Data-driven MFAC for a class of discrete-time nonlinear systems with RBFNN

A survey of methods for handling initial state shifts in iterative learning control

This paper introduces three types of controllers: a PID-type iterative learning controller, an adaptive iterative learning controller, and an optimal iterative learning controller, and reviews the history and research status of initial shifts rectifying algorithms. Initial state shifts have attracted research attention because they affect both the tracking performance and system stability. This study focuses on the current common initial shifts rectifying methods and analyzes the underlying mechanism in detail. To verify the effectiveness of the presented initial shifts rectifying algorithms, we simulated those using ideal first- and second-order systems. Finally, directions for the future development of iterative learning control (ILC) and some challenging topics related to initial shifts rectifying for ILC are presented. This article aims to introduce recent developments and advances in initial shifts rectifying algorithms and discuss the directions for their further exploration.

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 Data-Driven ILC Framework for a Class of Nonlinear Discrete-Time Systems

In this article, we propose a data-driven iterative learning control (ILC) framework for unknown nonlinear nonaffine repetitive discrete-time single-input-single-output systems by applying the dynamic linearization (DL) technique. The ILC law is constructed based on the equivalent DL expression of an unknown ideal learning controller in the iteration and time domains. The learning control gain vector is adaptively updated by using a Newton-type optimization method. The monotonic convergence on the tracking errors of the controlled plant is theoretically guaranteed with respect to the 2-norm under some conditions. In the proposed ILC framework, existing proportional, integral, and derivative type ILC, and high-order ILC can be considered as special cases. The proposed ILC framework is a pure data-driven ILC, that is, the ILC law is independent of the physical dynamics of the controlled plant, and the learning control gain updating algorithm is formulated using only the measured input-output data of the nonlinear system. The proposed ILC framework is effectively verified by two illustrative examples on a complicated unknown nonlinear system and on a linear time-varying system.

Data-Based Security Fault Tolerant Iterative Learning Control under Denial-of-Service Attacks

This paper mainly studies the data-based security fault tolerant iterative learning control (SFTILC) problem of nonlinear networked control systems (NCSs) under sensor failures and denial-of-service (DoS) attacks. Firstly, the radial basis function neural network (RBFNN) is used to approximate the sensor failure function and a DoS attack compensation mechanism is proposed in the iterative domain to lessen the impact of DoS attacks. Then, using the dynamic linearization technology, the nonlinear system considering failures and network attacks is transformed into a linear data model. Further, based on the designed linearization model, a new data-based SFTILC algorithm is designed to ensure the satisfactory tracking performance of the system. This process only uses the input and output data of the system, and the stability of the system is proved by using the compression mapping principle. Finally, a digital simulation is used to demonstrate the effectiveness of the proposed SFTILC algorithm.

Model-Free Adaptive Control for Unknown MIMO Nonaffine Nonlinear Discrete-Time Systems With Experimental Validation

In this article, a model-free adaptive control (MFAC) algorithm based on full form dynamic linearization (FFDL) data model is presented for a class of unknown multi-input multi-output (MIMO) nonaffine nonlinear discrete-time learning systems. A virtual equivalent data model in the input-output sense to the considered plant is established first by using the FFDL technology. Then, using the obtained data model, a data-driven MFAC algorithm is designed merely using the inputs and outputs data of the closed-loop learning system. The theoretical analysis of the monotonic convergence of the tracking error dynamics, the bounded-input bounded-output (BIBO) stability, and the internal stability of the closed-loop learning system is rigorously proved by the contraction mapping principle. The effectiveness of the proposed control algorithm is verified by a simulation and a quad-rotor aircraft experimental system.

Novel Data and Neural Network-Based Nonlinear Adaptive Switching Control Method

We propose an adaptive nonlinear control method for a discrete-time dynamical system. First, the nonlinear term is decomposed into a previous sampling instant term and an unknown increment term, which are determined using an intelligent estimation algorithm based on adaptive fuzzy neural networks. The problem of obtaining accurate input data due to the unknown current control signal in unmodeled dynamics using conventional estimation algorithms is addressed, and the conservativeness is reduced. Furthermore, historical data of the controlled plant are leveraged, and the data in the nonlinear term containing repeated estimation information are disregarded. Then, we apply the proposed decomposition method for the nonlinear term to design nonlinear switching controllers. One linear and two nonlinear adaptive controllers are designed, all with compensation of the nonlinear term at the previous sampling instant and increment estimation. These three adaptive controllers coordinately operate the plant by switching rules to guarantee the stability of the controlled plant and to improve the system performance. The stability and convergence of the system are analyzed and verified. Finally, simulation examples are used to verify the effectiveness of the proposed method and compare it with existing methods to confirm its superior performance.

