Model Predictive Control Algorithm Research Articles

Motion planning of multiple unmanned vehicles using sequential convex programming‐based distributed model predictive control

AbstractThis article tackles the complex challenge of multi‐vehicle motion planning by presenting the novel Sequential Convex Programming‐based Distributed Model Predictive Control (SCP‐DMPC) algorithm. Existing methods often struggle with the nonconvex nature of optimization in multi‐vehicle motion planning, frequently compromising on computational efficiency. SCP‐DMPC innovatively combines the predictive control of DMPC with the optimization prowess of SCP to address these issues efficiently, while adhering to both physical and operational constraints. To ensure precise attainment of target poses, a three‐stage control strategy is introduced, with theoretical analysis on its recursive feasibility and asymptotic stability, enhancing the reliability of the algorithm. Moreover, a heuristic‐based deadlock resolution scheme is devised to prevent vehicle stalling, a common issue in cooperative motion. Validated through simulations in challenging scenarios, including symmetric position swapping and obstacle‐laden formation transition, SCP‐DMPC demonstrates superior adaptability, precision, and efficiency. These results underscore its potential for robust, real‐time unmanned vehicle applications, suggesting new directions for future research and development in the field.

Good Prophets Know When the End Is Near

We consider a class of online decision-making problems with exchangeable actions, where in each period a controller is presented an input type drawn from some stochastic arrival process. The controller must choose an action, and the final objective depends only on the aggregate type-action counts. Such a framework encapsulates many online stochastic variants of common optimization problems with knapsack, bin packing, and generalized assignment as canonical examples. In such settings, we study a natural model-predictive control algorithm. We introduce general conditions under which this algorithm obtains uniform additive loss (independent of the horizon) compared with an optimal solution with full knowledge of arrivals. Our condition builds on the recently introduced compensated coupling technique, providing a unified view of how uniform additive loss arises as a consequence of the geometry of the underlying decision-making problem. Our characterization allows us to derive uniform loss algorithms for several new settings, including the first such algorithm for online stochastic bin packing. It also lets us study the effect of other modeling assumptions, including choice of horizon, batched decisions, and limited computation. In particular, we show that our condition is fulfilled by the above-mentioned problems when the end of the time horizon is known sufficiently long before the end. In contrast, if at a late stage, there is still uncertainty about the end of the time horizon we show that such uniform loss guarantees are impossible to achieve. We use real and synthetic data to illustrate our findings. This paper was accepted by J. George Shanthikumar, data science. Funding: This work was supported by the Division of Mathematical Sciences [Grant 1839346]; the Division of Electrical, Communications and Cyber Systems [Grant 1847393]; and the Army Research Laboratory [Grant W911NF-17-1-0094]. The authors also gratefully acknowledge support from the NSF [Grants ECCS-1847393, CNS-195599, and DMS-1839346], AFOSR [Grant FA9550-23-1-0068], an ARL award [Grant W911NF-17-1-0094], and ARO MURI [Grant W911NF-19-1-0217]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.04307 .

MPC-TD3 Trajectory Tracking Control for Electrically Driven Unmanned Tracked Vehicles

To address the trajectory tracking issue of unmanned tracked vehicles, the majority of studies employ the Model Predictive Control (MPC). The MPC imposes high demands on model accuracy. Due to factors such as environmental interference, actuator constraints, and the nonlinearity of vehicles under high-speed conditions, dynamic and kinematic models fail to accurately delineate the motion process of tracked vehicles. Aiming at the problem of insufficient trajectory tracking precision of unmanned tracked vehicles, a trajectory tracking controller jointly controlled by the Twin Delayed Deep Deterministic policy gradient (TD3) algorithm and the MPC algorithm is developed. During offline training, the agent acquires the discrepancies between the model and the environment under various working conditions and optimizes its own network; during online reasoning, the agent adaptively compensates the output of the MPC based on the vehicle state. The experimental results indicate that, compared with the pure MPC algorithm, the MPC algorithm compensated based on the TD3 algorithm reduces the lateral errors by 41.67% and 22.55%, respectively, in circular and double-lane-change trajectory conditions.

