Robust Model Predictive Control Research Articles

Convex distributed robust model predictive control for collision and obstacle avoidance

AbstractThe article proposes a convex distributed robust model predictive control algorithm for collision avoidance in multi‐agent systems with additive disturbances, which utilizes the concept of tube model predictive control to address the disturbances. To tackle the coupled collision avoidance constraints, each agent integrates assumed nominal position and input trajectories from its neighbors, rather than relying on actual ones. Compatibility constraints are then designed using the normal vector of the constructed separating hyperplanes for collision avoidance and the residual collision avoidance margin of the optimal solutions at the last time step to restrict deviations between assumed and actual trajectories and ensure consistency among the agents. The nonconvex collision and obstacle avoidance constraints are convexified using the concept of safe sets, transforming them into time‐varying closed polyhedral constraints while accounting for the impact of disturbances. Particularly, the residual collision avoidance margin is incorporated into the construction of safe sets for the satisfaction of coupled collision avoidance constraints. Consequently, the original collision avoidance optimal control problems can be efficiently and simultaneously solved for all agents using standard quadratic programming techniques. Under the design of local terminal constraint sets for each agent, the proposed algorithm ensures a rigorous analysis of robust constraint satisfaction for collision avoidance constraints, as well as an assessment of recursive feasibility and closed‐loop stability. The effectiveness of the algorithm is demonstrated through an illustrative example, and simulation results validate its ability to successfully achieve collision and obstacle avoidance even in the presence of disturbances.

Bi-level path tracking control of tractor semi-trailers by coordinated active front steering and differential braking

In recent years, autonomous tractor semi-trailers have been considered a promising solution for transportation on highways, ports, and large logistics centers to improve safety and efficiency. However, due to the complicated dynamics introduced by articulation structure, there are still challenges in achieving high-precision path tracking and stability control for tractor semi-trailers, especially in critical scenarios. In this work, a bi-level path tracking control scheme for the autonomous tractor semi-trailer is proposed. At the higher level, a robust model predictive controller coordinating active front steering and differential braking is devised for addressing path tracking, stability control and robustness for an autonomous tractor semi-trailer. At the lower level, incorporating a logic switching mechanism, the designed optimal braking torque distribution module and the PID-based longitudinal control module prioritize the implementation of differential braking and target speed tracking. Simulation results demonstrate that the proposed control strategy offers remarkable path tracking performance in three designed testing scenarios.

Virtual unmodeled dynamic and data-driven nonlinear robust predictive control

This study presents a novel approach for controlling an industrial process that exhibits uncertainty and significant nonlinear features. The proposed method utilizes a virtual unmodeled dynamic and data-driven nonlinear robust predictive control strategy. The representation of a controlled object involves a composite state space model that combines both linear and high-order nonlinear elements. Moreover, a robust model predictive controller is developed using the linear component. In addition, the notion of one-step optimal feedforward is used in combination with a compensating controller to handle the high-order nonlinear factor specifically. Subsequently, a compensation controller with incremental characteristics is developed for a modified version of the high-order nonlinear term. Furthermore, the stability conditions of the closed-loop system are derived, and an analysis is conducted on the stability and convergence of the proposed approach. The TTS20 three-capacity water tank was utilized in both simulations and practical scenarios. The study demonstrated that the suggested approach successfully reduces system output variations and enhances overall performance in response to unpredictable changes in the process’s dynamic features.

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.

Optimal scheduling of integrated energy system considering renewable energy uncertainties based on distributionally robust adaptive MPC

The uncertainty of renewable energy makes the optimal scheduling of integrated energy systems (IES) challenging and complex. The paper suggests a novel two-stage optimized scheduling model based on distributionally robust adaptive model predictive control (DRAMPC), which effectively improves scheduling accuracy and efficiency while taking robustness and economy into account. In the day-ahead stage, the multi-objective distributionally robust optimization (MODRO) model is composed based on the imprecise dirichlet model (IDM), which incorporates robustness and operating cost metrics into the optimization objective to achieve synergistic optimization of robustness and economy. The adaptive step double-loop model predictive control (ASDL-MPC) utilizes the dual closed-loop feedback of renewable energy output prediction errors and operating cost prediction errors to adaptively adjust the rolling time step, correcting the day-ahead scheduling bias while improving scheduling efficiency. The model is resolved using the cross-entropy-radar scanning differential evolution (CE-RSDE) algorithm. The results show that the DRAMPC model can balance economy and robustness, improving the economy of IES by 2.27% while ensuring robustness. The ASDL-MPC intra-day rolling optimization further improves scheduling accuracy and also increases computational efficiency by 6.58%.