An Enhanced Full-Form Model-Free Adaptive Controller for SISO Discrete-Time Nonlinear Systems

This study focuses on the full-form model-free adaptive controller (FFMFAC) for SISO discrete-time nonlinear systems, and proposes enhanced FFMFAC. The proposed technique design incorporates long short-term memory neural networks (LSTMs) and fuzzy neural networks (FNNs). To be more precise, LSTMs are utilized to adjust vital parameters of the FFMFAC online. Additionally, due to the high nonlinear approximation capabilities of FNNs, pseudo gradient (PG) values of the controller are estimated online. EFFMFAC is characterized by utilizing the measured I/O data for the online training of all introduced neural networks and does not involve offline training and specific models of the controlled system. Finally, the rationality and superiority are verified by two simulations and a supporting ablation analysis. Five individual performance indices are given, and the experimental findings show that EFFMFAC outperforms all other methods. Especially compared with the FFMFAC, EFFMFAC reduces the RMSE by 21.69% and 11.21%, respectively, proving it to be applicable for SISO discrete-time nonlinear systems.

Data-Driven Performance-Prescribed Reinforcement Learning Control of an Unmanned Surface Vehicle

An unmanned surface vehicle (USV) under complicated marine environments can hardly be modeled well such that model-based optimal control approaches become infeasible. In this article, a self-learning-based model-free solution only using input-output signals of the USV is innovatively provided. To this end, a data-driven performance-prescribed reinforcement learning control (DPRLC) scheme is created to pursue control optimality and prescribed tracking accuracy simultaneously. By devising state transformation with prescribed performance, constrained tracking errors are substantially converted into constraint-free stabilization of tracking errors with unknown dynamics. Reinforcement learning paradigm using neural network-based actor-critic learning framework is further deployed to directly optimize controller synthesis deduced from the Bellman error formulation such that transformed tracking errors evolve a data-driven optimal controller. Theoretical analysis eventually ensures that the entire DPRLC scheme can guarantee prescribed tracking accuracy, subject to optimal cost. Both simulations and virtual-reality experiments demonstrate the remarkable effectiveness and superiority of the proposed DPRLC scheme.

AMT Starting Control as a Soft Starter for Belt Conveyors Using a Data-Driven Method

Automated mechanical transmission (AMT) is used as a soft starter in this paper. To improve the soft starting quality, a novel data-driven method is studied. By analyzing and comparing five common soft-starting acceleration curves, a segmented acceleration curve is put forward to be used as the soft-starting acceleration curve for the AMT. Based on the prototype model free adaptive control (MFAC) method, a modified MFAC method with jerk compensation is given to control the AMT output shaft’s angular acceleration and reduce driveline shock. Compared with the methods of prototype MFAC and traditional proportion integration differentiation (PID), the modified MFAC method with jerk compensation can better control the AMT output shaft’s angular acceleration and has excellent characteristics in terms of small tracking error and smaller shock. The research results provide a novel data-driven method for AMT as a soft starter.

Data-Driven Iterative Learning Control for Nonlinear Discrete-Time MIMO Systems

This article considers the tracking control of unknown nonlinear nonaffine repetitive discrete-time multi-input multi-output systems. Two data-driven iterative learning control (ILC) schemes are designed based on two equivalent dynamic linearization data models of an unknown ideal learning controller, which exists theoretically in the iteration domain. The two control schemes provide ways of selecting learning controllers based on the complexity of the controlled nonlinear systems. The learning control gain matrixes of the two learning controllers are optimized through the steepest descent method using only the measured input-output data of the nonlinear systems. The proposed ILC approaches are pure data-driven since no model information of the controlled systems is involved. The stability and convergence of the proposed ILC approaches are rigorously analyzed under reasonable conditions. Numerical simulation and an experiment based on a Gantry-type linear motor drive system are conducted to verify the effectiveness of the proposed data-driven ILC approaches.

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

In this paper, a novel data-driven predictive iterative learning control (DDPILC) scheme based on a radial basis function neural network (RBFNN) is proposed for a class of repeatable nonaffine nonlinear discrete-time systems subjected to nonrepetitive external disturbances. First, by utilizing the dynamic linearization technique (DLT) with a newly introduced and unknown system parameter pseudopartial derivative (PPD) and designing a new RBFNN estimation algorithm along the iterative learning axis for addressing the unknown PPD and the unknown nonrepetitive external disturbances, a data-driven prediction model is established. It is theoretically shown that by constructing a composite energy function (CEF) with respect to the modeling error for the first time, the convergence of the modeling error via the proposed DLT-based RBFNN modeling method can be guaranteed, and the convergence speed is tunable. Then, a DDPILC with a disturbance compensation term is designed, and the convergence of the tracking control error is analyzed. Finally, simulations of a train operation system reveal that even if the train suffers from randomly varying load disturbances and nonlinear running resistance, the proposed scheme can make both the modeling error and the tracking control error decrease successively with increasing operation number.

