Multi-dimensional Taylor Network Research Articles

Adaptive asymptotic tracking control of constrained nonlinear MIMO systems subject to unknown hysteresis input: A novel network-based strategy

This paper presents a referential adaptive asymptotic tracking control scheme for nonlinear multi-input and multi-output (MIMO) systems with time-varying full-state constraints and unknown hysteresis input. In order to achieve good asymptotic tracking effect, a zero-limit positive continuous function is introduced into the adaptive backstepping design process while thoroughly considering the impact of disturbance-like terms on the tracking effect. Additionally, a new variable is also imported to replace the reciprocal of unknown coefficient of the Bouc–Wen hysteresis model. Then, a new adaptive law about the new variable is added by combining the positive function, which can not only lessen the impact of the unknown hysteresis input on the tracking effect, but also avoid the “singularity” problem. Aiming at the time-varying full-state constraints, a appropriate time-varying log-type barrier Lyapunov function (TLBLF) is constructed to ensure that all the states of the system are restricted within the constraint scope. Finally, a significant adaptive asymptotic tracking scheme is designed based on multi-dimensional Taylor network (MTN) approximation technology. Apart from achieving high-precision asymptotic tracking performance, the proposed scheme ensures the boundedness of all signals of the closed-loop system without violating the full-state constraints. And, three simulations are given to verify the effectiveness of the scheme.

A Finite-Time Path Tracking Control Scheme for Unmanned Vehicles Based on Multidimensional Taylor Network and Adaptive Filtering

Aiming at the path tracking control problem of unmanned vehicles under the conditions of model uncertainty and measurement noise, a finite-time path tracking control scheme based on multidimensional Taylor network (MTN) is proposed. The MTN model is used to characterize the uncertainty of the unmanned vehicle model, and the improved back propagation (BP) algorithm is used as its learning algorithm; an adaptive MTN filter is designed to filter out the measurement noise, MTN is used as a filter, and the least mean square (LMS) algorithm is used as its learning algorithm; an MTN finite-time controller is designed to perform precise path tracking control on the unmanned vehicle, which can quickly and accurately track the reference path; according to the finite-time control theory, the convergence proof verifies the effectiveness of the proposed method through unmanned vehicle simulation experiments.

Composite anti-disturbance predictive control of unmanned systems with time-delay using multi-dimensional Taylor network

A composite anti-disturbance predictive control strategy employing a Multi-dimensional Taylor Network (MTN) is presented for unmanned systems subject to time-delay and multi-source disturbances. First, the multi-source disturbances are addressed according to their specific characteristics as follows: (A) an MTN data-driven model, which is used for uncertainty description, is designed accompanied with the mechanism model to represent the unmanned systems; (B) an adaptive MTN filter is used to remove the influence of the internal disturbance; (C) an MTN disturbance observer is constructed to estimate and compensate for the influence of the external disturbance; (D) the Extended Kalman Filter (EKF) algorithm is utilized as the learning mechanism for MTNs. Second, to address the time-delay effect, a recursive τ−step-ahead MTN predictive model is designed utilizing recursive technology, aiming to mitigate the impact of time-delay, and the EKF algorithm is employed as its learning mechanism. Then, the MTN predictive control law is designed based on the quadratic performance index. By implementing the proposed composite controller to unmanned systems, simultaneous feedforward compensation and feedback suppression to the multi-source disturbances are conducted. Finally, the convergence of the MTN and the stability of the closed-loop system are established utilizing the Lyapunov theorem. Two exemplary applications of unmanned systems involving unmanned vehicle and rigid spacecraft are presented to validate the effectiveness of the proposed approach.