A Novel Method for a Pursuit–Evasion Game Based on Fuzzy Q-Learning and Model-Predictive Control

This paper explores a pursuit–evasion game (PEG) based on quadrotors by combining fuzzy Q-learning (FQL) and model-predictive control (MPC) algorithms. Initially, the FQL algorithm is employed to perceive, make decisions, and predict the trajectory of the evader. Based on the position and velocity information of both players in the game, the pursuer quadrotor determines its action strategy using the FQL algorithm. Subsequently, a state feedback controller is designed using the MPC algorithm, with reference inputs derived from the FQL algorithm. Within each MPC cycle, the FQL algorithm dynamically provides reference inputs to the MPC, thereby enhancing its robust control and dynamic optimization for the quadrotor. Finally, simulation results verify the effectiveness of the proposed algorithm.

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.

Dual-time-scale zone economic model predictive control of micro gas turbine cogeneration systems

The utilization of decentralized micro gas turbine combined heat and power (MGT-CHP) units is considered as a prospective technique in power generation due to its high levels of fuel utilization rates and low emissions. However, the inherent strong coupling and complex timescale multiplicity make it challenging to realize optimal operation. To this end, this paper first establishes a precise mechanism model to attain a thorough understanding of the system properties. By conducting singular perturbation theory, the complex nonlinear system is decomposed into a fast power subsystem and a slow heat subsystem. Then, a dual-time-scale zone economic model predictive control (D-ZEMPC) algorithm, which is comprised of a fast EMPC and a slow EMPC, is applied to achieve dynamic synergy between heat and power supply by actively coordinating the two sub-controllers. Moreover, a zone tracking method is introduced for room temperature control, thereby yielding increased freedom in balancing the economic profits and thermal comfort. The simulation results in three scenarios along with the qualitative and quantitative discussions show that compared with the other two centralized EMPC algorithms, the proposed D-ZEMPC can significantly alleviate computational loads and reduce the simulation time by over 64.5 % while maintaining required thermal comfort with minimum fuel consumption.

Integrated urban wastewater system operation: Performance evaluation and sewer network's operation implications

ABSTRACT The paper deals with the operation of the Integrated Urban Wastewater System as composed of the Sewer Network and associated Wastewater Treatment Plant. The performance of the integrated system is defined in terms of appropriate, selected, performance indicators of both subsystems. Both subsystems are connected and interact by a piping system. It is shown how the performance of the Integrated Urban Wastewater System is affected by various Sewer Network control scenarios: (1) only the Sewer Network outlet valve opening is controlled, (2) all the Sewer Network valves are controlled by a Model Predictive Control algorithm developed for minimizing the environmental impact of the subsystem and modified by constraining it in terms of Sewer Network outlet valve opening. More specific, it is proven that the Sewer Network outlet valve opening has an important role in the performances of the integrated system, and that already existing Sewer Network control strategies can be altered in such a way that they will enhance these performances.

Optimal Fast-charging Strategy for Cylindrical Li-ion Cells

This paper presents an innovative approach to optimize the fast-charging strategy for cylindrical Li-ion NMC 3Ah cells, with a focus on enhancing both charging efficiency and thermal safety. Leveraging the power of Model Predictive Control (MPC), we introduce a cost function that approximates the thermal safety boundary of Li-ion batteries, revealing a relationship between temperature gradient and state of charge. Our proposed approach formulates the fast and safe charging problem as an optimal output regulator problem, incorporating thermal safety margin constraints. To solve the optimization problem, we develop an MPC algorithm. Our charge control structure incorporates an equivalent circuit model coupled with a thermal equation for battery state of charge and temperature estimation. Through numerical validation with real experimental data obtained from testing an NMC 3Ah cylindrical cell, we demonstrate that our approach respects the battery’s electrical and thermal constraints throughout the charging process.