A Novel Dual Successive Projection-Based Model-Free Adaptive Control Method and Application to an Autonomous Car

In this paper, a novel model-free adaptive control (MFAC) algorithm based on a dual successive projection (DuSP)-MFAC method is proposed, and it is analyzed using the introduced DuSP method and the symmetrically similar structures of the controller and its parameter estimator of MFAC. Then, the proposed DuSP-MFAC scheme is successfully implemented in an autonomous car "Ruilong" for the lateral tracking control problem via converting the trajectory tracking problem into a stabilization problem by using the proposed preview-deviation-yaw angle. This MFAC-based lateral tracking control method was tested and demonstrated satisfactory performance on real roads in Fengtai, Beijing, China, and through successful participation in the Chinese Smart Car Future Challenge Competition held in 2015 and 2016.

Model-free adaptive integral terminal sliding mode predictive control for a class of discrete-time nonlinear systems

In this paper, a new model-free adaptive digital integral terminal sliding mode predictive control scheme is proposed for a class of nonlinear discrete-time systems with disturbances. The characteristic of the proposed control approach is easy to be implemented because it merely adopts the input and output data model of the system based on compact form dynamic linearization (CFDL) data-driven technique, while the technique of perturbation estimation is applied to estimate the disturbance term of the system. Moreover, by means of combining model predictive control and CFDL digital integral terminal sliding mode control (CFDL-DITSMC), the CFDL digital integral terminal sliding mode predictive control (CFDL-DITSMPC) method is proposed, which can further improve the tracking accuracy and disturbance rejection performance in comparison with the CFDL model-free adaptive control, neural network quasi-sliding mode control and the CFDL-DITSMC scheme. Meanwhile, the stability of the proposed approach is guaranteed by theoretical analysis, and the effectiveness of the proposed method is also illustrated by numerical simulations and the experiment on the two-tank water level control system.

Data-Driven Model-Free Adaptive Control Based on Error Minimized Regularized Online Sequential Extreme Learning Machine

Model-free adaptive control (MFAC) builds a virtual equivalent dynamic linearized model by using a dynamic linearization technique. The virtual equivalent dynamic linearized model contains some time-varying parameters, time-varying parameters usually include high nonlinearity implicitly, and the performance will degrade if the nonlinearity of these time-varying parameters is high. In this paper, first, a novel learning algorithm named error minimized regularized online sequential extreme learning machine (EMREOS-ELM) is investigated. Second, EMREOS-ELM is used to estimate those time-varying parameters, a model-free adaptive control method based on EMREOS-ELM is introduced for single-input single-output unknown discrete-time nonlinear systems, and the stability of the proposed algorithm is guaranteed by theoretical analysis. Finally, the proposed algorithm is compared with five other control algorithms for an unknown discrete-time nonlinear system, and simulation results show that the proposed algorithm can improve the performance of control systems.

Prescribed Performance Model-Free Adaptive Integral Sliding Mode Control for Discrete-Time Nonlinear Systems

This paper studies the data-driven prescribed performance control (PPC) problem for a class of discrete-time nonlinear systems in the presence of tracking error constraints. By using the equivalent dynamic linearization technique and constructing a novel transformed error strategy, an adaptive integral sliding mode controller is designed such that the tracking error converges to a predefined neighborhood. Meanwhile, the presented control scheme can effectively ensure that the convergence rate is less than a predefined value and maximum overshoot is not smaller than a preselected constant. In addition, better tracking performance can be achieved by regulating the design parameters appropriately, which is more preferable in the practical application. Contrary to the existing PPC results, the new proposed control law does not use either the plant structure or any knowledge of system dynamics. The efficiency of the proposed control approach is shown with two simulated examples.

Adaptive-Observer-Based Data Driven Voltage Control in Islanded-Mode of Distributed Energy Resource Systems

In this paper, an adaptive observer based data driven control scheme is proposed for the voltage control of dispatchable distributed energy resource (DER) systems which work in islanded operation. In the design procedure of the proposed control scheme, we utilize the novel transformation and linearization technique for the islanded DER system dynamics, which is proper for the proposed data driven control algorithm. Moreover, the pseudo partial derivative (PPD) parameter matrix can be estimated online by multiple adaptive observers. Then, the adaptive constrained controller is designed only based on the online identification results derived from the input/output (I/O) data of the controlled DER system. It is theoretically proven that all the signals in the closed-loop control system are uniformly ultimately bounded based on the Lyapunov stability analysis approach. In addition, the results of the simulation comparison are given to verify the voltage control effect of the proposed control scheme.