State of charge estimation for the lithium-ion battery based on fractional-order multi-dimensional Taylor network

To accurately estimate the state of charge (SOC) of the lithium-ion battery (LiB), a fractional-order multi-dimensional Taylor network (FMTN) model was proposed in the study. With two open datasets of LiBs, the performance of the FMTN model on the SOC estimation is evaluated and compared with multi-dimensional Taylor network (MTN), back propagation neural network (BPNN), and dual-stage attention gate recurrent unit neural network (DA-GRUNN) models. With the datasets of B0005 and B0006 LiBs, the SOC estimation accuracy of the FMTN-6 model is 34 %, 32 %, and 37 %, 45 % higher than that of the MTN-6 and BPNN-3 models, respectively. The estimation time consumptions of the FMTN-6 model are increased by 2.8 % and 3.9 % and reduced by 49.5 % and 52.8 % compared with that of the MTN-6 and BPNN-3 models, respectively. With the open dataset of real driving conditions, the root-mean-square error of the SOC estimation of the FMTN model is reduced by 48 % compared with that of the MTN model. Besides, with the datasets at 25 °C and 45 °C, the SOC estimation accuracy of the FMTN model is improved by 17 % and 18 % compared with that of the DA-GRUNN model, respectively.

Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation

Aiming at the problems of identification difficulties and low identification accuracy in modelling and identification of multiple-input multiple-output (MIMO) nonlinear Gaussian time-varying systems, this paper proposes an identification scheme based on the step-by-step approximation of multidimensional Taylor network (MTN). The aim of this paper is to improve the modelling of complex nonlinear systems so as to improve the prediction performance and control effect of the system. Different from the traditional multidimensional Taylor network identification method, this method adopts an order-by-order approximation strategy, which seeks its parameters sequentially from the lower order to the higher order, and continuously optimises the parameter weights during the parameter seeking process. Firstly, the nonlinear function model is approximated as a polynomial form by the order-by-order Taylor expansion, and then the weight parameters of each order of the Taylor expansion are calculated and updated step by step by using the algorithm based on the Variable Forgetting Factor Recursive Least Squares (VFF-RLS) method. Through iterative optimized of these parameters, dynamic weight assignment to each order of the Taylor expansion is achieved. A parameter-identified nonlinear function model is finally obtained, which can more accurately describe the dynamic behaviour and characteristics of the system. Finally, an arithmetic simulation is carried out through an example to verify the effectiveness of the proposed method.

Adaptive fixed-time tracking control for nonlinear systems subject to asymmetric input saturation

For nonlinear systems with asymmetric input saturation, an adaptive fixed-time control strategy via multi-dimensional Taylor network (MTN) is proposed to effectively solve the tracking control problem. Firstly, the Gaussian error function and the differential mean value theorem are used to simulate the asymmetric input saturation model, that is, the nonlinear model is transformed into a linear model with a bounded perturbation. Secondly, MTNs are applied to control the design process, which approximate the nonlinear structures with linear combination of polynomials. Thirdly, in addition to the tracking error converging to an arbitrarily small neighborhood around the origin within a fixed time, the proposed control scheme not only guarantees that any signal in the controlled system remains bounded, but also avoids the problem of finite-time control relying on the initial state. Finally, three examples are used to validate the feasibility and superiority of the scheme.

Adaptive finite‐time tracking control of nonlinear systems subject to input hysteresis and multiple objective constraints

AbstractIn this article, the problem of adaptive finite‐time tracking control for a class of nonlinear systems subject to backlash‐like input hysteresis and multiple objective constraints is investigated. For the purpose of realizing multiple objective constraints, a new time‐varying barrier function (TVBF) is introduced to ensure that all objective constraint functions are always within the defined range. Meanwhile, based on the combination of the command filter approach and adaptive backstepping control, an error compensation system (ECS) is supplied to reduce the impact of filter error on control performance. Additionally, the problem of “singularity” caused by hysteresis is avoided by linearizing the backlash‐like hysteresis model, and Nussbaum‐type function is also applied to reduce the influence of hysteresis on the stability of the system. Then, by combining multi‐dimensional Taylor network (MTN) technology and command filter backstepping approach, an adaptive finite‐time control strategy is designed. The proposed control strategy ensures that all the signals in the closed‐loop system realize finite‐time semi‐globally uniformly ultimately bounded (SGUUB), and the output signal of the system can track the reference signal greatly while adhering to multiple objective constraints. Finally, the effectiveness of the proposed control strategy is verified by a practical simulation example.

