RBFNN-Based Data-Driven Predictive Iterative Learning Control for Nonaffine Nonlinear Systems

A novel intelligent control of discrete-time nonlinear systems in the presence of output saturation

In this paper, a model free control method for a class of discrete time nonlinear systems is introduced. A type-3 fuzzy system estimates the unknown parameters required by the control system. The control system only uses the input and output data of the plant and therefore does not need to know its mathematical equations. On the other hand, the phenomenon of output saturation is a challenging problem for all control systems, addressed in detail in the proposed method. The convergence of the proposed method is guaranteed, and the control system is very robust in the face of changes in the dynamics of the plant. The simulation results on discrete-time nonlinear systems show that the proposed method is very accurate despite the high speed of convergence. In addition, the proposed method is robust for modeling uncertainties and has a better root mean square error and step response time compared to the other methods. Also, a comparison has been made between type-1 to type-3 fuzzy systems and control system based on trial and error, which shows firstly the importance of the presence of fuzzy system and secondly the superiority of type-3 fuzzy system compared to the other two types.

Adaptive fuzzy iterative learning control based neurostimulation system and in-silico evaluation

Closed-loop neural stimulation has been an effective treatment for epilepsy patients. Currently, most closed-loop neural stimulation strategies are designed based on accurate neural models. However, the uncertainty and complexity of the neural system make it difficult to build an accurate neural model, which poses a significant challenge to the design of the controller. This paper proposes an Adaptive Fuzzy Iterative Learning Control (AFILC) framework for closed-loop neural stimulation, which can realize neuromodulation with no model or model uncertainty. Recognizing the periodic characteristics of neural stimulation and neuronal firing, Iterative Learning Control (ILC) is employed as the primary controller. Furthermore, a fuzzy optimization module is established to update the internal parameters of the ILC controller in real-time. This module enhances the anti-interference ability of the control system and reduces the influence of initial controller parameters on the control process. The efficacy of this strategy is evaluated using a neural computational model. The simulation results validate the capability of the AFILC strategy to suppress epileptic states. Compared with ILC-based closed-loop neurostimulation schemes, the AFILC-based neurostimulation strategy has faster convergence speed and stronger anti-interference ability. Moreover, the control algorithm is implemented based on a digital signal processor, and the hardware-in-the-loop experimental platform is implemented. The experimental results show that the control method has good control performance and computational efficiency, which provides the possibility for future application in clinical research.

A Novel Accelerated Multistage Learning Control Mechanism via Virtual Performance Reduction

This study uses a multistage learning mechanism concept to investigate the accelerated learning control for stochastic systems. In this mechanism, the learning iterations are divided into successive stages, with each stage comprising several iterations. The learning gain is constant in each stage to accelerate the learning process and decreases it from one stage to another to eliminate the noise effect asymptotically. The critical issue is determining the switching iteration when a new stage starts. This study resolves this issue by calculating a virtual performance index of the mean-squared input error and its estimated upper bound. Specifically, the ideal, practical, and improved multistage learning control schemes are proposed to determine the switching iteration and generate the learning gain sequence. The ideal scheme achieves the best performance at the cost of a large computation burden, and the practical scheme saves computation cost, but the performance is not excellent. The improved scheme significantly approximates the best performance by introducing additional stretching parameters to the performance index. Illustrative simulations are provided to verify the theoretical results.

Event-triggered based predictive iterative learning control with random packet loss compensation for nonlinear networked systems

In this paper, a novel event-triggered predictive iterative learning control (ET-PILC) method with random packet loss compensation (RPLC) mechanism is proposed for unknown nonlinear networked systems with random packet loss (RPL). First, a new RPLC mechanism is designed by utilizing both the historical and predictive data information to avoid the deterioration of control performance due to RPL. Then, a new event-triggered condition is designed based on the proposed RPLC mechanism to save communication resources and reduce computational burden. Moreover, the convergence of the modeling error and tracking control error are analyzed theoretically, and simulation results are given to demonstrate the effectiveness of the proposed method further.

Data-driven set-point learning control with ESO and RBFNN for nonlinear batch processes subject to nonrepetitive uncertainties

This paper proposes an extended state observer (ESO) based data-driven set-point learning control (DDSPLC) scheme for a class of nonlinear batch processes with a priori P-type feedback control structure subject to nonrepetitive uncertainties, by only using the process input and output data available in practice. Firstly, the unknown process dynamics is equivalently transformed into an iterative dynamic linearization data model (IDLDM) with a residual term. A radial basis function neural network is adopted to estimate the pseudo partial derivative information related to IDLDM, and meanwhile, a data-driven iterative ESO is constructed to estimate the unknown residual term along the batch direction. Then, an adaptive set-point learning control law is designed to merely regulate the set-point command of the closed-loop control structure for realizing batch optimization. Robust convergence of the output tracking error along the batch direction is rigorously analyzed by using the contraction mapping approach and mathematical induction. Finally, two illustrative examples from the literature are used to validate the effectiveness and advantage of the proposed design.