Robust Model Predictive Control for Systems Affected by Constant and Norm 2 Bounded Disturbance

Robust Model Predictive Control for Systems Affected by Constant and Norm 2 Bounded Disturbance

Receding optimal synthesis of robust consensus for multi-agent systems with limited communication

ABSTRACT A novel strategy based on the robust distributed model predictive control (DMPC) is proposed in this paper to address the consensus of multi-agent systems subjected to unknown-but-bounded disturbances with limited communication range. The proposed strategy utilises the formulation of the tube-based predictive control and has the ability to handle the explicit input constraints and achieve the bounded consensus with initial communication topology preserved under the disturbances. In this proposed strategy, a novel constraint is designed to guarantee the connectivity of the system under the disturbances, and the synthesis methods are proposed for the controller. Meanwhile, it is proved that the proposed algorithm in this paper is recursively feasible, the connectivity can always be preserved and the system can finally reach bounded consensus under the disturbances. A simulation example is provided to demonstrate the proposed robust DMPC-based strategy.

Robust learning control for autonomous vehicle with network delays and disturbances

This paper deals with a robust learning nonlinear model predictive control (RL-NMPC) scheme under time-varying delays and disturbances. It is well known that the in-vehicle network has considerable advantages over the traditional point-to-point communication. However, on the other hand, these technologies would also induce the probability of time-varying delays, which would be a hazard in the active safety of over-actuated autonomous vehicles (AVs). To enjoy the advantages and deal with in-vehicle network delays and external disturbances, a robust learning nonlinear model predictive control (RL-NMPC) scheme is proposed. First, the machine learning (Support Vector Machine called SVM) method is adopted to train delayed measurement signals and disturbances. Then, according to the predictions of the SVM and corrupted sensory signals, the Unscented Kalman filter (UKF) is applied to acquire accurate predictions of the vehicle motion states. Furthermore, the NMPC scheme is used to generate real-time control signals by solving an open-loop optimization problem. The main purpose of the addressed problem is to design a robust learning controller to ensure that the AVs can track the desirable path and run smoothly suffering network delays and disturbances. Finally, simulations with a full-vehicle model are carried out to show the effectiveness of our proposed control scheme.

Data-driven ensemble optimal compensation control for partially known delayed and persistently disturbed nonlinear systems

In almost all industrial processes, the development of an accurate mathematical model that comprehensively characterizes the regulated system poses a substantial obstacle. Diverse factors, such as unidentified system components and time-varying external disturbances, contribute to this phenomenon. This can result in a disparity between the model and the plant and thereby compromising the performance of the designed controller. In this study, a novel data-driven ensemble optimal compensation control framework is proposed for partially known nonlinear systems with state delays and structural disturbances. Initially, the estimated system model is leveraged to construct a robust fuzzy model predictive controller (RFMPC) based on the Lyapunov–Krasovskii functional (LKF), ensuring the input-to-state stability (ISS) of the plant. Then, a reinforcement learning (RL)-based compensator is assembled to gradually minimize the model-plant mismatch across the entire state space. To streamline the training process of the compensator and facilitate its stability, a dynamic network update scheme is devised, incorporating a moving average gradient calculation method and a learning rate tuning strategy. Furthermore, comparative discussions with some prevalent methods are demonstrated. With the established control framework, the performance of the RFMPC can be securely enhanced, and convergence is ensured within a narrow proximity to equilibrium, despite time-varying perturbation dynamics. By integrating this approach with deep learning (DL) methods, the efficacy of numerous industrial processes could be significantly improved. A numerical simulation and a discretized continuous-time stirring tank reactor (CSTR) example validate the effectiveness and benefits of the proposed control strategy.