Nonlinear Decoupling Control With ANFIS-Based Unmodeled Dynamics Compensation for a Class of Complex Industrial Processes

Complex industrial processes are multivariable and generally exhibit strong coupling among their control loops with heavy nonlinear nature. These make it very difficult to obtain an accurate model. As a result, the conventional and data-driven control methods are difficult to apply. Using a twin-tank level control system as an example, a novel multivariable decoupling control algorithm with adaptive neural-fuzzy inference system (ANFIS)-based unmodeled dynamics (UD) compensation is proposed in this paper for a class of complex industrial processes. At first, a nonlinear multivariable decoupling controller with UD compensation is introduced. Different from the existing methods, the decomposition estimation algorithm using ANFIS is employed to estimate the UD, and the desired estimating and decoupling control effects are achieved. Second, the proposed method does not require the complicated switching mechanism which has been commonly used in the literature. This significantly simplifies the obtained decoupling algorithm and its realization. Third, based on some new lemmas and theorems, the conditions on the stability and convergence of the closed-loop system are analyzed to show the uniform boundedness of all the variables. This is then followed by the summary on experimental tests on a heavily coupled nonlinear twin-tank system that demonstrates the effectiveness and the practicability of the proposed method.

Lazy-Learning-Based Data-Driven Model-Free Adaptive Predictive Control for a Class of Discrete-Time Nonlinear Systems

In this paper, a novel data-driven model-free adaptive predictive control method based on lazy learning technique is proposed for a class of discrete-time single-input and single-output nonlinear systems. The feature of the proposed approach is that the controller is designed only using the input-output (I/O) measurement data of the system by means of a novel dynamic linearization technique with a new concept termed pseudogradient (PG). Moreover, the predictive function is implemented in the controller using a lazy-learning (LL)-based PG predictive algorithm, such that the controller not only shows good robustness but also can realize the effect of model-free adaptive prediction for the sudden change of the desired signal. Further, since the LL technique has the characteristic of database queries, both the online and offline I/O measurement data are fully and simultaneously utilized to real-time adjust the controller parameters during the control process. Moreover, the stability of the proposed method is guaranteed by rigorous mathematical analysis. Meanwhile, the numerical simulations and the laboratory experiments implemented on a practical three-tank water level control system both verify the effectiveness of the proposed approach.

Dual RBFNNs-Based Model-Free Adaptive Control With Aspen HYSYS Simulation

In this brief, we propose a new data-driven model-free adaptive control (MFAC) method with dual radial basis function neural networks (RBFNNs) for a class of discrete-time nonlinear systems. The main novelty lies in that it provides a systematic design method for controller structure by the direct usage of I/O data, rather than using the first-principle model or offline identified plant model. The controller structure is determined by equivalent-dynamic-linearization representation of the ideal nonlinear controller, and the controller parameters are tuned by the pseudogradient information extracted from the I/O data of the plant, which can deal with the unknown nonlinear system. The stability of the closed-loop control system and the stability of the training process for RBFNNs are guaranteed by rigorous theoretical analysis. Meanwhile, the effectiveness and the applicability of the proposed method are further demonstrated by the numerical example and Aspen HYSYS simulation of distillation column in crude styrene produce process.

Online Learning ARMA Controllers With Guaranteed Closed-Loop Stability

This paper presents a novel online block adaptive learning algorithm for autoregressive moving average (ARMA) controller design based on the real data measured from the plant. The method employs ARMA input-output models both for the plant and the resulting closed-loop system. In a sliding window, the plant model parameters are identified first offline using a supervised learning algorithm minimizing an ε -insensitive and regularized identification error, which is the window average of the distances between the measured plant output and the model output for the input provided by the controller. The optimal controller parameters are then determined again offline for another sliding window as the solution to a constrained optimization problem, where the cost is the ε -insensitive and regularized output tracking error and the constraints that are linear inequalities of the controller parameters are imposed for ensuring the closed-loop system to be Schur stable. Not only the identification phase but also the controller design phase uses the input-output samples measured from the plant during online learning. In the developed online controller design method, the controller parameters can always be kept in a parameter region providing Schur stability for the closed-loop system. The ε -insensitiveness provides robustness against disturbances, so does the regularization better generalization performance in the identification and the control. The method is tested on benchmark plants, including the inverted pendulum and dc motor models. The method is also tested on an emulated and also a real dc motor by online block adaptive learning ARMA controllers, in particular, Proportional-Integral-Derivative controllers.