Robust Model Predictive Control Scheme Research Articles

Robust Model Predictive Control for an Ion Beam Shepherd in a large-debris removal mission

The increasing accumulation of space debris poses significant risks to spacecraft, making the development of effective debris mitigation technologies necessary. This paper explores the Ion Beam Shepherd (IBS) method as a potential contactless solution for deorbiting large debris objects. The IBS system concept involves a spacecraft equipped with an ion thruster to direct a controlled ion beam at the debris, generating a small force that gradually lowers its orbit. A proposed configuration of the chaser’s actuator system integrates radial and out-of-plane cold-gas thrusters along with in-track ion thrusters to enhance control and safety while maintaining low mission costs. A robust Model Predictive Control (MPC) strategy is implemented, using the theory of MPC for Tracking to ensure accurate positioning and effective deorbiting. This theoretical approach addresses uncertainties and perturbations to robustly guarantee safe distances between the chaser and the debris. Additionally, a new ray-marching-based algorithm is introduced to estimate the force and torque exerted by the ion beam on the target, considered as a 6 degrees of freedom object, improving simulation accuracy and control performance assessment. A comprehensive simulation of the deorbit of a large debris object is performed, demonstrating the potential of the IBS technology for future large-debris removal missions. This research advances the conceptual framework and control techniques for the IBS technology, advancing towards its future implementation in space debris mitigation.

A novel learning-based robust model predictive control strategy and case study for application in optimal control of FCEVs

With the gradual implementation of carbon-neutral policies, fuel cell electric vehicles (FCEVs) have gained widespread recognition as a promising solution. Due to multi-source electromechanical coupling, the powertrain of FCEVs constitutes a complex nonlinear system, necessitating an advanced energy management strategy for effective control to enhance economic performance. In this study, a novel learning-based robust model predictive control (LRMPC) is proposed for a 4WD FCEV, integrating a high-confidence velocity estimation model and an accurate state observation model to enhance energy-saving potential, robustness, and real-time application performance under various driving conditions. To enhance robustness and adaptability, deep forest with superior feature fusion abilities is employed to generate future velocity reference datasets based on FCEV operating scenarios. To improve state observation accuracy and control effectiveness, a novel built-in state observation model based on machine learning algorithms is established, leveraging knowledge of nonlinear systems within the FCEV powertrain. Subsequently, to enhance the real-time applicability of LRMPC, an explicit control scheme for multidimensional mapping based on explicit data tables is utilized for accurate state transformation, incorporating input features such as vehicle states and component states. Simulation evaluations and hardware-in-the-loop tests demonstrate the improved economic performance and real-time application ability of LRMPC, showcasing its promising performance.

Resilient robust model predictive load frequency control for smart grids with air conditioning loads

AbstractThis paper investigates the robust model predictive load frequency control problem for smart grids with wind power under cyber attacks. To accommodate intermittent power generation, the demand response of the system is considered by involving the air conditioning loads in the frequency regulation. In addition, the system uncertainties produced by the air conditioning load users and wind turbines when replacing traditional generator sets are considered. By using the cone complementary linearization algorithm and the linear matrix inequality technique, a resilience robust model predictive control strategy with mixed performance indexes is proposed. Furthermore, a rigorous derivation of the recursive feasibility of robust model predictive control is given. Finally, the simulation results of the two‐area load frequency control scheme show that the proposed model predictive control strategy is capable of realizing the load frequency control of the multi‐area smart grid and is robust to the parameter uncertainties and frequency regulation of the system. The results also show that the proposed model predictive control strategy has some resistance to cyber attacks and external disturbances.

