Robust Model Predictive Control Scheme Research Articles

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‐tolerant MPC: 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.

Robust adaptive model predictive control with persistent excitation conditions

For constrained linear systems with bounded disturbances and parametric uncertainty, we propose a robust adaptive model predictive control strategy with online parameter estimation. Constraints enforcing persistently exciting closed loop control actions are introduced for a set-membership parameter identification scheme. The algorithm requires the online solution of a convex program, satisfies constraints robustly, and ensures recursive feasibility and input-to-state stability. Almost sure convergence to the actual system parameters is demonstrated under assumptions on stabilizability, reachability, and tight disturbance bounds.

Robust MPC for polytopic uncertain systems via a high-rate network with the round-robin scheduling.

This article is concerned with the robust model predictive control (RMPC) problem for polytopic uncertain systems under the round-robin (RR) scheduling in the high-rate communication channel. From a set of sensors to the controller, several sensors transmit the data to the remote controller via a shared high-rate communication network, data collision might happen if these sensors start transmissions at the same time. For the sake of preventing data collision in the high-rate communication channel, a communication scheduling known as RR is used to arrange the data transmission order, where only one node with token is allowed to send data at each transmission instant. In accordance with the token-dependent Lyapunov-like approach, the aim of the problem addressed is to design a set of controllers in the framework of RMPC such that the asymptotical stability of the closed-loop system is guaranteed. By taking the effect of the underlying RR scheduling in the high-rate communication channel into consideration, sufficient conditions are obtained by solving a terminal constraint set of an auxiliary optimization problem. In addition, an algorithm including both off-line and online parts is provided to find a sub-optimal solution. Finally, two simulation examples are used to demonstrate the usefulness and effectiveness of the proposed RMPC strategy.

Reconfiguration of flow-based networks with back-up components using robust economic MPC

This paper addresses the post-fault selection of an actuators configuration for flow-based networks with back-up components. The proposed reconfiguration methodology consists of an offline and an online phase. On the one hand, an offline analysis looks for the minimal configurations for which the economic cost of the (best) steady-state trajectory that can be achieved using a robust model predictive control (MPC) policy is admissible. On the other hand, at fault detection time, an online search for the best actuators configuration to cope with the transient induced by the fault is conducted in the superset of each minimal configuration calculated offline. With this strategy, the final new configuration is computed by sequentially solving a set of mixed-integer programs whose constraints are derived from single-layer robust MPC schemes coupled with local controllers designed for the a priori minimal configurations identified offline. A portion of a water transport network is used to show the performance the proposed solution.

Robust and Resilient Distributed MPC for Cyber-Physical Systems Against DoS Attacks

In this paper, considering the ubiquitously existing cyber attacks in cyber-physical systems (CPSs), we present a robust and resilient distributed model predictive control (MPC) strategy for CPSs with multi-agent architecture under denial-of-service (DoS) attacks to achieve the goal of cooperative regulation with all agents' states being regulated to their equilibrium. Each agent in the CPSs is subject to external disturbances, and the communication channels among agents might be affected by randomly occurring DoS attacks. To tackle these issues, firstly, a novel robustness constraint is designed to handle the uncertainties in the MPC algorithm. By adding this constraint, the state of the nominal system can be confined in a shrinking and tighter range compared to the classical MPC approach, thus resulting in enhanced robustness against uncertainties. Furthermore, a lengthened sequence transmission strategy is proposed to mitigate the effect of the lack of information in the communication channels induced by DoS attacks. At each time instant, the controller of each agent utilizes the predicted state information to compensate for the transmission block-out from one agent to another. Moreover, recursive feasibility for the control framework and the closed-loop stability for the overall system are guaranteed by theoretical analysis. Finally, simulation and comparison studies demonstrate the effectiveness of the proposed robust and resilient distributed MPC strategy.

Output based resilient model predictive control of Cyber–Physical Systems under cover attacks

In this article, a state estimate based robust model predictive control strategy is developed for networked cyberphysical systems under false data injections. The core of the proposed approach consists in elaborating an observed based general framework whose main feature relies on its adaptability to different classes of attacks. The main feature of the proposed scheme relies on the capability to mitigate undesired system behaviors due to external malicious actions. This is achieved by showing that an augmented state-estimate/estimation error set-membership conditions allow us to quickly detect data integrity anomalies and, as a consequence, to implement adequate counter-measures. In particular, set-theoretic model predictive arguments are combined with the perturbation analysis and sequential quadratic programming in order to reduce as much as possible the occurrence of refresh procedures on the communication network when resilient command actions are no longer available. As one of its main merits, these arguments allow to remove the constructive assumptions present in very recent competitors. In this respect, the framework is customized for covert attacks by specifying actuation and detection phases and proving feasibility and closed-loop stability properties. The core of the resulting solution exploits output feedback receding horizon and set-theoretic control ideas so that the resilient nature of the virtual control moves is formally put in light.

Corrigendum to ‘Research on robust model predictive control strategy of wind turbines to reduce wind power fluctuation’

Corrigendum to ‘Research on robust model predictive control strategy of wind turbines to reduce wind power fluctuation’

Robust Tube-Based Model Predictive Control for Wave Energy Converters

This paper proposes an efficient robust tube-based model predictive control (RTMPC) strategy for energy-maximization control of wave energy converters (WECs) subject to constraints due to safety considerations. Compared with the existing MPC strategies developed for the WEC control problem, the RTMPC method provides an effective approach to explicitly handle plant-model mismatches with guaranteed constraint satisfaction, contributing to improved energy capture efficiency. The fundamental idea is to integrate disturbance invariant sets into the MPC scheme for energy-maximization control to form a tube-based predictive controller, which enhances the robustness of MPC for a WEC without increasing online computational complexity. The resulting RTMPC controller can bound the WEC plant trajectories in a tube centered around a nominal WEC model trajectory, and uncertainties from un-modeled WEC dynamics and unmeasured disturbances can be mitigated by an error feedback portion. Numerical simulations demonstrate the effectiveness of the proposed control strategy.