A Novel Fuzzy Logic Switched MPC for Efficient Path Tracking of Articulated Steering Vehicles

This paper introduces a novel fuzzy logic switched model predictive control (MPC) algorithm for articulated steering vehicles, addressing significant path tracking challenges due to varying road conditions and vehicle speeds. Traditional single-model and parameter-based controllers struggle with tracking errors and computational inefficiencies under diverse operational conditions. Therefore, a kinematics-based MPC algorithm is first developed, showing strong real-time performance but encountering accuracy issues on low-adhesion surfaces and at high speeds. Then, a 4-DOF dynamics-based MPC algorithm is designed to enhance tracking accuracy and control stability. The proposed solution is a switched MPC strategy, integrating a fuzzy control system that dynamically switches between kinematics-based and dynamics-based MPC algorithms based on error, solution time, and heading angle indicators. Subsequently, simulation tests are conducted using SIMULINK and ADAMS to verify the performance of the proposed algorithm. The results confirm that this fuzzy-based MPC algorithm can effectively mitigate the drawbacks of single-model approaches, ensuring precise, stable, and efficient path tracking across diverse adhesion road conditions.

Research on anti-rollover control of three-axle rescue vehicle based on active suspension and differential braking

Abstract. Due to its intricate operational environment, substantial mass, and elevated center of mass, the three-axle emergency rescue vehicle is more prone to rollover. This study aims to enhance the operational stability and mitigate rollover risks by establishing a rollover dynamic model with 11 degrees of freedom. Using the coupling characteristics of vehicle dynamics and tire force, an anti-rollover control strategy of the three-axle vehicle based on the cooperative work of differential braking and active suspension is proposed. According to the vehicle motion characteristics, the active suspension controller is built by using a fuzzy PID algorithm, and the differential braking controller is built by using the improved adaptive model predictive control algorithm. The step and fishhook tests of differential braking, active suspension control and joint control are carried out respectively. The simulation results show that the joint control strategy can effectively reduce the rollover tendency of the vehicle, and further improve the anti-rollover ability of the vehicle compared with the single system control.

Trajectory Tracking of Unmanned Logistics Vehicle Based on Event-Triggered and Adaptive Optimization Parameters MPC

Unmanned logistics vehicle (ULV) realize the automation and intelligence of cargo transportation, which improves the efficiency, cost-effectiveness and safety of logistics and distribution, while the trajectory tracking control of ULV is the key technology to ensure their safe and efficient delivery of goods. In order to solve the trajectory tracking problem of ULV in the process of delivering goods, this paper proposes a model predictive control (MPC) method based on event-triggered and fuzzy adaptive optimization parameters. Firstly, the dynamics model of the ULV is established. Secondly, an event-triggered mechanism is introduced to establish ET-MPC, while a disturbance observer is designed considering the external disturbance and the controller calculation discarding the nonlinear term. Thirdly, the advantages of fuzzy control and MPC algorithms are integrated, and the four important parameters in the MPC controller are adaptively optimized by fuzzy control, and the improved MPC control strategy is designed. Finally, the CarSim-Matlab/Simulink co-simulation platform and the experimental vehicle platform are constructed to verify the effectiveness of the improved MPC trajectory tracking controller proposed in this paper. The results show that the improved MPC control strategy can reduce the computation time of the controller, and the total number of triggering times of the controller is reduced by 46.44% compared with the classical MPC, which reduces the computational complexity of the controller and improves the accuracy and smoothness of the trajectory tracking of the ULV.

Distributed power system coordination via parametric optimization and ADMM

In this paper we present an efficient model predictive control algorithm for distributed coordination of an electrical power system comprising many spatially distributed controllable units. The coordination problem is formulated using parametric solutions of local optimization problems corresponding to individual subsystems leading to favorable problem structure which can be split across all subsystems and nodes in the network. The structure of the obtained coordination problem is exploited to develop a very efficient solution algorithm based on an ADMM technique. The key features of the overall approach are: (i) private data of individual subsystems are protected, (ii) simple and efficient on-line computations, (iii) parallelization of computation across all subsystems and all nodes in the network. Efficiency of the proposed control strategy is demonstrated on a number of numerical case studies of varying size.