Effluent quality prediction of the sewage treatment based on a hybrid neural network model: Comparison and application

The accurate prediction and assessment of effluent quality in wastewater treatment plants (WWTPs) are paramount for the efficacy of sewage treatment processes. Neural network models have exhibited promise in enhancing prediction accuracy by simulating and analyzing diverse influent parameters. In this study, a back propagation neural network hybrid model based on a tent chaotic map and sparrow search algorithm (Tent_BP_SSA) was developed to predict the effluent quality of sewage treatment processes. The prediction performance of the propose hybrid model was compared with traditional neural network models using five performance indicators (MAE, RMSE, SSE, MAPE and R2). Specifically, in comparison with the prior Tent_BP_SSA, Tent_BP_SSA2 demonstrated notable enhancements, with the R2 increasing from 0.9512 to 0.9672, while MAE, RMSE, SSE, and MAPE decreased by 9.62%, 18.84%, 24.80%, and 47.10%, respectively. These indicators collectively affirm that the utilization of higher-order input parameters ensures improved accuracy of the Tent_BP_SSA2 hybrid model in predicting effluent quality. Moreover, the Tent_BP_SSA2 model exhibited robust prediction ability (R2 of 0.9246) when applied to assess the effluent quality of an actual sewage treatment plant. The incorporation of integrated models comprising the sparrow search optimizing algorithm, tent chaotic mapping, and higher-order magnitude decomposition of input parameters has demonstrated the capacity to enhance the accuracy of effluent quality prediction. This study illuminates novel perspectives on the prediction of effluent quality and the assessment of effluent warnings in WWTPs.

Learning From Human Demonstrations for Wheel Mobile Manipulator: An Unscented Model Predictive Control Approach

Industry 4.0 requires new production models to be more flexible and efficient, which means that robots should be capable of flexible skills to adapt to different production and processing tasks. Learning from demonstration (LfD) is considered as one of the promising ways for robots to obtain motion and manipulation skills from humans. In this article, a framework that enables a wheel mobile manipulator to learn skills from humans and complete the specified tasks in an unstructured environment is developed, including a high-level trajectory learning and a low-level trajectory tracking control. First, a modified dynamic movement primitives (DMPs) model is utilized to simultaneously learn the movement trajectories of a human operator's hand and body as reference trajectories for the mobile manipulator. Considering that the auxiliary model obtained by the nonlinear feedback is hard to accurately describe the behavior of mobile manipulator with the presence of uncertain parameters and disturbances, a novel model is established, and an unscented model predictive control (UMPC) strategy is then presented to solve the trajectory tracking control problem without violating the system constraints. Moreover, a sufficient condition guaranteeing the input to state practical stability (ISpS) of the system is obtained, and the upper bound of estimated error is also defined. Finally, the effectiveness of the proposed strategy is validated by three simulation experiments.

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.

Guaranteeing Global Stability for Neuro-Adaptive Control of Unknown Pure-Feedback Nonaffine Systems via Barrier Functions

Most existing approximation-based adaptive control (AAC) approaches for unknown pure-feedback nonaffine systems retain a dilemma that all closed-loop signals are semiglobally uniformly bounded (SGUB) rather than globally uniformly bounded (GUB). To achieve the GUB stability result, this article presents a neuro-adaptive backstepping control approach by blending the mean value theorem (MVT), the barrier Lyapunov functions (BLFs), and the technique of neural approximation. Specifically, we first resort the MVT to acquire the intermediate and actual control inputs from the nonaffine structures directly. Then, neural networks (NNs) are adopted to approximate the unknown nonlinear functions, in which the compact sets for maintaining the approximation capabilities of NNs are predetermined actively through the BLFs. It is shown that, with the developed neuro-adaptive control scheme, global stability of the resulting closed-loop system is ensured. Simulations are conducted to verify and clarify the developed approach.

