Open-loop Prediction Research Articles

Nonlinear system identification using modified variational autoencoders

This research proposes a methodology for identifying nonlinear systems using input/output data and deep learning generative models. Our framework integrates Variational Autoencoders (VAE) with Nonlinear Autoregressive with exogenous input (NARX) in a unified identification structure to address overfitting in nonlinear system identification using NARX structures. Specifically, we modify a variational autoencoder by replacing the decoder module with a NARX model using the latent space information captured from the VAE encoder module as one of the exogenous inputs. Following the training phase, the decoder module can be used as a nonlinear model of the system. We evaluate the efficacy of our approach by performing open-loop prediction tests on data from four nonlinear benchmark systems: Cascaded tanks, Gas furnace, Silverbox, and Wiener-Hammerstein. The proposed VAE-NARX method reported Root Mean Squared Error (RMSE) of 8.23×10−3, 16.69×10−3, 0.002×10−3 and 0.037×10−3 respectively. Our results demonstrate that our proposed method achieves similar and outperforms prediction performances to standard identification techniques and can enhance the performance of traditional nonlinear system identification methods based on multi-layer perceptron models.

SoC-Modified Core Temperature Estimation of Lithium-Ion Battery Based on Control-Oriented Electro-Thermal Model

Lithium-ion batteries and their control technologies are the key points to electrification and intelligence of transportation. Dynamic thermal management is one of the key technologies for intelligent battery management systems. Real-time monitoring of information about the temperature characteristics inside the battery is important for effective and safe thermal management. This paper firstly constructs a distributed control-oriented electro-thermal coupling model which contains multidimensional internal information about the cell. Based on the proposed model, improved parameter identification methods are used to construct offline database of model parameters. The electrical and thermal parameters are identified by applying recursive least squares with variable forgetting factor (VFFRLS) and particle swarm optimization (PSO) separately. Finally, a SoC-modified core temperature estimation method is proposed, which adopts discrete-time nonlinear observer (DNLO) to modify SoC and adapative Kalman filter (AKF) to estimate core temperature. The method takes into account the sensitivity of the output results to nonlinear, time-varying battery systems. The results show that the root-mean-square error (RMSE) of SoC estimation is 1.75 % and the mean absolute error (MAE) is 0.65 % for the proposed temperature method under wide temperature points (-5, 25, 45 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> C). The proposed core temperature estimation method possesses better robustness and universality, with RMSE of 0.61 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> C and MAE of 0.56 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^ {\circ }$</tex-math></inline-formula> C. Compared with the open-loop prediction method, the accuracy is improved about 0.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^ {\circ }$</tex-math></inline-formula> C under extreme loadfiles with uncertainty.

Compound Event-Triggered Distributed MPC for Coupled Nonlinear Systems.

This article investigates the event-triggered distributed model predictive control (DMPC) for perturbed coupled nonlinear systems subject to state and control input constraints. A novel compound event-triggered DMPC strategy, including a compound triggering condition and a new constraint tightening approach, is developed. In this event-triggered strategy, two stability-related conditions are checked in a parallel manner, which relaxes the requirement of the decrease of the Lyapunov function. An open-loop prediction scheme to avoid periodic transmission is designed for the states in the terminal set. As a result, the number of triggering and transmission instants can be reduced significantly. Furthermore, the proposed constraint tightening approach solves the problem of the state constraint satisfaction, which is quite challenging due to the external disturbances and the mutual influences caused by dynamical coupling. Simulations are conducted at last to validate the effectiveness of the proposed algorithm.

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.

Guaranteed Closed-Loop Learning in Model Predictive Control

In this article, we propose a novel learning-based model predictive control framework for nonlinear systems which is able to guarantee closed-loop learning of the controlled system. We consider a cost function that combines a general economic cost with a user-defined learning cost function that aims at incentivizing learning of the unknown system. In particular, due to the finite horizon of the MPC scheme and to the presence of disturbances, the open-loop trajectory usually differs from the closed-loop one. Such a mismatch causes existing learning-based MPC schemes to only show a learning phase in the open-loop prediction, without providing any formal guarantee on the actual closed-loop learning. In this article, we show how existing MPC schemes can be easily modified in order to guarantee closed-loop learning of the system by including a suitable discount factor in the chosen learning cost function, and implementing an additional constraint in the original MPC scheme. We show that various techniques for online learning the system dynamics, such as kinky inference methods, Gaussian processes, or parametric approaches, can be used within the proposed general framework.