Extension of a low-tech Model Predictive Control (MPC) algorithm for grid-supportive heat pump operation

This paper presents the further development of a low-tech Model Predictive Control (MPC) for the grid-friendly operation of heat pumps. The developed algorithm is already available in the literature [1] and successfully implemented in multiple buildings. The overall goal is, to predictively optimize comfort parameters taking into account weather forecast data for 48 h. A simple mathematical building model and an optimization function are used to calculate the heating (or cooling) requirement and determine the optimum heating (cooling) output curve over time.Based on the initial results, the algorithm is extended to include an energy price forecast. This modification enables the simultaneous optimization of comfort and heat supply costs. This forecast-based cost & comfort function is designed for the use of heat pumps in buildings with thermally activated components (TAB). The extension enables the MPC to process day-ahead electricity prices or other price signals in addition to weather forecast data. This means that the operation of heat pumps can be shifted to periods that are beneficial to the grid.The algorithm is analysed and validated in a Matlab/Simulink building simulation for a heating period of one sample month. A case study with different price scenarios is the main part of this paper. Depending on the assumed price fluctuation, the simulation leads to cost savings between 6.65 % and 12.5 % for the observation period of one month. The simulation results thus show that heat generation can be shifted to times with lower electricity prices, which leads to a significant reduction in heating costs without any significant loss of comfort. In conclusion, the developed low-tech MPC enables grid-supportive operation of heat pumps.

Comparison of Model Predictive Control Algorithms Based on Different Reference Models

<div>Model predictive control (MPC) plays a crucial role in advancing intelligent vehicle technologies. Controllers designed based on various vehicle reference models, including kinematic and dynamic models (both linear and nonlinear), often demonstrate significant differences in control performance. This study contributes by comparing three different MPC control methods and proposing a comprehensive evaluation criterion that considers tracking accuracy, stability, and computational efficiency across various MPC designs. Joint simulations using CarSim and MATLAB/Simulink reveal distinct performance characteristics among the MPC variants. Specifically, kinematic MPC (KMPC) exhibits superior performance at low speeds, linear model predictive control (LMPC) performs best at moderate speeds, and nonlinear MPC (NMPC) achieves optimal performance at high speeds. These findings highlight the adaptive nature of MPC strategies to varying vehicle dynamics and operational conditions, emphasizing the importance of selecting the appropriate MPC design based on the speed regime for maximizing control effectiveness in intelligent vehicles.</div>

Disturbance observer‐based finite‐time control of a photovoltaic‐battery hybrid power system

AbstractHerein, the load power control of the stand‐alone photovoltaic‐battery hybrid power system (HPS) has been investigated. The underlying HPS consists of a boost DC‐DC converter, a non‐isolated bidirectional half‐bridge converter, a photovoltaic (PV) panel, and a battery pack. On the PV side, a disturbance observer‐based finite‐time terminal sliding mode control (FTSMC) is used to regulate the DC bus to the desired voltage, in the presence of irradiation variation and load changes. On the battery side, the load power control system is constructed, based on a model predictive control (MPC) algorithm, with constraints on state‐of‐charge (SOC) and maximum current value of the battery to improve the battery life cycle and high reliability of the system. To highlight the benefits of the closed‐loop system, the analytical proofs and numerical analysis are presented from a comparative viewpoint. The experimentally derived results, by implementation on TMS320F28335 digital signal processing (DSP), are also presented and discussed for practical justification.

Real-time regulation of detention ponds via feedback control: Balancing flood mitigation and water quality

