Echo State Network-Based Backstepping Adaptive Iterative Learning Control for Strict-Feedback Systems: An Error-Tracking Approach

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.

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.

Fault-tolerant control for nonlinear systems with a dead zone: Reinforcement learning approach

This paper focuses on the adaptive reinforcement learning-based optimal control problem for standard nonstrict-feedback nonlinear systems with the actuator fault and an unknown dead zone. To simultaneously reduce the computational complexity and eliminate the local optimal problem, a novel neural network weight updated algorithm is presented to replace the classic gradient descent method. By utilizing the backstepping technique, the actor critic-based reinforcement learning control strategy is developed for high-order nonlinear nonstrict-feedback systems. In addition, two auxiliary parameters are presented to deal with the input dead zone and actuator fault respectively. All signals in the system are proven to be semi-globally uniformly ultimately bounded by Lyapunov theory analysis. At the end of the paper, some simulation results are shown to illustrate the remarkable effect of the proposed approach.

Growing Echo State Network With an Inverse-Free Weight Update Strategy

An echo state network (ESN) draws widespread attention and is applied in many scenarios. As the most typical approach for solving the ESN, the matrix inverse operation of high computational complexity is involved. However, in the modern big data era, addressing the heavy computational burden problem is necessary. In order to reduce the computational load, an inverse-free ESN (IFESN) is proposed for the first time in this article. Besides, an incremental IFESN is constructed to attain the network topology with theoretical proof on the training error's monotone decline property. Simulations and experiments are conducted on several numerical and real-world time-series benchmarks, and corresponding results indicate that the proposed model is superior to some existing models and possesses excellent practical application potential. The source code is publicly available at https://github.com/LongJin-lab/the-supplementary-file-for-CYB-E-2021-04-0944.

Iterative Rectifying Methods for Nonrepetitive Continuous-Time Learning Control Systems

To implement iterative learning control (ILC), one of the most fundamental hypotheses is the strict repetitiveness (i.e., iteration-independence) of the controlled systems, especially of their plant models. This hypothesis, however, results in difficulties of developing theoretic analysis methods and promoting practical applications for ILC, especially in the presence of continuous-time systems, which is the motivation of the current paper to cope with robust tracking problems of continuous-time ILC systems subject to nonrepetitive (i.e., iteration-dependent) uncertainties. Based on integrating an iterative rectifying mechanism, continuous-time ILC can effectively address the ill effects of the multiple nonrepetitive uncertainties that arise from the system models, initial states, load and measurement disturbances, and desired references. Furthermore, a robust convergence analysis method is presented for continuous-time ILC by combining a contraction mapping-based method and a system equivalence transformation method. It is disclosed that regardless of continuous-time ILC systems with zero or nonzero system relative degrees, the robust tracking tasks in the presence of nonrepetitive uncertainties can be accomplished, together with the boundedness of all the system trajectories being ensured. Two examples are included to verify the validity of our robust tracking results for nonrepetitive continuous-time ILC systems.

Funnel tracking control for nonlinear servo drive systems with unknown disturbances

In this paper, a novel robust tracking control strategy based on funnel control is proposed for servo drive systems with unknown disturbances. A modified funnel variable is defined and incorporated into the control design to guarantee the tracking error within a prescribed boundary. To reject the bounded disturbances, a robust integral of the sign of the error (RISE) controller based on the funnel variable is proposed for servo drive systems. Moreover, the desired compensation technique is incorporated into the developed controller to reduce the sensor noise. The proposed robust controller theoretically guarantees asymptotic tracking control performance with external disturbances. The closed-loop system convergence is analyzed via the Lyapunov stability theory. Comparative numerical and experimental results of the servo drive system are provided.