Robust EMPC-Based Frequency-Adaptive Grid Voltage Sensorless Control for an LCL-Filtered Grid-Connected Inverter

A robust explicit model predictive control (EMPC)-based frequency-adaptive grid voltage sensorless control is developed for a grid-connected inverter (GCI) via a linear matrix inequality (LMI) approach under the model parametric uncertainties as well as distorted and imbalanced grid voltages. In order to ensure the quality of grid currents injected into the utility grid even when the system model parameters vary, the proposed control scheme is accomplished by an enhanced prediction model rather than the conventional prediction model obtained by fixed parameters. Furthermore, an LMI-based observer is integrated with the disturbance observer to improve the reference tracking performance and to reject disturbances. The proposed observer is employed for the grid frequency-adaptive control without the need for grid voltage sensors. The proposed current controller and observer employ the LMI scheme to maintain a stable and robust operation of the GCI. The discrete-time frequency response and pole-zero map analyses are utilized to examine the system performance including the stability and robustness against parametric uncertainties. Comprehensive simulation and experimental tests as well as theoretical analyses clearly validate the robustness of the proposed control scheme under various harsh test conditions with non-ideal and unexpected grid and system parametric uncertainties.

Robust Constrained Model Predictive Voltage Control Scheme and its Classification

In this study, a prospective power system is suggested (PPS), predictive current control (PCC), enhanced voltage control (EVC), model predictive control (MPC), induction motor (IM) circuit. Instead of monitoring the torque and speed as in conventional MP DTC, the stator voltage is directly regulated in the suggested PVC model thanks to the predictive control theory. A voltage source inverter's use of a model predictive control approach. For all potential voltage vectors produced by the inverter, this method forecasting value of the load using a discrete model of the system. "Voltage-source converter based high voltage direct current (VSC-HVDC)" connected offshore wind farms using a "model predictive control (MPC)" based Enhanced Voltage Control Strategy (EVCS) (OWFs). All wind farm generator (WTGs) and wind farm side VSCs are effectively synchronized in the proposed Midi controller EVCS to maintain voltages within a practical range and reduce system power loss. Review of induction motor defects, including mechanical and insulating issues. The summary of static current signature of machine failures. Numerous useful feature extraction techniques have been introduced for induction motor problem detection.

Superiority of model predictive control with robust and stable approach for sliding wheeled mobile systems in the presence of obstacles

AbstractIn this paper, we present two distinct linear Model Predictive Control (MPC) methods for controlling mobile robots in the presence of obstacles while considering the wheel slip. Predictability of the controller enables the robot to automatically choose an alternative path to avoid obstacles. However, environmental conditions and disturbances, including slip, may impact the system model. Therefore, to accurately represent the system, slip angle and slip ratio are factored into the modeling process. Then the kinematic model is linearized using the successive method to reduce computational cost. Next, both Stable MPC (SMPC) and Robust MPC have been designed and implemented on the linearized time‐variant model to control the robot. The superiority of the robust predictive control method over the stable method has been discussed in terms of safety and optimal performance considering wheel slip. Finally, based on experimental tests, it has been found that the robust predictive controller is more effective than stable control when the surface is slippery and there is an obstacle in front of the robot. However, in a case where the wheel slip is neglectable, SMPC can be a better choice in presence of obstacles due to the lower computational cost.

Linear Matrix Inequality-Based Robust Model Predictive Speed Control for a Permanent Magnetic Synchronous Motor with a Disturbance Observer

In this paper, a linear matrix inequality (LMI)-based robust model predictive speed control (RMPSC) with a disturbance observer (DOB) is proposed to guarantee stability and control performance against the parameter uncertainty and disturbance of a permanent magnetic synchronous motor (PMSM). All external torques applied to the PMSM are defined as disturbance, estimated by the DOB, and used to construct the RMPSC method. The proposed DOB and RMPSC are determined by a multiple LMI-based optimization approach. Furthermore, parameter uncertainty within a certain range, due to manufacturing errors or aging deterioration, is considered and a systematic tuning method is proposed to obtain the optimal gains. Finally, an offline optimization method is developed that ensures a low computational load to enable real-time processing. Simulation results demonstrate the effectiveness and validity of the proposed control method.

