18.34%, 5.73%, and 10.16% on the November test set, respectively. The numerical results validate the practical value of the proposed DRL algorithm in addressing economic operation issues in MGs, as it demonstrates the algorithm’s ability to effectively leverage the energy storage system to reduce the operating costs across a range of scenarios.

Comparison and analysis of predictive control of induction motor without weighting factors

The research and promotion of electric drive systems for new energy transportation equipment is an important link in the realization of low-carbon transportation. Model predictive control is an effective new control strategy for electrical drive systems. Taking the three phase induction motor drive system as the research object, three kinds of model predictive torque control methods are reviewed and analyzed in depth, and a theoretical proof of Pareto optimality of MPC methods without weighting factors is established. Predictive torque control is a classical model predictive control method for induction motor drives. When using it, a trial-and-error method is usually used to set appropriate weighting factors for different control objectives, which strongly depends on the designer’s experience. By changing the structure of the cost function, the sequential model predictive control eliminates the weighting factors and improves the control effect of the stator current. The even-handed model predictive control utilizes the interaction error and considers all the control objectives at the same time, so that the optimization order of the control objectives changes with the working conditions, which further improves the control performance. Through theoretical analysis and experimental test, this paper illustrates the performance differences between traditional predictive torque control, sequential model predictive control and even-handed model predictive control.

Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator

This article proposes a new incremental model predictive control (IMPC) strategy, which allows for constrained control of a robot manipulator, while the resulting incremental model is derived without a concrete mathematical system model. First, to reduce dependence on the nominal model of robot manipulators, the continuous-time nonlinear system model is approximated by an incremental system using the time-delay estimation (TDE). Then, based on the incremental system, the tracking IMPC is designed in the framework of MPC without terminal ingredients. Thus, compared with existing MPC methods, the nominal mathematical model is not required. Moreover, we investigate reachable reference trajectories and confirm the local input-to-state stability (ISS) of IMPC, considering the bounded TDE error as the disturbance of the incremental system. For reachable reference trajectories, the local ISS of IMPC is analyzed using the continuity of the value function, and the cumulative error bound is not overconservative. Finally, several real-time experiments are conducted to verify the effectiveness of IMPC. Experimental results show that the system can achieve optimal control performance while guaranteeing that input and state constraints are not violated.

Enhancing Feedback Steering Controllers for Autonomous Vehicles With Deep Monte Carlo Tree Search

Steering control is a vital function for autonomous vehicles, whose performance largely determines the driving safety. The widely used feedback steering controllers degrade significantly when vehicles drive at high speeds. This is mainly because these controllers can not effectively exploit nonlinear vehicle dynamics and future road information. Hence, the steering actions generated by these controllers can not achieve accurate and stable path tracking performance. To overcome this limitation, we propose a deep learning based Monte Carlo Tree Search (DeepMCTS) method to enhance the feedback controllers. Due to the accuracy of the learning-based model in characterizing nonlinear vehicle dynamics and the lookahead search ability of MCTS, the control performance of the feedback controllers can be enhanced significantly. Different from MPC methods, which leverage vehicle dynamics and future road information via online optimization, our method relies on the efficient tree search process. Hence, our method can avoid heavy computational burden. Testing results validate the proposed method can achieve better tracking accuracy and stability in high speeds scenarios.

Comparative Study of DC/AC Inverter Control Techniques for Three Phase Grid Connected PV System

The goal of this project is to develop and analyze a three-phase grid-connected photovoltaic (PV) system with a 250KW power capacity with expandable property. The PI, Slide, and MPC methodologies are used to test three distinct inverter current control techniques. The dynamic performances of the three inverter control techniques are virtually comparable under grid connected working conditions, although the dynamic performances of the traditional PI control technique are slightly better and smoother than the other two inverter control techniques. The unity power factor criterion was reached by all techniques. The output power levels obtained using the sliding mode inverter control method are higher than those obtained using the PI and MPC methods. MPC's DC link voltage readings are also consistent and match the intended voltage levels.