Adaptive Multi-Switching-Based Global Tracking Control for Switched Nonlinear Systems With Prescribed Performance

This paper is concerned with the tracking control for a class of switched nonlinear systems subject to prescribed performance. Firstly, a barrier function and a normalized function are introduced to achieve prescribed performance control, which ensures that the tracking error evolves within prescribed boundary. Then, multi-dimensional Taylor network provides a new approach for how to estimate the nonlinearity arising from the backstepping control process. Significantly, the proposed multi-switching-based adaptive controller realizes that all signals in the closed-loop system are globally uniformly ultimately bounded while ensuring asymptotic tracking. Different from most existing network-approximation-based control strategies, the developed method in this paper is not only independent of the initial state, but also can achieve global stability. Finally, it is easy to verify the effectiveness of the proposed control method through two simulations. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This research is motivated by the fact that the control ideas of many practical engineering systems can be provided by making a profound study on switched nonlinear systems. However, most of the existing results focused on semi-global stability of systems. Therefore, this study devotes to develop a novel adaptive prescribed performance control strategy, which can not only ensure global stability of closed-loop system but also realize the asymptotic tracking of the switched nonlinear systems. It is worth noting that the proposed control approach has great significance for many practical systems, such as circuit systems and single-link inverted pendulum systems.

A two-stage fault diagnosis strategy for air handling units via a backpropagation multidimensional Taylor network fitter and a novel statistical process control

Faults in Heating, Ventilation, and Air Conditioning Air Handling Units can lead to increased energy consumption and failure to meet human comfort standards. Accurate and prompt fault diagnosis of Air Handling Units is therefore critical. Although widely-used deep learning methods have shown high precision in fault diagnosis, they present two main drawbacks: 1) deep learning approaches are often “black box” models lacking interpretability and rely on labeled data; 2) their complex structures entail substantial computational resources, which may not be conducive to timely fault diagnosis. To overcome these challenges, this paper introduces a method for diagnosing faults in air handling units that combines a novel statistical process control strategy, a backpropagation multidimensional Taylor network fitter, and a D-matrix approach. The backpropagation multidimensional Taylor network, using a polynomial network with only one hidden layer, approximates nonlinear functions. Compared to deep learning models, it maintains high accuracy with a simpler structure, enabling rapid fault diagnosis. Additionally, the novel statistical process control strategy employs the Markov property for fault detection, characterized by low false alarm rates, interpretability, robustness, minimal labeled data requirements, and suitability for real-time monitoring. Experimental results validate the effectiveness of our method in diagnosing faults in air handling units, achieving an average precision of 99.9%, surpassing several commonly used techniques.

Adaptive prescribed performance tracking control for uncertain nonlinear systems with unknown backlash-like hysteresis

In this paper, an adaptive prescribed performance tracking control(PPTC) problem of uncertain nonlinear systems with unknown hysteresis input is investigated. For the purpose of implementing the PPTC, a performance function and an error conversion function are introduced. Moreover, a backlash-like hysteresis model is adopted to describe the hysteresis nonlinearity, which makes the controller design feasible. Additionally, by converting the backlash-like hysteresis model into a linear model with bounded error, the difficulties caused by hysteresis behavior on controller design are settled. Thus, integrating multi-dimensional Taylor network(MTN) approximation technique into adaptive backstepping method, an adaptive control scheme for uncertain nonlinear systems is proposed. Apart from ensuring that all signals of the closed-loop system keep bounded, the proposed control scheme not only makes the tracking error converge to an arbitrarily small neighborhood around the origin, but also guarantees the tracking error trajectory within the limits set by PPTC. Ultimately, two simulations are applied to verify the validity of the proposed control scheme.