Distributed Double-Layered Dynamic Matrix Control for Large-Scale System

A distributed double-layered dynamic matrix control is proposed for large-scale systems. In the scheme, a large-scale system is first decomposed into several low-dimensional subsystems, and then a double-layered dynamic matrix control algorithm with distributed structure is developed for these subsystems. The distributed open-loop prediction equation of each subsystem is formed based on the predicted output of each local subsystem and effects of its interconnecting neighbor subsystems. Due to simultaneous optimization, at each prediction, the coupling effects of neighbor subsystems are not available in time. Thus, the assumed value is utilized instead. In the economic optimization stage, conflicts may occur among different economic optimization goals. Utopia-tracking strategy is introduced to optimize multiple steady-state targets. Then, the obtained steady-state target values are taken as reference values and tracked in subsequent dynamic control. The actual control move for each subsystem is finally calculated. The proposed algorithm is tested on Shell heavy oil fractionator benchmark, and the effectiveness is demonstrated by comparing with the typical double-layered dynamic matrix control algorithm.

Learning nonlinear state–space models using autoencoders

We propose a methodology for the identification of nonlinear state–space models from input/output data using machine-learning techniques based on autoencoders and neural networks. Our framework simultaneously identifies the nonlinear output and state-update maps of the model. After formulating the approach and providing guidelines for tuning the related hyper-parameters (including the model order), we show its capability in fitting nonlinear models on different nonlinear system identification benchmarks. Performance is assessed in terms of open-loop prediction on test data and of controlling the system via nonlinear model predictive control (MPC) based on the identified nonlinear state–space model.

Observer-Predictor-Based Predictive Torque Control of Induction Machine for Robustness Improvement

In the finite control set model predictive control (FCS-MPC) of induction motors, the mismatched motor parameters will inevitably lead to model predictive errors, and then reduce the control performance. At present, the evaluation methods of the prediction errors caused by mismatched parameters and of improving robustness have become the research hotspots of FCS-MPC of induction motors. In this article, an observer-predictor-based predictive torque control of induction machine is proposed in order to improve the prediction accuracy. In the stator current prediction equation, this article abandons the traditional open-loop prediction equation and proposes a closed-loop stator current prediction equation. In the stator flux prediction equation, this article abandons the traditional stator flux prediction model based on voltage model, and proposes a discrete hybrid prediction model combining voltage model and current model, where the proportional-integral regulator is used to switch the voltage model to the current model. Second, the stability and parameter design principles of the closed-loop stator current prediction model and the closed-loop stator flux prediction model are analyzed. Finally, the experimental results show that the proposed method is superior to the traditional method in dynamic performance, steady-state performance, and parameter robustness.