Event-Triggered Cooperative Model-Free Adaptive Iterative Learning Control for Multiple Subway Trains With Actuator Faults

This article investigates the issue of speed tracking and dynamic adjustment of headway for the repeatable multiple subway trains (MSTs) system in the case of actuator faults. First, the repeatable nonlinear subway train system is transformed into an iteration-related full-form dynamic linearization (IFFDL) data model. Then, the event-triggered cooperative model-free adaptive iterative learning control (ET-CMFAILC) scheme based on the IFFDL data model for MSTs is designed. The control scheme includes the following four parts: 1) the cooperative control algorithm is derived by the cost function to realize cooperation of MSTs; 2) the radial basis function neural network (RBFNN) algorithm along the iteration axis is constructed to compensate the effects of iteration-time-varying actuator faults; 3) the projection algorithm is employed to estimate unknown complex nonlinear terms; and 4) the asynchronous event-triggered mechanism operated along the time domain and iteration domain is applied to lessen the communication and computational burden. Theoretical analysis and simulation results show that the effectiveness of the proposed ET-CMFAILC scheme, which can ensure that the speed tracking errors of MSTs are bounded and the distances of adjacent subway trains are stabilized in the safe range.

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.

Demand forecasting model for time-series pharmaceutical data using shallow and deep neural network model

Demand forecasting is a scientific and methodical assessment of future demand for a critical product.The effective Demand Forecast Model (DFM) enables pharmaceutical companies to be successful in the global market. The purpose of this research paper is to validate various shallow and deep neural network methods for demand forecasting, with the aim of recommending sales and marketing strategies based on the trend/seasonal effects of eight different groups of pharmaceutical products with different characteristics. The root mean squared error (RMSE) is used as the predictive accuracy of DFMs. This study also found that the mean RMSE value of the shallow neural network-based DFMs was 6.27 for all drug categories, which was lower than deep neural network models. According to the findings, DFMs based on shallow neural networks can effectively estimate future demand for pharmaceutical products.

A Probabilistically Quantized Learning Control Framework for Networked Linear Systems

In this article, we consider quantized learning control for linear networked systems with additive channel noise. Our objective is to achieve high tracking performance while reducing the communication burden on the communication network. To address this problem, we propose an integrated framework consisting of two modules: a probabilistic quantizer and a learning scheme. The employed probabilistic quantizer is developed by employing a Bernoulli distribution driven by the quantization errors. Three learning control schemes are studied, namely, a constant gain, a decreasing gain sequence satisfying certain conditions, and an optimal gain sequence that is recursively generated based on a performance index. We show that the control with a constant gain can only ensure the input error sequence to converge to a bounded sphere in a mean-square sense, where the radius of this sphere is proportional to the constant gain. On the contrary, we show that the control that employs any of the two proposed gain sequences drives the input error to zero in the mean-square sense. In addition, we show that the convergence rate associated with the constant gain is exponential, whereas the rate associated with the proposed gain sequences is not faster than a specific exponential trend. Illustrative simulations are provided to demonstrate the convergence rate properties and steady-state tracking performance associated with each gain, and their robustness against modeling uncertainties.

Prediction of suicidal ideation among Chinese college students based on radial basis function neural network

Background

Suicide is one of the leading causes of death for college students. The predictors of suicidal ideation among college students are inconsistent and few studies have systematically investigated psychological symptoms of college students to predict suicide. Therefore, this study aims to develop a suicidal ideation prediction model and explore important predictors of suicidal ideation among college students in China.

Methods

We recruited 1,500 college students of Sichuan University and followed up for 4 years. Demographic information, behavioral and psychological information of the participants were collected using computer-based questionnaires. The Radial Basis Function Neural Network (RBFNN) method was used to develop three suicidal ideation risk prediction models and to identify important predictive factors for suicidal ideation among college students.

Results

The incidence of suicidal ideation among college students in the last 12 months ranged from 3.00 to 4.07%. The prediction accuracies of all the three models were over 91.7%. The area under curve scores were up to 0.96. Previous suicidal ideation and poor subjective sleep quality were the most robust predictors. Poor self-rated mental health has also been identified to be an important predictor. Paranoid symptom, internet addiction, poor self-rated physical health, poor self-rated overall health, emotional abuse, low average annual household income per person and heavy study pressure were potential predictors for suicidal ideation.

Conclusions

The study suggested that the RBFNN method was accurate in predicting suicidal ideation. And students who have ever had previous suicidal ideation and poor sleep quality should be paid consistent attention to.