Evolutionary optimization assisted delayed deep cycle reservoir modeling method with its application to ship heave motion prediction

As one emerging reservoir modeling method, cycle reservoir with regular jumps (CRJ) provides one effective tool for many time series analysis tasks such as ship heave motion prediction. However, the shallow learning structure of single CRJ model limits its memory capacity and leads to unsatisfactory prediction performance. In order to pursue the stronger dynamic characteristic description of time series data, a delayed deep CRJ model is presented in this paper by integrating the deep learning framework with delay links and the evolutionary optimization for mixed-integer problem. Different from the basic CRJ model with only one reservoir, delayed deep CRJ builds multiple serial reservoirs with inserting the delay links between adjacent reservoirs. Due to the design of dynamic deep learning structure, the memory capacity is enlarged to improve ship heave motion prediction. Aiming at the mix-integer optimization problem in delayed deep CRJ model, a heuristic evolutionary optimization scheme based on the stepwise differential evolution algorithm is applied to determine the delayed deep CRJ parameters automatically. The stepwise differential evolution assisted delayed deep CRJ model can avoid the non-optimal solution resulted from the manual parameter setting effectively. Finally, one numerical example and the real experiment data are utilized to validate the methods and the results demonstrate that delayed deep CRJ model has better prediction performance in contrast to the basic CRJ method.

A Fuzzy System Based Iterative Learning Control for Nonlinear Discrete-Time Systems with Iteration-Varying Uncertainties

In this paper, we consider an iterative learning control problem for a class of unknown discrete-time nonlinear systems with iteration-varying initial error, iteration-varying system parameters, iteration-varying external disturbance, iteration-varying desired output, and iteration-varying control direction. These iteration-varying uncertainties are not required to take any particular structure such as the high-order internal model and only need to satisfy certain boundedness conditions. We propose an iterative learning control law with an adaptive iteration-varying fuzzy system to overcome all the uncertainties and achieve the learning control objective. Furthermore, we present a sufficient condition for designing adaptive gains and prove the convergence of the learning error to a small value as the trial number is large enough. Finally, we use two simulation examples to demonstrate all the theoretical results.

Echo State Networks for Practical Nonlinear Model Predictive Control of Unknown Dynamic Systems

Nonlinear model predictive control (NMPC) of industrial processes is changeling in part because the model of the plant may not be completely known but also for being computationally demanding. This work proposes an extremely efficient reservoir computing (RC)-based control framework that speeds up the NMPC of processes. In this framework, while an echo state network (ESN) serves as the dynamic RC-based system model of a process, the practical nonlinear model predictive controller (PNMPC) simplifies NMPC by splitting the forced and the free responses of the trained ESN, yielding the so-called ESN-PNMPC architecture. While the free response is generated by the forward simulation of the ESN model, the forced response is obtained by a fast and recursive calculation of the input-output sensitivities from the ESN. The efficiency not only results from the fast training inherited by RC but also from a computationally cheap control action given by the aforementioned novel recursive formulation and the computation in the reduced dimension space of input and output signals. The resulting architecture, equipped with a correction filter, is robust to unforeseen disturbances. The potential of the ESN-PNMPC is shown by application to the control of the four-tank system and an oil production platform, outperforming the predictive approach with a long-short term memory (LSTM) model, two standard linear control algorithms, and approximate predictive control.

Asymptotic Tracking Control for Uncertain MIMO Systems: A Biologically Inspired ESN Approach

In this study, a biologically inspired echo state network (ESN)-based method is established for the asymptotic tracking control of a class of uncertain multi-input multi-output (MIMO) systems. By mimicking the characters of real biological systems, a diversified multiclustered echo state network (DMCESN) is proposed in this work and then it is applied to deal with the modeling uncertainties and coupling nonlinearities in the control systems. Different from the most existing neural network (NN)-based control methods that only ensure the uniform ultimate boundedness result, the proposed method can allow the tracking error to achieve asymptotic convergence through rigorous theoretical analysis. The effectiveness of the proposed method is also confirmed by numerical simulation by comparing with multilayer feedforward network-based control scheme and traditional ESN-based control, admitting better tracking performance of the proposed control.

Neural-Network-Based Adaptive Singularity-Free Fixed-Time Attitude Tracking Control for Spacecrafts

In this article, a neural-network-based adaptive fixed-time control scheme is proposed for the attitude tracking of uncertain rigid spacecrafts. A novel singularity-free fixed-time switching function is presented with the directly nonsingular property, and by introducing an auxiliary function to complete the switching function in the controller design process, the potential singularity problem caused by the inverse of the error-related matrix could be avoided. Then, an adaptive neural controller is developed to guarantee that the attitude tracking error and angular velocity error can both converge into the neighborhood of the equilibrium within a fixed time. With the proposed control scheme, no piecewise continuous functions are required any more in the controller design to avoid the singularity, and the fixed-time stability of the entire closed-loop system in the reaching phase and sliding phase is analyzed with a rigorous theoretical proof. Comparative simulations are given to show the effectiveness and superiority of the proposed scheme.