IMPROVED CONSTRAINT HANDLING APPROACH FOR PREDICTIVE FUNCTIONAL CONTROL USING AN IMPLIED CLOSED-LOOP PREDICTION

Predictive Functional Control is a simple alternative to the traditional PID controller which has the capability to handle process constraints more systematically. Nevertheless, the most basic form of PFC has suffered from ill-posed prediction due to its simplicity in formulation and assumption of constant future input dynamics. Although some constraints can be satisfied, nevertheless the performance may be very conservative due to this issue. The main objective of this paper is to improve the constrained performance of a PFC controller with a minimum modification of the existing formulation. Specifically, a novel constraint handling approach for PFC is proposed based on an implied closed-loop prediction. Instead of assuming a constant input as deployed in the conventional open-loop prediction, the implied closed-loop input dynamics are utilised to detect future constraint violations. In addition, a future perturbation is introduced into the prediction structure as an extra degree of freedom for satisfying the constraints. Two simulation results confirm that the proposed approach gives far less conservative constraint handling and thus better control performance compared to the nominal PFC. Furthermore, this novel implementation also alleviates the well-known tuning difficulties and prediction inconsistency issues that are associated with conventional PFC when handling constraints. ABSTRAK: Kawalan Kefungsian Ramalan adalah alternatif mudah kepada kawalan tradisional PID yang mempunyai kekangan keupayaan bagi mengawal proses secara lebih tersusun. Namun, keadaan paling asas pada kesan PFC adalah daripada ramalan tak teraju-rapi yang disebabkan oleh formula ringkas dan anggapan dinamik input yang sama bagi masa depan. Walau kekangan ini dapat diatasi, namun prestasi akan berubah secara konservatif disebabkan oleh isu ini. Objektif utama kajian ini adalah bagi membaiki kekangan prestasi kawalan PFC dengan modifikasi minimum formula yang ada. Secara spesifik, pendekatan nobel kawalan PFC dicadangkan berdasarkan ramalan lingkaran-tertutup. Selain anggapan input tetap seperti yang dilakukan pada ramalan lingkaran-terbuka yang konservatif, dinamik input yang dibuat pada lingkaran-tertutup telah digunakan bagi mengesan kekangan masa depan yang bertentangan. Tambahan, gangguan yang bakal berlaku pada masa depan telah diperkenalkan ke dalam struktur ramalan sebagai tambahan darjah pada kebebasan bagi mengatasi kekangan. Dua dapatan simulasi kajian menyetujui pendekatan yang dicadangkan dan menyebabkan sangat kurang kekangan pengendalian pada sistem konservatif, oleh itu kawalan yang lebih bagus pada prestasi berbanding pada PFC nominal. Selain itu, pendekatan nobel ini juga menghilangkan kesukaran pelarasan yang dikenali ramai dan ramalan isu tidak konsisten yang terdapat pada PFC konvensional apabila mengendali kekangan.

Deep representation-based packetized predictive compensation for networked nonlinear systems

The design of networked nonlinear control system is a very challenging problem due to the coupling of the system uncertainties (e.g., model accuracy, noise, nonlinearity) and network effects (e.g., packet dropouts, time delay). In this paper, a deep representation-based predictive compensation method is proposed for networked nonlinear systems with packet-dropouts in the feedback and forward channel. Different from the existing compensation methods based on open-loop prediction, the proposed method is based on feedback compensation and does not require a nominal system model, so that it can avoid the coupling of system uncertainties and network effects as well as the occupation of network bandwidth. Specifically, a deep sequence to sequence learning scheme is firstly employed to encode the correlations of state and control sequences into deep feature representations. Furthermore, within the embedding space spanned by the learned features, according to the state-control sequence of each sampling step, a prediction of the next control command is generated as compensation for packet dropout. The stability of the overall system is rigorously proved by the Lyapunov theory, which reveals that the control errors for the networked control systems with packet dropouts asymptotic converge to a small neighborhood of the origin. We further evaluate the performance of the proposed strategy on a wheeled mobile robots simulation platform, and the experimental results demonstrate that our method can achieve high compensation accuracy and robustness concerning packet dropouts, even in the case of the maximum continuous packet dropouts specified by the network communication protocol.

Robust Predictive Torque Control of Permanent Magnet Synchronous Machine Using Discrete Hybrid Prediction Model

In the prediction stage of finite control set-predictive torque control for permanent magnet synchronous machine (PMSM), the mismatched parameters will inevitably bring about the predictive errors, which will cause the wrong selection of voltage vector in the optimization stage, and even affect the stability of the entire control system. In order to eliminate the prediction errors, a discrete hybrid prediction model-based predictive torque control (DHPM-PTC) of PMSM is proposed to improve robustness. In the stator current prediction model, the traditional open-loop prediction model is abandoned, and the closed-loop model prediction equation is established. In the stator flux prediction model, this article gets rid of the traditional open-loop integral prediction model, and establishes the closed-loop flux prediction model integrating the current model and the voltage model. Secondly, the stability and parameter design principles of the closed-loop current prediction model and the closed-loop flux prediction model are discussed. Finally, the verification of the proposed algorithm is made on a PMSM test platform. The test results indicate that the proposed DHPM-PTC is superior to the traditional predictive torque control (T-PTC) in dynamic, steady and robust performances.