Detention ponds can mitigate flooding and improve water quality by allowing the settlement of pollutants. Typically, they are operated with fully open orifices and weirs (i.e., passive control). Active controls can improve the performance of these systems: orifices can be retrofitted with controlled valves, and spillways can have controllable gates. The real-time optimal operation of its hydraulic devices can be achieved with techniques such as Model Predictive Control (MPC). A distributed quasi-2D hydrologic-hydrodynamic coupled with a reservoir flood routing model is developed and integrated with an MPC algorithm to estimate the operation of valves and movable gates in real-time. The control optimization problem is adapted to switch from a flood-related algorithm focusing on mitigating floods to a heuristic objective function that aims to increase the detention time when no inflow hydrographs are predicted. The case studies show the potential results of applying the methods developed in a catchment in Sao Paulo, Brazil. The performance of MPC compared to alternatives that do not change the operation over time with either fully or partially open valves and gates are tested. Comparisons with HEC-RAS 2D indicate volume and peak flow errors of approximately 1.4% and 0.91% for the watershed module. Simulating two consecutive 10-year storms shows that the MPC strategy can achieve peak flow reductions of 79%. In contrast, the passive scenario has nearly half of the performance (41%). A 1-year continuous simulation results show that the passive scenario with 25% of the valves opened can treat 12% more runoff compared to the developed MPC approach, with an average detention time of approximately 6 h. For the MPC approach, the average detention time is nearly 14 h, indicating that both control techniques can treat similar volumes; however, the proxy water quality for the MPC approach is enhanced due to the longer detention times achieved.

A PLC-Embedded Implementation of a Modified Takagi–Sugeno–Kang-Based MPC to Control a Pressure Swing Adsorption Process

The paper presents a case study that applies a model predictive control (MPC) approach in a Micro850 programmable logic controller (PLC) to a laboratory pressure swing adsorption (PSA) process used for separating gas mixtures of CO2 and CH4. PLC is an industrial hardware characterized by its robustness to hazardous environments and limited computational capacities, which poses computational challenges for MPC implementation. This paper’s main contribution is the application of the modified Takagi–Sugeno–Kang-based MPC (MTSK-MPC) algorithm to this PSA unit, which provides features to investigate and implement feasible MPC designs in PLCs. The investigation consists of a sensitivity analysis of how some design parameters influence the PLC memory and the MPC implementation and a comparative evaluation of the computational processing from different MPC algorithms and simulations. The comparison comprises software-in-the-loop simulations with three algorithms in the PC: an implicit MPC, an explicit MPC, and the MTSK-MPC. Additionally, it includes a hardware-in-the-loop simulation with the implemented MTSK-MPC in Micro850. The results show that the MPC algorithms achieve close performance, tracking setpoint changes and rejecting output disturbances, with the MTSK-MPC presenting the lower processing time among the MPCs in the PC. The study concludes that the implementation of MTSK-MPC in the Micro850 is feasible.

Trajectory-Tracking Control of Unmanned Vehicles Based on Adaptive Variable Parameter MPC

Aiming at the problems of the poor trajectory-tracking performance and low control accuracy of unmanned vehicles under complex working conditions, we first estimate the lateral force of tires using the square root cubature Kalman filter (SRCKF) in order to correct the lateral stiffness of the tires online, which reduces the model bias caused by constant lateral stiffness, and then adopt a Gaussian function-based adaptive time-domain model predictive control method to improve the trajectory-tracking control accuracy of unmanned vehicles under complex working conditions. Finally, the proposed control algorithm is validated via Carsim and MATLAB/Simulink joint simulation. The results show that compared with the classical model predictive control (MPC) algorithm, the proposed control algorithm reduces the average lateral tracking error by 73.07% and the peak beta and the peak yaw rate by 50.89% and 47.51%, respectively, so that the unmanned vehicle is able to maintain good tracking performance and control accuracy.

Output feedback distributed economic model predictive control for parallel system in process networks

Abstract This paper proposes a distributed economic model predictive control algorithm for parallel systems which uses only output feedback. Such parallel systems are a fundamental system architecture frequently encountered in process networks where, in many cases, the state of the plant is not measurable. Economic performance is a key consideration in the operation of such industrial plants and it is of interest to develop theoretically rigorous approaches to tackle what is a practically very relevant scenario. The competitive couplings and competitive constraints inherent in parallel systems are explicitly addressed in the proposed controller design framework. Three measures are considered for optimization of such parallel systems including an economic stage cost function, energy efficiency and tracking accuracy. An economic cost function is optimized by the resulting distributed controller which can realize global control performance while also reducing the computational time for large-scale parallel systems. Stability of the system is formally proved using the principles of dissipativity. Finally, the effectiveness of the proposed theoretical approach is verified by both numerical simulation and experimentation to demonstrate practical relevance.