Event-triggered model predictive control for dynamic energy management of electric vehicles in microgrids

The rapidly increasing charging demand of electric vehicles (EVs) represents a significant new load with myriad uncertainties. This paper proposes an event-triggered model predictive control (ET-MPC) method for dynamic energy management of EVs in microgrids (MGs). The study novelties lie in the forecasting models of EV status in an environment of MGs and the event-triggered mechanism for dynamic energy management of EVs. Firstly, the characteristics of EVs from different types of MGs are analysed by fitting the EV states with different probability distributions to improve the accuracy of forecasting of their status. Secondly, an ET-MPC method focusing on the energy management of EVs is first proposed to achieve coordination between the computational efficiency and optimisation impact of EVs. The event-triggered mechanism is achieved by monitoring the errors between the real EV states and their forecast values, which is only required to carry out optimisation when the forecast error of the EV states meet a set trigger level. Numerical simulations show that unlike time-triggered MPC methods—with long calculation times and fixed mechanisms—the ET-MPC method proposed achieves nearly the same energy management impact with a significantly shorter calculation overhead.

Energy Function Based Finite Control Set Predictive Control Strategy for Single-Phase Split Source Inverters

This article presents energy-function based model predictive control (EF-MPC) for single-phase split source inverters. Unlike conventional MPC methods, the proposed EF-MPC is designed by considering the stability of inverter. According to the Lyapunov's direct method, the stability of inverter can be assured if the derivative of energy-function is always negative. Motivated from this fact, the design of cost function in EF-MPC is based on the energy function which involves dc- and ac-side inductor current errors. It is shown that the coefficient used in the formulation of energy function is redundant which eliminates the weighting factor required in the multiobjective cost function. Elimination of the weighting factor not only simplifies the controller design in the practical implementation, but also removes the weighting factor tuning process needed in the conventional predictive methods. Another advantage of the proposed EF-MPC is that the amplitude of low-frequency component in the dc-side inductor current is suppressed. The steady-state and dynamic performances of the proposed EF-MPC are investigated experimentally under linear and nonlinear loads. In both cases, the dc-side variables are regulated at the desired values while the sinusoidal output voltage with low total harmonic distortion is obtained in the ac-side.

Finite Control Set–Model Predictive Control of H8 Inverter Considering Dead-Time Effect for PMSM Drive Systems With Reduced Conducted Common-Mode EMI and Current Distortions

To reduce the conducted common-mode (CM) electromagnetic interference (EMI) and current total harmonic distortion (THD) in permanent magnet synchronous motor drive systems, this article proposes a finite control set–model predictive control (FCS–MPC) method for an H8 inverter considering the dead-time (DT) effect. In a real system, the DT causes unexpected peak common-mode voltages (CMVs) and distortion of the inverter output voltage, which deteriorates both the CM EMI and current THD. The conventional double active voltage vector (VV) based MPC methods with an H6 inverter may not be a good solution because of the numerous CMV variations and the limit of the VV transitions. In contrast, the proposed FCS–MPC method allows all VV transitions possible without the peak CMVs by instantly operating the series-connected switch of the H8 inverter based on the previous VV, predicted current sector, and next optimal VV. Furthermore, the nonlinearity of the inverter output voltage due to the DT is compensated in a discrete-time model used for the current prediction, considering the calculation delay of the digital controller. Consequently, the current THD as well as the CM EMI can be improved. The simulation and experimental results are presented to verify the effectiveness of the proposed method.

Stochastically predictive co-optimization of the speed planning and powertrain controls for electric vehicles driving in random traffic environment safely and efficiently

With inevitable random disturbance in traffic scenarios, electric vehicles (EVs) may face the driving safety issue, while, if operated over cautiously, the frequent speed variation deteriorates the energy economy of the EV. This conflict provokes a desire to understand the energy consumption behavior of EVs in a stochastic driving environment and reveal the corresponding energy optimal control policy. For addressing these issues, this paper develops a chance constraint stochastic model predictive control (CC-MPC) method for simultaneously optimizing the speed planning and the powertrain energy management strategy, which cooperates with a bi-level prediction model for estimating the future driving environment. Validated by massive car-following cases in the urban traffic flow, the proposed CC-MPC increases the success rate (no constraint violation) to 87%, while the deterministic MPC methods only achieve a success rate of 27%. Although the proposed CC-MPC method generates a sensitive driving style to variations of the driving environment, the conflict between energy economy and driving safety has been successfully removed. Validations suggest that when safety probability is 0.9, the success rate is 84% with only 0.8% deterioration in energy economy compared with the energy consumption resulting from the MPC with perfect knowledge of the leading vehicle speed.