An anti-disturbance lane-changing trajectory tracking control method combining extended Kalman filter and robust tube-based model predictive control

This paper proposes a trajectory tracking control method combining extended Kalman filter (EKF) and robust tube-based model predictive control (RTMPC) methods to improve the anti-disturbance capability during lane-changing maneuver of automated vehicles. A time-based quintic polynomial function is introduced for the implementation of trajectory planning to obtain the desired reference trajectory. The planned trajectory is input to the nominal system-oriented model predictive controller (MPC) in RTMPC for optimization to obtain the optimal control of the nominal system. The EKF collects the state measurements of the current instant and the optimal state estimates of the previous instant, and performs filtering to obtain the optimal state estimates of the current instant. The optimal estimate of the current state and the current state of the nominal system are input into the auxiliary control law of RTMPC to obtain the control of the actual system. Comparative numerical simulation experiments are conducted to analyze robustness and sensitivity of the proposed method. The results show that the control method combining EKF and RTMPC can optimize the trajectory tracking performance of the vehicle system, especially in the lateral displacement and the yaw-rate control. When the amplitude of measurement noise reaches the maximum, the optimization effect of lateral control is most significant in experiments. And the optimization effect in the control of lateral displacement and yaw angle continues to enhance with the increase of measurement disturbance. Therefore, this study can provide a reference for the anti-interference lane change trajectory tracking strategy of automated vehicles in the future.

Robust H∞ observer-based model predictive controller for uncertain linear discrete-time systems due to external disturbances

This article investigates an observer-based robust model predictive control (RMPC) design to control the uncertain discrete-time linear systems with disturbances. To make a more practical scheme, it is supposed that the uncertain system has been faced with unknown disturbance and input constraints. The proposed RMPC approach is based on a state feedback control design that ensures the [Formula: see text] performance criterion to attenuate disturbance affections. Furthermore, in view of practical application, the control law is constructed based on the estimated states obtained from the Luenberger observer. Based on Lyapunov’s theory, the input to state practically stability (ISPS) of the closed-loop system is ensured. Appropriate conditions for the ISPS of the closed-loop system and the estimation error are obtained in terms of online linear matrix inequalities (LMIs) which lead to obtaining the time-varying gain matrices of both controller and observer. Finally, to validate the obtained results, the proposed approach is applied to a numerical example and it is compared with the existing control scheme and the superiority is proved.

Robust Learning-Based Model Predictive Control for Intelligent Vehicles With Unknown Dynamics and Unbounded Disturbances

Robust Learning-Based Model Predictive Control for Intelligent Vehicles With Unknown Dynamics and Unbounded Disturbances

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.

Robust model predictive control with polytopic model uncertainty through System Level Synthesis

We propose a robust model predictive control (MPC) method for discrete-time linear systems with polytopic model uncertainty and additive disturbances. Optimizing over linear time-varying (LTV) state feedback controllers has been successfully used for robust MPC when only additive disturbances are present. However, it is challenging to design LTV state feedback controllers in the face of model uncertainty whose effects are difficult to bound. To address this issue, we propose a novel approach to over-approximate the effects of both model uncertainty and additive disturbances by a filtered additive disturbance signal. Using the System Level Synthesis framework, we jointly search for robust LTV state feedback controllers and the bounds on the effects of uncertainty online, which allows us to reduce the conservatism and minimize an upper bound on the worst-case cost in robust MPC. We provide a comprehensive numerical comparison of our method and representative robust MPC methods from the literature. Numerical examples demonstrate that our proposed method can significantly reduce the conservatism over a wide range of uncertainty parameters with comparable computational effort as the baseline methods.

Self-filtering based on the fault ride-through technique using a robust model predictive control for wind turbine rotor current

This paper studies the possibility of connecting Wind Farms (WF) to the electric grid with the use of finite space model predictive command (FS-MPC) to manage wind farms to improve the quality of the current output from the doubly-fed induction generator (DFIG) with considering fault ride-through technique. This proposed system can generate active power and enhance the power factor. Furthermore, the reduction of harmonics resulting from the connection of non-linear loads to the electrical grid is achieved through the self-active filtering mechanism in DFIGs-WF, facilitated by the now algorithm proposed. FS-MPC technique has the ability to improve system characteristics and greatly reduce active power ripples. Therefore, MATLAB software is used to implement and verify the safety, performance, and effectiveness of this designed technique compared to the conventional strategy. The results obtained demonstrated the effectiveness of the proposed algorithm in handling the four operational modes (Maximum power point tracking, Delta, Fault, and Filtering). Additionally, the suggested technique exhibited flexibility, robustness, high accuracy, and fast dynamic response when compared to conventional strategies and some recently published scientific works. On the other hand, the THD value of the current was significantly reduced, obtaining at one test time the values 56.87% and 0.32% before and after filtering, respectively 27.50% and 0.26% at another time of testing, resulting in an estimated THD reduction percentage of 99.43% and 99.05%, respectively. These high percentages prove that the quality of the stream is excellent after applying the proposed strategy.

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.