Design and Analysis of Data-Driven Learning Control: An Optimization-Based Approach

Learning to perform perfect tracking tasks based on measurement data is desirable in the controller design of systems operating repetitively. This motivates this article to seek an optimization-based design and analysis approach for data-driven learning control systems by focusing on iterative learning control (ILC) of repetitive systems with unknown nonlinear time-varying dynamics. It is shown that perfect output tracking can be realized with updating inputs, where no explicit model knowledge but only measured input-output data are leveraged. In particular, adaptive updating strategies are proposed to obtain parameter estimations of nonlinearities. A double-dynamics analysis approach is applied to establish ILC convergence, together with boundedness of input, output, and estimated parameters, which benefits from employing properties of nonnegative matrices. Simulations are implemented to verify the validity of our optimization-based adaptive ILC.

Transparent Digital Twin for Output Control Using Belief Rule Base

A transparent digital twin (DT) is designed for output control using the belief rule base (BRB), namely, DT-BRB. The goal of the transparent DT-BRB is not only to model the complex relationships between the system inputs and output but also to conduct output control by identifying and optimizing the key parameters in the model inputs. The proposed DT-BRB approach is composed of three major steps. First, BRB is adopted to model the relationships between the inputs and output of the physical system. Second, an analytical procedure is proposed to identify only the key parameters in the system inputs with the highest contribution to the output. Being consistent with the inferencing, integration, and unification procedures of BRB, there are also three parts in the contribution calculation in this step. Finally, the data-driven optimization is performed to control the system output. A practical case study on the Wuhan Metro System is conducted for reducing the building tilt rate (BTR) in tunnel construction. By comparing the results following different standards, the 80% contribution standard is proved to have the highest marginal contribution that identifies only 43.5% parameters as the key parameters but can reduce the BTR by 73.73%. Moreover, it is also observed that the proposed DT-BRB approach is so effective that iterative optimizations are not necessarily needed.

Bridging Reinforcement Learning and Iterative Learning Control: Autonomous Motion Learning for Unknown, Nonlinear Dynamics

This work addresses the problem of reference tracking in autonomously learning robots with unknown, nonlinear dynamics. Existing solutions require model information or extensive parameter tuning, and have rarely been validated in real-world experiments. We propose a learning control scheme that learns to approximate the unknown dynamics by a Gaussian Process (GP), which is used to optimize and apply a feedforward control input on each trial. Unlike existing approaches, the proposed method neither requires knowledge of the system states and their dynamics nor knowledge of an effective feedback control structure. All algorithm parameters are chosen automatically, i.e. the learning method works plug and play. The proposed method is validated in extensive simulations and real-world experiments. In contrast to most existing work, we study learning dynamics for more than one motion task as well as the robustness of performance across a large range of learning parameters. The method’s plug and play applicability is demonstrated by experiments with a balancing robot, in which the proposed method rapidly learns to track the desired output. Due to its model-agnostic and plug and play properties, the proposed method is expected to have high potential for application to a large class of reference tracking problems in systems with unknown, nonlinear dynamics.

Data-Driven-Based Event-Triggered Control for Nonlinear CPSs Against Jamming Attacks

This brief considers the security control problem for nonlinear cyber-physical systems (CPSs) against jamming attacks. First, a novel event-based model-free adaptive control (MFAC) framework is established. Second, a multistep predictive compensation algorithm (PCA) is developed to make compensation for the lost data caused by jamming attacks, even consecutive attacks. Then, an event-triggering mechanism with the dead-zone operator is introduced in the adaptive controller, which can effectively save communication resources and reduce the calculation burden of the controller without affecting the control performance of systems. Moreover, the boundedness of the tracking error is ensured in the mean-square sense, and only the input/output (I/O) data are used in the whole design process. Finally, simulation comparisons are provided to show the effectiveness of our method.

A Study on Regional GDP Forecasting Analysis Based on Radial Basis Function Neural Network with Genetic Algorithm (RBFNN-GA) for Shandong Economy

Gross domestic product (GDP) is an important indicator for determining a country's or region's economic status and development level, and it is closely linked to inflation, unemployment, and economic growth rates. These basic indicators can comprehensively and effectively reflect a country's or region's future economic development. The center of radial basis function neural network and smoothing factor to take a uniform distribution of the random radial basis function artificial neural network will be the focus of this study. This stochastic learning method is a useful addition to the existing methods for determining the center and smoothing factors of radial basis function neural networks, and it can also help the network more efficiently train. GDP forecasting is aided by the genetic algorithm radial basis neural network, which allows the government to make timely and effective macrocontrol plans based on the forecast trend of GDP in the region. This study uses the genetic algorithm radial basis, neural network model, to make judgments on the relationships contained in this sequence and compare and analyze the prediction effect and generalization ability of the model to verify the applicability of the genetic algorithm radial basis, neural network model, based on the modeling of historical data, which may contain linear and nonlinear relationships by itself, so this study uses the genetic algorithm radial basis, neural network model, to make, compare, and analyze judgments on the relationships contained in this sequence.