Neural Control of Robot Manipulators With Trajectory Tracking Constraints and Input Saturation

This article presents a control scheme for the robot manipulator's trajectory tracking task considering output error constraints and control input saturation. We provide an alternative way to remove the feasibility condition that most BLF-based controllers should meet and design a control scheme on the premise that constraint violation possibly happens due to the control input saturation. A bounded barrier Lyapunov function is proposed and adopted to handle the output error constraints. Besides, to suppress the input saturation effect, an auxiliary system is designed and emerged into the control scheme. Moreover, a simplified RBFNN structure is adopted to approximate the lumped uncertainties. Simulation and experimental results demonstrate the effectiveness of the proposed control scheme.

Adaptive fuzzy PID cross coupled control for multi-axis motion system based on sliding mode disturbance observation

Multi-axis motion system is widely applied in commercial industrial machines such as precision CNC machine tools, Robot manipulator and laser cutting machines, etc. Contour accuracy plays a major role for the multi-axis servo motion system. The contour machining accuracy is related to the synthesis of single-axis position accuracy and multi-axis linkage accuracy. Only improving the single-axis tracking performance cannot effectively guarantee the machining accuracy of multi-axis system. The primary objective of this study was to design a contour control method to improve single-axis tracking accuracy and multi-axis contour accuracy. A control strategy that combines a sliding mode tracking controller, a disturbance observer and an adaptive fuzzy PID cross coupled controller is proposed. Sliding mode control is simple and has strong robustness to parameter changes and disturbance, which is especially suitable for control of such as non-linear multi-axis motion system. Besides, disturbance is inevitable in practical application, which degrades the motion accuracy. In order to eliminate the influence of external disturbance and uncertainty, disturbance observer is adopted to accurately estimate external disturbance and reduce the chattering phenomenon of sliding mode control, then improve the single-axis tracking accuracy. In order to further consider the coordination between different motion axes and improve the contour accuracy, the PID cross coupled control is used. Owing to conventional PID control cannot satisfy the multi-axis servo motion system with nonlinearity and uncertainty, an adaptive fuzzy method with on-line real-time PID parameters adjustment is proposed. The three-axis motion platform driven by PMLSM is used as the control object, to analysis the influence of disturbance observer on sliding mode control signal and analysis adaptive fuzzy PID cross coupled control performance respectively. The disturbance observer is used to observe the disturbance signal and estimate the disturbance well. The chattering of the sliding mode control signal is obviously improved. Next, compared with the conventional PID-CCC control, adaptive fuzzy PID- CCC control can significantly reduce the tracking error, the contour accuracy is also obviously improved. The disturbance observer can effectively eliminate the influence of external disturbance, reduce the chattering of sliding mode control, and ensure the single-axis accurate tracking. The self-adaptive fuzzy PID cross coupled controller can eliminate the influence of the dynamic characteristics mismatching and parameter difference of each axis, and improve contour accuracy. The simulation results clearly demonstrate the effectiveness of the proposed control method.

NN Reinforcement Learning Adaptive Control for a Class of Nonstrict-Feedback Discrete-Time Systems

This article investigates an adaptive reinforcement learning (RL) optimal control design problem for a class of nonstrict-feedback discrete-time systems. Based on the neural network (NN) approximating ability and RL control design technique, an adaptive backstepping RL optimal controller and a minimal learning parameter (MLP) adaptive RL optimal controller are developed by establishing a novel strategic utility function and introducing external function terms. It is proved that the proposed adaptive RL optimal controllers can guarantee that all signals in the closed-loop systems are semiglobal uniformly ultimately bounded (SGUUB). The main feature is that the proposed schemes can solve the optimal control problem that the previous literature cannot deal with. Furthermore, the proposed MPL adaptive optimal control scheme can reduce the number of adaptive laws, and thus the computational complexity is decreased. Finally, the simulation results illustrate the validity of the proposed optimal control schemes.