Tube-based MPC strategy for load frequency control of multi-area interconnected power system with HESS

With the rapid development of power generation technology and the increasing demand from power users, multi-area interconnected power systems have become a development trend. This article proposes a new robust tube-based model predictive control strategy (MPC) for multi-area interconnected power systems with hybrid energy storage systems (HESS), based on the application of HESS to optimize the performance of load frequency control in power systems. The proposed strategy is mainly based on a new robustness constraint, which effectively handles uncertain disturbances within interconnected power system by compressing the disturbance invariant set. This strategy effectively alleviates the problems caused by inconsistency in multi-area interconnection modes. In addition, a sufficient stability criterion is derived to ensure the robust stability of the system, even under uncertain disturbances. By modeling a four-area interconnected power system with HESS, the frequency fluctuations of different methods are compared and discussed in each area. Based on the constructed software-in-the-loop setup, the effectiveness and feasibility of the proposed strategy are verified by experiments.

A two-timescale neurodynamic approach to robust distributed model predictive control for nonlinear systems

In this paper, a robust distributed model predictive control strategy is proposed for nonlinear dynamical systems affected by bounded disturbances. Grounded on sequential quadratic programming, a two-timescale recurrent neural network paradigm is deployed for solving minimax optimization problems. Sufficient criteria for the two-timescale recurrent neural network are delineated, which specifically guarantee its stability and optimality. Under these conditions, it is demonstrated that the recurrent neural network converges to optimal solutions, thereby enhancing the robustness of the control strategy. The simulation results exhibit significantly enhanced convergence in comparison to the mono-timescale recurrent neural network.

A novel RMPC strategy for three-phase inverters operating in grid-connected and standalone modes

One of the main features of microgrids is the capability of operating in both grid-connected (GC) and standalone (SA) modes. This paper presents a novel dual mode robust model predictive control (RMPC) strategy for a three-phase inverter with an LCL filter in both GC and SA operating modes under the filter’s parameter uncertainty. At first, a disturbance observer gain is obtained by solving a linear matrix inequality (LMI), which is determined to preserve the stability of the algorithm. The designed disturbance observer takes into account the polytopic uncertainty of system parameters. A performance index with two weighting matrices is then defined and solved in an infinite horizon by turning it into an optimization problem under LMI constraints. The performance of the control strategy highly depends on the weighting matrices. Hence, an optimization algorithm is formulated to ascertain the best matrices values for both GC and SA operation modes. Given the nonlinearity issue, particle swarm optimization (PSO) is employed to derive the optimal weighting matrices offline. To evaluate the proposed control strategy’s effectiveness, simulations and experiments are performed under several scenarios in both GC and SA operating modes. The results reveal the proposed control strategy’s powerfulness compared to other techniques in the presence of grid voltage and load current disturbances for both inverter operating modes.

A novel robust MPC scheme established on LMI formulation for surge instability of uncertain compressor system with actuator constraint and piping acoustic

This paper presents a new control method for surge instability of the compressor system. Due to the importance of the active control approach in improving the efficiency of the compressor system, a new scheme based on the model predictive control (MPC) technique has been considered to control surge which gives the benefits of control signal optimization by considering the constraints on states and input. Because of designing a novel MPC by using of linear matrix inequality scheme, the optimization problem is solved in less time and with less complexity. The proposed method is able to consider the limitation of the close coupled valve actuator and also covers the uncertainty on the model. In addition, the developed model describes the nonlinear behaviour of the compressor system and handles the effects of the pipe on surge instability. Using Lyapunov theory, the stability of the closed-loop system under the proposed robust active controller is shown. The simulation results show the high pressure and high efficiency operation of the system under study in different operating conditions.

An integrated tube robust iterative learning model predictive control strategy based on dynamic partial least squares algorithm for batch processes

AbstractIn this paper, an integrated tube robust iterative learning model predictive control (Tube‐RILMPC) strategy based on the dynamic partial least squares (DyPLS) identified algorithm is proposed. The problems of large amount of online data calculation and input and output variable dimensions disaster in the original variable space are solved. This integrated Tube‐RILMPC strategy enhances the tracking performance and robustness of two‐dimensional (2D) control system. The output trajectories of system are located in the tube the nominal trajectory, which reduces the modelling error caused by the uncertain model. Based on the worst‐case performance index of ellipsoidal uncertainty and polytopic uncertainty, a robust iterative learning control (ILC) strategy is designed. Finally, the superiority of the proposed control algorithm is verified by comparative simulation.

