Iterative Learning Model Predictive Control Research Articles

A learning‐based hierarchical energy management control strategy for hybrid electric vehicles

AbstractIn this work, a novel energy management control framework is developed for hybrid electric vehicles (HEVs) driving in car‐following scenarios. In order to enhance the energy efficiency while maintaining the driving safety, a hierarchical control approach consisting of an upper level speed tracking control scheme and a lower level energy management control strategy is proposed. For the upper level tracking control system, an iterative learning model predictive control (ILMPC) scheme is developed to guarantee the tracking performance and the driving safety simultaneously. Additionally, a model predictive control (MPC) algorithm is adopted at the lower level to optimize the torque distribution in real‐time based on the driving cycles generated by the upper level control system. With the proposed hierarchical control framework, HEVs are able to improve the energy efficiency significantly by taking the advantages of the operational repeatability. The convergence of the proposed control strategy is analyzed rigorously, and its effectiveness is illustrated through numerical simulations.

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.

Data-Driven Iterative Learning Model Predictive Control With Self-Modified Prior Knowledge.

Iterative learning model predictive control (ILMPC) has become an excellent data-driven intelligent control strategy for digitized batch manufacturing, featured by the progressive improvement of tracking performance along trials, and the persistent rejection of stochastic disturbance along time. The point-to-point learning mechanism of existing ILMPC generally relies on identical operating conditions along trials to guarantee the integrity and accuracy of historical data. However, the variations of production requirements usually lead to trial-varying operating references and durations, resulting in incomplete and inaccurate historical information for the iterative learning of subsequent trials. To promote the adaptability and flexibility of ILMPCs with unconformable prior information, a data-driven self-modification scheme is originally embedded into ILMPC in this article to transfer the prior knowledge contained in the historical operating data into the form consistent with the condition of each current trial. The control actions are imitated along trials by an adaptive deep neural network (DNN), which is then utilized to generate reference control signals for iterative learning in each trial. For attenuating the influence of the considerable DNN approximation error in early trials with limited data accumulation, the 2-D optimization of ILMPC is performed under a tube control frame to ensure the time-domain bounded stability. Based on the intrinsic recursive feasibility and the guaranteed time-domain stability, the iteration-domain bounded convergence of the developed ILMPC system is theoretically validated. Simulations on the nonlinear injection molding process verify the superiority of the proposed method in adapting to significant changes in operating reference and duration.

A Novel Event-Triggered Iterative Learning Model Predictive Control for Linear Systems

A Novel Event-Triggered Iterative Learning Model Predictive Control for Linear Systems

Model Predictive Iterative Learning Control Design for Battery Optimal Electro-Thermal Management Under Daily-Variant State-of-Charge Patterns

Model Predictive Iterative Learning Control Design for Battery Optimal Electro-Thermal Management Under Daily-Variant State-of-Charge Patterns

A two-dimensional model predictive iterative learning control based on the set point learning strategy for batch processes

Although conventional two-dimensional model predictive iterative learning control (2D-MPILC) based on an extended non-minimum state space (ENMSS) model can avoid designing an observer, it only relies on feedback to passively deal with time delay. This passive treatment for time delay hinders the further improvement of control performance. To address this shortcoming, a two-dimensional model predictive iterative learning control strategy based on the set point learning (2D-SPL-MPILC) is proposed. Firstly, a set point learning strategy is developed to improve the ability to deal with time delay. Based on the error of the previous batch, the set point learning strategy perceives the system dynamics in advance, and then outputs this advance perception in the form of the predictive set point. Secondly, a novel ENMSS model is constructed on the basis of the predictive tracking error between the predictive set point and the actual output. Since the predictive tracking error integrates the predictive set point, this novel ENMSS model has certain predictive ability. Finally, based on this novel ENMSS model, a novel two-dimensional model predictive iterative learning control (2D-MPILC) method, which is called 2D-SPL-MPILC method, is designed. Because this controller contains the perception of future process dynamics, it can reduce the impact of time delay and improve the control performance. The case studies on the packing pressure control in injection molding process and batch reactors demonstrate the effectiveness of the presented 2D-SPL-MPILC strategy.

Event-Based Switching Iterative Learning Model Predictive Control for Batch Processes With Randomly Varying Trial Lengths.