Towards a Comprehensive Assessment of Statistical versus Soft Computing Models in Hydrology: Application to Monthly Pan Evaporation Prediction

This paper evaluates six soft computational models along with three statistical data-driven models for the prediction of pan evaporation (EP). Accordingly, improved kriging—as a novel statistical model—is proposed for accurate predictions of EP for two meteorological stations in Turkey. In the standard kriging model, the input data nonlinearity effects are increased by using a nonlinear map and transferring input data from a polynomial to an exponential basic function. The accuracy, precision, and over/under prediction tendencies of the response surface method, kriging, improved kriging, multilayer perceptron neural network using the Levenberg–Marquardt (MLP-LM) as well as a conjugate gradient (MLP-CG), radial basis function neural network (RBFNN), multivariate adaptive regression spline (MARS), M5Tree and support vector regression (SVR) were compared. Overall, all the applied models were highly capable of predicting monthly EP in both stations with a mean absolute error (MAE) < 0.77 mm and a Willmott index (d) > 0.95. Considering periodicity as an input parameter, the MLP-LM provided better results than the other methods among the soft computing models (MAE = 0.492 mm and d = 0.981). However, the improved kriging method surpassed all the other models based on the statistical measures (MAE = 0.471 mm and d = 0.983). Finally, the outcomes of the Mann–Whitney test indicated that the applied soft computational models do not have significant superiority over the statistical ones (p-value > 0.65 at α = 0.01 and α = 0.05).

Iterative Learning Model Predictive Control Based on Iterative Data-Driven Modeling

Iterative learning model predictive control (ILMPC) has been recognized as an effective approach to realize high-precision tracking for batch processes with repetitive nature because of its excellent learning ability and closed-loop stability property. However, as a model-based strategy, ILMPC suffers from the unavailability of accurate first principal model in many complex nonlinear batch systems. On account of the abundant process data, nonlinear dynamics of batch systems can be identified precisely along the trials by neural network (NN), making it enforceable to design a data-driven ILMPC. In this article, by using a control-affine feedforward neural network (CAFNN), the features in the process data of the former batch are extracted to form a nonlinear affine model for the controller design in the current batch. Based on the CAFNN model, the ILMPC is formulated in a tube framework to attenuate the influence of modeling errors and track the reference trajectory with sustained accuracy. Due to the control-affine structure, the gradients of the objective function can be analytically computed offline, so as to improve the online computational efficiency and optimization feasibility of the tube ILMPC. The robust stability and the convergence of the data-driven ILMPC system are analyzed theoretically. The simulation on a typical batch reactor verifies the effectiveness of the proposed control method.

Learning Tracking Control Over Unknown Fading Channels Without System Information

A novel data-driven learning control scheme is proposed for unknown systems with unknown fading sensor channels. The fading randomness is modeled by multiplicative and additive random variables subject to certain unknown distributions. In this scheme, we propose an error transmission mode and an iterative gradient estimation method. Unlike the conventional transmission mode where the output is directly transmitted back to the controller, in the error transmission mode, we send the desired reference to the plant such that tracking errors can be calculated locally and then transmitted back through the fading channel. Using the faded tracking error data only, the gradient for updating input is iteratively estimated by a random difference technique along the iteration axis. This gradient acts as the updating term of the control signal; therefore, information on the system and the fading channel is no longer required. The proposed scheme is proved effective in tracking the desired reference under random fading communication environments. Theoretical results are verified by simulations.

Convergence Analysis of Saturated Iterative Learning Control Systems With Locally Lipschitz Nonlinearities

In this article, the robust trajectory tracking problem of iterative learning control (ILC) for uncertain nonlinear systems is considered, and the effects from locally Lipschitz nonlinearities, input saturations, and nonzero system relative degrees are treated. A saturated ILC algorithm is given, with the convergence analysis exploited using a composite energy function-based approach. It is shown that the tracking error can be guaranteed to converge both pointwisely and uniformly. Furthermore, the input updating signal can be ensured to eventually satisfy the input saturation requirements with increasing iterations. Two examples are given to demonstrate the validity of saturated ILC for systems with the relative degree of one, input saturation, and locally Lipschitz nonlinearity.