Robust control of wind turbines to reduce wind power fluctuation

AbstractThe wind power generation system of a 5 MW horizontal axis wind turbine has a high wind energy conversion efficiency. The proportion of installed capacity in practical production applications is increasing year on year, so that the stability of its operation becomes a central factor in determining the productivity of the wind farm in question. This paper takes a 5 MW wind turbine as the research object and proposes a parameter‐adaptive robust model predictive control method to achieve self‐optimization of controller parameters through a Bayesian optimization approach. A robust model predictive control strategy, aiming to reduce the power fluctuation while maximizing the power output, is developed in this paper to enhance the dynamic economic performance under uncertain wind speed variation. A Bayesian algorithm is used in this paper to optimize the parameters of the controller. Moreover, wind speeds are simulated using TurbSim for different turbulence intensities of 5%, 10%, and 15% turbulence. Finally, the robust model predictive control toolbox in MATLAB is designed and simulated. The results show that the operational instability of the wind energy system is overcome. Meanwhile, the robustness of the wind energy system operation is improved compared to the traditional model predictive control approach.

Safe Motion Planning and Control Framework for Automated Vehicles with Zonotopic TRMPC

Model mismatches can cause multi-dimensional uncertainties for the receding horizon control strategies of automated vehicles (AVs). The uncertainties may lead to potentially hazardous behaviors when the AV tracks ideal trajectories that are individually optimized by the AV's planning layer. To address this issue, this study proposes a safe motion planning and control (SMPAC) framework for AVs. For the control layer, a dynamic model including multi-dimensional uncertainties is established. A zonotopic tube-based robust model predictive control scheme is proposed to constrain the uncertain system in a bounded minimum robust positive invariant set. A flexible tube with varying cross-sections is constructed to reduce the controller conservatism. For the planning layer, a concept of safety sets, representing the geometric boundaries of the ego vehicle and obstacles under uncertainties, is proposed. The safety sets provide the basis for the subsequent evaluation and ranking of the generated trajectories. An efficient collision avoidance algorithm decides the desired trajectory through the intersection detection of the safety sets between the ego vehicle and obstacles. A numerical simulation and hardware-in-the-loop experiment validate the effectiveness and real-time performance of the SMPAC. The result of two driving scenarios indicates that the SMPAC can guarantee the safety of automated driving under multi-dimensional uncertainties.

A Learning-and-Tube-Based Robust Model Predictive Control Strategy for Plug-In Hybrid Electric Vehicle

A Learning-and-Tube-Based Robust Model Predictive Control Strategy for Plug-In Hybrid Electric Vehicle

Robust model predictive control for continuous nonlinear systems with the quasi-infinite adaptive horizon algorithm

The control input derived from model predictive control (MPC) scheme depends on the receding horizon whose length needs to be determined. Design length is also a trade-off between computational complexity and optimization metrics. To this end, a framework for adaptive selection of the horizon length has been developed for discrete systems in previous works. In this paper, this framework is extended to continuous nonlinear systems. A new algorithm is presented to solve the problem of how to adaptively select the horizon length. Then, according to the traditional method and the robust MPC scheme based on tubes, the recursive feasibility and robustness of the algorithm (the adaptive horizon nonlinear model predictive control, called AH-NMPC) for quasi-infinite time domain adaptive horizontal continuous-time nonlinear systems are proved. Finally, the NMPC controller is used to perform path-tracking experiments on an autonomous vehicle to verify the good effects of the algorithm (AH-NMPC).

SVD-Based Robust Distributed MPC for Tracking Systems Coupled in Dynamics With Global Constraints.