Heuristic open-loop output feedback model predictive control for control of intermittent transonic wind tunnel

For intermittent transonic wind tunnel (ITWT), Mach number and total pressure are crucial features of the flow field in the test section. However, they are typically difficult to control due to system nonlinearities, uncertainties, coupling and delays. This paper proposes an output feedback model predictive control (MPC) strategy to ensure the tracking of Mach number and total pressure of the ITWT to a specified reference trajectory. The proposed approach includes open-loop prediction, steady state target calculation (SSTC) and dynamic control, where the lower layer dynamic control tracks the steady state target obtained from the upper SSTC layer. By adding an artificial disturbance in the identified linear parameter varying (LPV) model for ITWT, and utilizing the resulting LPV model in both SSTC and dynamic control layers, a heuristic open-loop output feedback MPC approach is proposed. The experimental results for the control of Mach number and total pressure for ITWT demonstrate the effectiveness of the proposed approach.

Design and Implementation of Luenberger Model-Based Predictive Torque Control of Induction Machine for Robustness Improvement

This letter proposes a Luenberger model-based predictive torque control (LM-PTC) of induction machine to compensate prediction error caused by mismatched parameters. In the traditional predictive torque control (T-PTC), stator current, stator flux vector, and electromagnetic torque are predicted in one sampling period by open-loop prediction model, which will inevitably lead to prediction error by mismatched parameters, first. Inspired by the idea of closed-loop Luenberger observer, in the torque and flux prediction, the feedback correction part is introduced into prediction equations for LM-PTC. Second, the steady prediction errors of T-PTC and LM-PTC are, respectively, analyzed with mismatched parameter. Finally, the proposed LM-PTC is verified by the comparison experiments including dynamic-state, transient-state, and steady-state experiments.

Multivariable offset-free MPC with steady-state target calculation and its application to a wind tunnel system

This paper addresses a computationally efficient MPC approach for set-point optimization and its application to an intermittent transonic wind tunnel (ITWT). In the presented method, the open-loop prediction, which adopts the Kalman filter to obtain the open-loop dynamic/steady state predictions of manipulated/controlled variables (MVs/CVs), is presented. Based on the open-loop prediction, a linearization steady-state model featured by the total pressure and the Mach number is used for set-points optimization in steady-state target calculation (SSTC), being formulated as a linear programming (LP) problem. Based on these set-points of MVs/CVs, the dynamic control computes the optimal control moves by solving a quadratic programming (QP) problem. The effectiveness of the proposed method is illustrated on ITWT, and satisfactory performances are obtained.

Power capability prediction for lithium-ion batteries using economic nonlinear model predictive control

Technical challenges facing determination of battery available power arise from its complicated nonlinear dynamics, input and output constraints, and inaccessible internal states. Available solutions often resorted to open-loop prediction with simplified battery models or linear control algorithms. To resolve these challenges simultaneously, this paper formulates an economic nonlinear model predictive control to forecast a battery's state-of-power. This algorithm is built upon a high-fidelity model that captures nonlinear coupled electrical and thermal dynamics of a lithium-ion battery. Constraints imposed on current, voltage, temperature, and state-of-charge are then taken into account in a systematic fashion. Illustrative results from several different tests over a wide range of conditions demonstrate that the proposed approach is capable of accurately predicting the power capability with the error less than 0.2% while protecting the battery from undesirable reactions. Furthermore, the effects of temperature constraints, prediction horizon, and model accuracy are quantitatively examined. The proposed power prediction algorithm is general and then can be equally applicable to different lithium-ion batteries and cell chemistries where proper mathematical models exist.

Closed loop identification of a piezoelectrically controlled radial gas bearing: Theory and experiment

Gas bearing systems have extremely small damping properties. Feedback control is thus employed to increase the damping of gas bearings. Such a feedback loop correlates the input with the measurement noise which in turn makes the assumptions for direct identification invalid. The originality of this article lies in the investigation of the impact of using different identification methods to identify a rotor-bearing systems’ dynamic model when a feedback loop is active. Two different identification methods are employed. The first method is open loop Prediction Error Method, while the other method is the modified Hansen scheme. Identification based on the modified Hansen scheme is conducted by identifying the Youla deviation system using subspace identification. Identification of the Youla deviation system is based on the Youla–Jabr–Bongiorno–Kucera parametrisation of plant and controller. By using the modified Hansen scheme, identification based on standard subspace identification methods can be used to identify the Youla deviation system of the gas bearing. This procedure ensures the input to the Youla deviation system, and the noise is uncorrelated even though the system is subject to feedback control. The effect of identifying the Youla deviation system compared to direct subspace identification of the gas bearing is further investigated through a simulation example. Experiments are conducted on the piezoelectrically controlled radial gas bearing. A dynamic model is identified using the modified Hansen scheme as well as using Prediction Error Method identification. The resulting models are compared for different imperfect nominal models, to examine under which conditions each method should be used.