Iterative learning model predictive control (ILMPC) has been recognized as an excellent batch process control strategy for progressively improving tracking performance along trials. However, as a typical learning-based control method, ILMPC generally requires the strict identity of trial lengths to implement 2-D receding horizon optimization. The randomly varying trial lengths extensively existing in practice can result in the insufficiency of learning prior information, and even the suspension of control update. Regarding this issue, this article embeds a novel prediction-based modification mechanism into ILMPC, to adjust the process data of each trial into the same length by compensating the data of absent running periods with the predictive sequences at the end point. Under this modification scheme, it is proved that the convergence of the classical ILMPC is guaranteed by an inequality condition relative with the probability distribution of trial lengths. Considering the practical batch process with complex nonlinearity, a 2-D neural-network predictive model with parameter adaptability along trials is established to generate highly matched compensation data for the prediction-based modification. To best utilize the real process information of multiple past trials while guaranteeing the learning priority of the latest trials, an event-based switching learning structure is proposed in ILMPC to determine different learning orders according to the probability event with respect to the trial length variation direction. The convergence of the nonlinear event-based switching ILMPC system is analyzed theoretically under two situations divided by the switching condition. The simulations on a numerical example and the injection molding process verify the superiority of the proposed control methods.

Iterative Learning Model Predictive Control With Fuzzy Neural Network for Nonlinear Systems

Due to the existence of strong nonlinearity and external disturbances, the controller design of complex nonlinear systems is a challenging problem. Therefore, it is necessary to design an effective robust predictive controller for this issue. In this paper, based on a fuzzy neural network, an iterative learning model predictive control (FNN-ILMPC) is designed for complex nonlinear systems. Firstly, a dynamic linearization technique (DIT) is used to establish a data-driven model, which only relies on input and output data. Since the established model contains an unknown disturbance term that may have an impact on the control performance, an FNN is used to evaluate the disturbance so that the uncertainty of the system is captured. Subsequently, based on the above data-driven model, an FNN-ILMPC strategy, considering the impact of external disturbances, is developed to eliminate the influence of disturbances. Then, it is proved that the designed controller can make both modeling error and tracking error decrease gradually and ensure the closed-loop system stability. Finally, experimental results verify the effectiveness and superiority of the designed controller.

High‐order iterative learning model predictive control for batch chemical processes

AbstractIn order to address two‐dimensional (2D) control issue for a class of batch chemical processes, we propose a novel high‐order iterative learning model predictive control (HILMPC) method in this paper. A set of local state‐space models are first constructed to represent the batch chemical processes by adopting the just‐in‐time learning (JITL) technique. Meanwhile, a pre‐clustered strategy is used to lessen the computational burden of the modelling process and improve the modelling efficiency. Then, a two‐stage 2D controller is designed to achieve integrated control by combining high‐order iterative learning control (HILC) on the batch domain with model predictive control (MPC) on the time domain. The resulting HILMPC controller can not only guarantee the convergence of the system on the batch domain, but also guarantee the closed‐loop stability of the system on the time domain. The convergence of the HILMPC method is ensured by rigorous analysis. Two examples are presented in the end to demonstrate that the developed method provides better control performance than its previous counterpart.

A novel two‐dimensional PID controller design using two‐dimensional model predictive iterative learning control optimization for batch processes

AbstractIt is known that the key indicators of batch processes are controlled by conventional proportional–integral–derivative (PID) strategies from the view of one‐dimensional (1D) framework. Under such conditions, the information among batches cannot be used sufficiently; meanwhile, the repetitive disturbances also cannot be handled well. In order to deal with such situations, a novel two‐dimensional PID controller optimized by two‐dimensional model predictive iterative learning control (2D‐PID‐MPILC) is proposed. The contributions of this paper can be summarized as follows. First, a novel two‐dimensional PID (2D‐PID) controller is developed by combining the advantages of a PID‐type iterative learning control (PIDILC) strategy and the conventional PID method. This novel 2D‐PID controller overcomes the aforementioned disadvantages and extends the conventional PID algorithm from one‐dimension to two‐dimensions. Second, the tuning guidelines of the presented 2D‐PID controller are obtained from the two‐dimensional model predictive control iterative control (2D‐MPILC) method. Thus, the proposed approach inherits the advantages of both PID control, PIDILC strategy, and 2D‐MPILC scheme. The superiority of the proposed method is verified by the case study on the injection modelling process.

Data-driven docking control of autonomous double-ended ferries based on iterative learning model predictive control

In large cities with harbors or rivers, ferry services have been a crucial part of public transport. Docking refers to the process of maneuvering a ferry to the designated mooring position by the quayside. To facilitate the transition towards increased autonomy in ferries, this paper proposes an iterative learning-based model predictive control (IL-MPC) strategy for the automatic docking of over-actuated double-ended ferries, in situations in which the hydrodynamic coefficients of a ferry are unknown. It uses the collected data from actual ferry docking operations or reliable simulations to build ferry states prediction model in a linear state-space form based on kernel regression, which reduces the model-solving complexity in MPC. Moreover, it improves its closed-loop control performance and modeling accuracy via an iterative learning scheme. The excitation control input signals have been optimized to create suitable initial data sets. Simulations are carried out considering three docking position types and results show that the open-loop prediction accuracy has been improved with the optimized excitation input signal and that closed-loop control performance has been enhanced with the increase of iterations.