This article presents a novel singular value decomposition (SVD)-based robust distributed model predictive control (SVD-RDMPC) strategy for linear systems with additive uncertainties. The system is globally constrained and consists of multiple interrelated subsystems with bounded disturbances, each of whom has local constraints on states and inputs. First, we integrate the steady-state target optimizer into the MPC problem through the offset cost function to formulate a modified single optimization problem for tracking changing targets from real-time optimization. Then, the concept of constraint tightening is utilized to enhance the robustness and ensure robust constraint satisfaction in the presence of interferences. On this basis, the SVD method is introduced to decompose the new optimization problem into several independent subsystems on the orthogonal projection space, and a distributed dual gradient algorithm with convergence proved is implemented to obtain the control of each nominal subsystem. The recursive feasibility is then ensured and the tracking ability of the strategy is analyzed. It is verified that for a target, the system can be steered to a neighborhood of the closest possible steady setpoint. At last, the effectiveness of the raised SVD-RDMPC strategy is established in two simulations on building temperature control and load frequency control.

Optimal oxygen excess ratio tracking of proton exchange membrane fuel cell with uncertainty based on robust model predictive control strategy

AbstractTo address the challenge of tracking the optimal oxygen excess ratio (OER) in the cell stack cathode of the proton exchange membrane fuel cell (PEMFC), which is subject to norm‐bounded parameter uncertainty and frequent external perturbations, this manuscript provides a novel robust model predictive control strategy with a state feedback control structure and hard constraints. We aim to minimize the tracking error of OER while maximizing the net power under varying operational conditions of the PEMFC. Initially, a control‐oriented model for the air supply system is built and its accuracy is validated by comparing it with experimental results. Next, we construct the discrete state‐space equations for optimal control and employ the linear matrix inequality (LMI) method to transform the problem of difficult min‐max optimization solutions into a convex optimization problem with LMI constraints. Finally, the effectiveness of the proposed control algorithm is validated through simulation. The results demonstrate the strong robustness and superiority of the proposed controller against uncertainties in plant parameters for robust OER trajectory tracking. It improves the transient performance through robust precision tracking applications, which will eventually accelerate PEMFC commercialization.

Constrained DNN-Based Robust Model Predictive Control Scheme with Adjustable Error Tube

This paper proposes a novel robust model predictive control (RMPC) scheme for constrained linear discrete-time systems with bounded disturbance. Firstly, the adjustable error tube set, which is affected by local error and error variety rate, is introduced to overcome uncertainties and disturbances. Secondly, the auxiliary control rate associated with the cost function is designed to minimize the discrepancy between the actual system and the nominal system. Finally, a constrained deep neural network (DNN) architecture with symmetry properties is developed to address the optimal control problem (OCP) within the constrained system while conducting a thorough convergence analysis. These innovations enable more flexible adjustments of state and control tube cross-sections and significantly improve optimization speed compared to the homothetic tube MPC. Moreover, the effectiveness and practicability of the proposed optimal control strategy are illustrated by two numerical simulations. In practical terms, for 2-D systems, this approach achieves a remarkable 726.23-fold improvement in optimization speed, and for 4-D problems, it demonstrates an even more impressive 7218.07-fold enhancement.

A robustly stabilizing fault‐tolerantMPC: A performance improvement‐based approach

AbstractIn terms of model predictive control (MPC) performance degradation caused by operational faults, in this article, a robust MPC strategy with active fault tolerance properties is proposed. The proposed strategy incorporates a fault supervision layer into the structure of conventional cost‐contracting formulation‐based robust MPC for the online update of the nominal controller model in the event of faults. The robust MPC is based on multiplant uncertainty, while the supervisory layer consists of a bank of unknown input observers and a decision‐making algorithm. Simulation results in a nonlinear polymerization reactor subject to process faults demonstrate that the proposed approach offers superior performance compared to the conventional strategy.