Non-linear Closed-Loop Identification of CSTR in the presence of a Non-stationary Disturbances

In this paper, a continuous stirred tank reactor (CSTR) is identified in closed loop using a direct prediction error based approach. This common process control system is represented by Hammerstein model, a memoryless non-linearity in cascade with a linear dynamic subsystem. In direct closed-loop identification, the process and noise models are identified using an open-loop prediction error minimization approach. The noise model is represented by an Auto Regressive Integrated Moving Average (ARIMA) model, as disturbances in chemical processes are often non-stationary, consisting of sequences of random steps. The Hammerstein system is identified in the presence of this non-stationary disturbance via a differencing based technique. Finally, simulation examples, validation tests and results comparisons are provided.

Optimal periodic scheduling for remote state estimation under sensor energy constraint

The authors consider a sensor scheduling problem for a scalar system observed by two sensors. The measurements derived from the two local sensors are sent over a bandwidth-limited network to a remote estimator. The bandwidth constraint allows at most one packet can be sent at each time step. Upon receiving the data, the estimator computes the optimal estimate of the state in the minimum mean-squared error sense. In consideration of simplicity as well as practical and efficient implementation, the authors focus on periodic scheduling scheme. The authors assume that the sensor energy is so limited that in each period there exist open-loop predictions at some steps, which makes the problem more challenging. Using some novel tools, it was shown that the `as uniformly as possible' scheme, originally proposed in an early work for minimising the average estimation error covariance when sensor energy is just enough, still holds true in this limited energy case but the optimal steps of open-loop prediction depend on the system parameters. Such a relationship between scheduling rule and system parameters is novel and does not exist in early works where sensor energy is just enough. Numerical examples are provided to demonstrate the key ideas of the proposed work.

Flexible synthesis of video frames based on motion hints.

In this paper, we propose the use of "motion hints" to produce interframe predictions. A motion hint is a loose and global description of motion that can be communicated using metadata; it describes a continuous and invertible motion model over multiple frames, spatially overlapping other motion hints. A motion hint provides a reasonably accurate description of motion but only a loose description of where it is applicable; it is the task of the client to identify the exact locations where this motion model is applicable. The focus of this paper is a probabilistic multiscale approach to identifying these locations of applicability; the method is robust to noise, quantization, and contrast changes. The proposed approach employs the Laplacian pyramid; it generates motion hint probabilities from observations at each scale of the pyramid. These probabilities are then combined across the scales of the pyramid starting from the coarsest scale. The computational cost of the approach is reasonable, and only the neighborhood of a pixel is employed to determine a motion hint probability, which makes parallel implementation feasible. This paper also elaborates on how motion hint probabilities are exploited in generating interframe predictions. The scheme of this paper is applicable to closed-loop prediction, but it is more useful in open-loop prediction scenarios, such as using prediction in conjunction with remote browsing of surveillance footage, communicated by a JPEG2000 Interactive Protocol (JPIP) server. We show that the interframe predictions obtained using the proposed approach are good both visually and in terms of PSNR.

A Predictive-Reactive Method for Improving the Robustness of Real-Time Data Services

Supporting timely data services using fresh data in data-intensive real-time applications, such as e-commerce and transportation management is desirable but challenging, since the workload may vary dynamically. To control the data service delay to be below the specified threshold, we develop a predictive as well as reactive method for database admission control. The predictive method derives the workload bound for admission control in a predictive manner, making no statistical or queuing-theoretic assumptions about workloads. Also, our reactive scheme based on formal feedback control theory continuously adjusts the database load bound to support the delay threshold. By adapting the load bound in a proactive fashion, we attempt to avoid severe overload conditions and excessive delays before they occur. Also, the feedback control scheme enhances the timeliness by compensating for potential prediction errors due to dynamic workloads. Hence, the predictive and reactive methods complement each other, enhancing the robustness of real-time data services as a whole. We implement the integrated approach and several baselines in an open-source database. Compared to the tested open-loop, feedback-only, and statistical prediction + feedback baselines representing the state of the art, our integrated method significantly improves the average/transient delay and real-time data service throughput.