Adaptive iterative extended state observer-based data-driven iterative learning model predictive control for semiconductor silicon single crystal batch process

Aiming at the problems of unstable batch control of key crystal quality parameters and susceptibility to batch-to-batch non-repetitive disturbances during repeated operation of single crystal furnaces, this paper proposes a data-driven iterative learning model predictive control method based on an adaptive iterative extended state observer (IESO) for designing melt temperature and crystal diameter learning controllers with disturbance suppression. By applying dynamic linearization techniques and model predictive control strategies along the iterative axis, an ILMPC scheme with disturbance compensation terms using only input and output data of the system is designed. Among them, adaptive IESO is used to estimate the disturbance compensation terms. Then, the theoretical analysis shows that the tracking error of the ILMPC scheme can converge to a bounded range as the number of iterations increases. The experimental results verify the effectiveness of the proposed control method, which not only ensures that the control system has learning ability, but also achieves stable and accurate control of crystal quality parameters.

A two-stage robust iterative learning model predictive control for batch processes

Iterative learning model predictive control (ILMPC) has been considered as potential control strategy for batch processes. ILMPC can converge to the desired reference trajectory with high precision along batches and ensure system stability within batches. However, as a model-based control method, the control performance of the ILMPC algorithm deteriorates when exists model parameter uncertainty. Therefore, guaranteeing system tracking performance in the case of model parameter uncertainty is a challenging task in the framework designing of ILMPC method. To this end, we develop a two-stage robust ILMPC strategy for batch processes, which integrates the robust iterative learning control (ILC) in the domain of batch-axis and robust model predictive control (MPC) in the domain of time-axis into one comprehensive control scheme. The integrated control law of the developed two-stage robust ILMPC algorithm is obtained by solving two convex optimization problems. As a result, the developed control method obtains faster convergence speed and better tracking performance in the case of model parameter uncertainty. Moreover, the convergence analysis of the system is presented. Finally, comparative simulations are provided to verify the superiority of the developed control algorithm.

Iterative learning model predictive control for multivariable nonlinear batch processes based on dynamic fuzzy PLS model

This paper proposes a latent variable nonlinear iterative learning model predictive control method (LV-NILMPC) based on the dynamic fuzzy partial least squares (DFPLS) model to achieve trajectory tracking and process disturbance suppression in multivariable nonlinear batch processes. The dynamic and nonlinear characteristics of the physical system are constructed by integrating the T-S fuzzy model into the regression framework of the dynamic partial least squares (PLS) inner model. The decoupling and dimensionality reduction characteristics of the DFPLS model automatically decompose a multivariable nonlinear system into multiple univariate subsystems operating independently in the latent variable space. Based on the DFPLS model, we design LV-NILMPC controllers corresponding to each latent variable subspace to track the projection of the reference trajectories. Compared with the previous control method, the method proposed in this paper has a faster convergence rate and smaller tracking error. The method is suitable for nonlinear, multivariable and strong coupling batch processes. Finally, the application of two cases shows that the method is effective.

Terminal constrained robust hybrid iterative learning model predictive control for complex time-delayed batch processes

This work mainly addresses terminal constrained robust hybrid iterative learning model predictive control against time delay and uncertainties in a class of complex batch processes with input and output constraints. In this work, an equivalently novel extended two-dimensional switched system is first constructed to represent the process model by introducing state difference, output error and new relaxation variable information. Then, a hybrid predictive updating controller is proposed and an optimal performance index function including terminal constraints is designed. Under the condition that the switching signal meets certain conditions, the solvable problem of model predictive control is realized by Lyapunov stability theory. Meanwhile, the design scheme of controller parameters is also given. In addition, the robust constraint set is adopted to overcome the disadvantage that the traditional asymptotic stability cannot converge to the origin when it involves disturbances, such that the system state converges to the constraint set and meets its expected value. Finally, the effectiveness of the proposed algorithm is verified by controlling the speed and pressure parameters of the injection molding process.

Tube-based iterative-learning-model predictive control for batch processes using pre-clustered just-in-time learning methodology

Iterative-learning-model predictive control (ILMPC) has been considered a potential control strategy for batch processes. ILMPC can converge to the desired reference trajectory with high precision along cycles and reject real-time disturbances within cycles. However, as a model-based control method, the control performance of the ILMPC algorithm deteriorates when it suffers the problem of model-plant mismatches. Therefore, simultaneously guaranteeing system convergence along the cycle-axis and robust stability on the time-axis is a challenging task in the framework designing of ILMPC control systems. To this end, we present a type of tube-based ILMPC strategy based on an empirical model for nonlinear batch processes. First, to describe the dynamic behavior of nonlinear batch processes as much as possible with the goal of low computational cost and high modeling accuracy, a pre-clustered just-in-time learning (JITL) model focused on operation data is developed. Then, an ancillary MPC controller is combined with the ILMPC algorithm to form a tube scheme to relieve the impact of model error. In addition, we construct an inverse model system (IMS) to systematically determine the first cycle control input trajectory of the proposed tube-based ILMPC algorithm. As a result, they simultaneously ensure the system convergence along the cycle-axis and robust stability on the time-axis. Still, they can improve convergence speed and tracking performance. Finally, comparative simulations demonstrate the superiority of the proposed control algorithm.