Robust model predictive control for constrained linear system based on a sliding mode disturbance observer

For perturbed continuous-time systems, this paper proposes a robust model predictive control (RMPC) strategy for the regulation problem, exploiting a sliding mode disturbance observer. The main advantage is that it effectively enables the RMPC to be designed based on a model with reduced uncertainties. The proposed sliding mode observer (SMO) is finite-time convergent allowing the estimation error of the additive disturbance to be explicitly bounded by a predictable and decreasing limit. Due to the compensation of the estimated disturbance, the uncertainty that the RMPC has to handle is reduced from the original disturbance to the estimation error of the disturbance. This ensures all the admissible state trajectories are limited within a shrinking neighborhood of the origin and the steady-state error is therefore reduced. Simulation results show the effectiveness of the proposed method.

Data-driven robust model predictive control for greenhouse temperature control and energy utilisation assessment

The greenhouse microclimate, especially temperature, is highly complex, and controlling it requires significant resources due to the greenhouses' inefficient design. The application of model predictive control is a promising strategy for temperature control and efficient greenhouse management. However, it does not account for the inaccuracies and uncertainties existing in the system, leading to sub-optimal temperatures. Therefore, this study proposes a comprehensive data-driven robust model predictive control framework for greenhouse temperature control and its energy utilisation assessment in the presence of uncertainties. First, an analytical model based on mass and energy balance and a data-driven model based on an artificial neural network is developed, and their prediction performance is compared. The artificial neural network demonstrates a higher prediction accuracy and is used as the system model in the proposed control framework. A robust model predictive control strategy, based on the minimax objective function and particle swarm optimisation algorithm, is developed to handle the uncertainties in the system. Results illustrate that in the presence of uncertainties, the robust model predictive control strategy outperforms the existing greenhouse climate management system and basic model predictive control with an RMSE of 0.32 °C and 0.60 °C for a two-day simulation period in winter and summer, respectively. Furthermore, the robust model predictive control strategy leads to an energy reduction of 9.67% and 23.61% in winter and summer. The proposed framework is flexible and general and can be applied to other greenhouses with different configurations and cultivated crops by fine-tuning it on the new data set.

Robust Stability Analysis of a Simple Data-Driven Model Predictive Control Approach

In this paper, we provide a theoretical analysis of closed-loop properties of a simple data-driven model predictive control (MPC) scheme. The formulation does not involve any terminal ingredients, thus allowing for a simple implementation without (potential) feasibility issues. The proposed approach relies on an implicit description of linear time-invariant systems based on behavioral systems theory, which only requires one input-output trajectory of an unknown system. For the nominal case with noise-free data, we prove that the data-driven MPC scheme ensures exponential stability for the closed loop if the prediction horizon is sufficiently long. Moreover, we analyze the robust data-driven MPC scheme for noisy output measurements for which we prove closed-loop practical exponential stability. The advantages of the presented approach are illustrated with a numerical example.

Tube‐based batch model predictive control for polystyrene polymerization reaction process

AbstractThis paper focuses on product quality control issue of polystyrene polymerization reaction process. A novel tube‐based batch model predictive control (BMPC) strategy based on a data‐driven model is presented, which is inspired by the tube‐based robust model predictive control (MPC) strategy. First, the dynamic behavior of the polystyrene polymerization reaction process is captured with high accuracy by establishing a just‐in‐time learning (JITL) model. Then, the built JITL model is regarded as the nominal system, and a BMPC is designed on the basis of JITL model to obtain the nominal trajectory, which is an integrated control system framework composed of iterative learning control (ILC) and MPC. Meanwhile, another auxiliary MPC (AMPC) is designed to minimize the deviation between the actual trajectory and the nominal trajectory, and the actual tracking errors are limited to the tube invariant set centered on the nominal errors to restrain the performance deterioration of the control system caused by the modeling errors. Finally, the effectiveness of the proposed tube‐based BMPC method is verified by simulating an industrial batch polystyrene polymerization reaction process. The results indicate that the presented control algorithm not only enhances the tracking performance of the system but also provides a more robust system stability than existing methods. This paper provides a new solution to improve the product quality of polystyrene polymerization reaction process.