Robust iterative learning model predictive control for repetitive motion of maglev planar motor

This paper presents a robust iterative learning model predictive control (RILMPC) scheme for repetitive trajectory tracking of a magnetically levitated (maglev) planar motor. The motivation lies in the improvement of tracking performance and disturbance rejection ability for the maglev system. Relying on the past error in the repetitive motion, the model discrepancy is persistently compensated with iterations to improve the prediction accuracy. The cost function that serves as the upper bound of the tracking error is then derived from the past control trajectory based on the Lipschitz property of disturbances. In the proposed RILMPC scheme, a minimal robust positive invariant set is introduced into the MPC optimisation to cope with unmodeled dynamics and disturbances. Furthermore, it is theoretically shown that the perturbed closed-loop system is stable, and the proposed RILMPC scheme is recursively feasible with perfect tracking performance under some conditions. Finally, comparative experiments carried out on a maglev planar motor demonstrate that the proposed control strategy possesses satisfactory transient/steady-state tracking performance and robustness against disturbances.

PDE Formation and Iterative Docking Control of USVs for the Straight-Line-Shaped Mission

In this paper, an intelligent control scheme of formation collision avoidance and iterative docking is proposed for full-actuated unmanned surface vehicles (USVs). The artificial potential field method is integrated into the partial differential equation (PDE) formation control approach, which can improve the collision-avoidance performance of the formation. During the docking process of the straight-line formation, the USV agent is expected to track the desired commands accurately. Considering the possibility of docking failure, an iterative learning model predictive control (ILMPC) scheme is introduced. Once the moving USV fails in docking on the stationary USV, the moving agent can return to the origin to re-execute the docking process. The ILMPC method has the advantages of model predictive control and the iterative learning, so it can consider the future process dynamics in the time domain and overcome periodic disturbances. Simulation results show that USVs can avoid collisions with each other in the straight-line-formation mission. Furthermore, the USV agent can dock one-by-one successfully when interference exists.

Latent variable point-to-point iterative learning model predictive control via reference trajectory updating

A latent variable point-to-point iterative learning model predictive control algorithm (LV-PTP-ILMPC) that is combined with the reference trajectory updating strategy is proposed in this paper. It is different from the traditional point-to-point iterative learning model predictive control (PTP-ILMPC), which is developed in the original variable space to track a fixed reference trajectory. The proposed algorithm uses a model constructed by dynamic partial least squares (DyPLS) to extract the principal components of multiple input variables in each batch and designs the PTP-ILMPC controller in the latent variable space. Moreover, creating a reference trajectory updated along the batch direction through the desired points. The updating reference trajectory, modified according to the tracking error information, fully utilizes the degrees of freedom of nonspecific tracking points in the latent variable space. The proposed algorithm uses DyPLS to decouple the multiple-input, multiple-output system (MIMO) into a single-input, single-output system, simplifying the multivariable control problem. In addition, the updated reference relaxes the constraints on the system output so that the algorithm has a faster convergence speed and a more comprehensive range of applications. Two studies are proposed to show the effectiveness of the algorithm.

Data-driven trajectory-tracking in automated parking system via iterative learning compensation and model predictive control

Automated parking system (APS) that explicitly considers the time efficiency of the motion has received large amounts of attention in recent years. Trajectory planning module in these APS delivered parking trajectory, which was expected to be precisely tracked by tracking module. However, the reference points of frequently used trackers were selected in the spatial domain, resulting in significant trajectory tracking errors with temporal information. In this paper, a tracking control method called ILC-MPC, which combined model predictive control (MPC) and iterative learning control (ILC), was proposed to improve the spatiotemporal tracking accuracy of the autonomous vehicle. ILC was utilized for longitudinal compensation using the error signal between historical and expected speed. Accordingly, the error model in the longitudinal direction was simplified to decrease the number of decision variables in MPC. Simulation experiments using CarSim were carried out to compare the proposed method with open-loop control, linear quadratic regulator (LQR), and pure MPC that had a similar computing time with ILC-MPC. ILC-MPC converged in a few iterations of the learning process and achieved the highest tracking accuracy in spatiotemporal domain among the mentioned methods.