Dynamic event-triggered adaptive tracking control for stochastic nonlinear systems with deferred time-varying constraints

This article investigates the problem of adaptive tracking control for stochastic nonlinear systems with deferred state constraints. The novel unified universal barrier function (UUBF) and deferred funnel error transformation are developed to handle various state constraints and adjust the tracking error more precisely, respectively. Multi-dimensional Taylor network (MTN) and dynamic event-triggered mechanism (DETM) are employed to design controller in the backstepping process, which can achieve full-state constraints and the tracking control after the preassigned time while conserving more communication resources. Finally, two simulation examples are presented to verify the effectiveness of the proposed control scheme.

Adaptive multi-dimensional Taylor network tracking control of time-varying delay nonlinear systems subject to input saturation

For the tracking control problem of a class of nonlinear systems with input saturation constraint and time-varying delay, an adaptive tracking control scheme based on multi-dimensional Taylor network (MTN) is designed, and the proposed control scheme has the advantages of simple structure and small computation. A Gaussian error function is introduced to transform the input saturation into a linear model with bounded error. The Lyapunov-Krasovskii function is constructed, and the nonlinearity of the system is approximated using MTN, and an adaptive control strategy is constructed based on the backstepping method. The results show that the proposed control method can both ensure that all signals in the closed-loop system are bounded and achieve convergence of the tracking error to a small neighborhood near the origin. Numerical simulations verify the effectiveness of the method.

Multi-dimensional Taylor network-based adaptive fixed-time tracking control for a class of nonlinear systems with input delay

For the nonlinear systems with input delay, an adaptive fixed-time tracking control strategy based on multi-dimensional Taylor network (MTN) is proposed for the first time. First, to address the main challenge brought by input delay, an auxiliary system is constructed, which transforms the input delay systems into non-delay systems. Second, the MTNs are introduced into the backstepping design process, which reduce the design difficulty by approximating unknown nonlinear functions. Thus, a control scheme subject to low complexity is obtained. Third, aside from ensuring that the tracking error converges within a small neighbourhood of the origin within a fixed-time, the designed control scheme not only makes all signals in the closed-loop system remain bounded, but also avoids the problem of finite-time control relying on initial state. Finally, three simulations are given to prove the feasibility and superiority of the proposed control scheme.

Adaptive finite‐time control for a class of stochastic nonlinear systems with input saturation constraints: A new approach based on multidimensional Taylor network

AbstractThis article proposes a novel multidimensional Taylor network (MTN)‐based adaptive finite‐time control approach for stochastic nonlinear systems with input saturation constraints. First, by introducing the hyperbolic tangent function, a piecewise smooth function is proposed to approximate the input saturation constraints, which can solve the problem caused by input saturation. Then, with the aid of MTN approximation theorem, a novel adaptive finite‐time control approach is proposed, which can guarantee that all signals of the closed‐loop system are semi‐globally finite‐time stability in probability (SGFTSP), the system output follows the given reference signal, meanwhile, the tracking error converges to a small neighborhood of the origin in finite‐time. Compared with the existing results, the proposed approach has the characteristics of simple structure and low calculation, which can achieve the satisfactory control performance with a reduced computational burden. In the end, the effectiveness of the proposed approach is validated by Lyapunov stability theory and two simulation experiments.

A novel network-based adaptive fault-tolerant control of switched nonlinear systems subject to multiple faults under prescribed performance

It is the first report about fault-tolerant-based prescribed performance control of switched nonlinear systems under multiple faults. The concerned faults include not only external faults but also actuator faults. In the process of backstepping control design, prescribed performance control is fully considered, and the combination of unknown nonlinear functions is estimated by multi-dimensional Taylor network. Finally, the developed adaptive fault-tolerant control strategy guarantees the boundedness of all controlled signals while prescribed tracking performance is satisfied. In an effort to further manifest the validity of the fault-tolerant controller, a numerical simulation and a practical simulation are introduced.

Contraction-Based Stochastic Model Predictive Control for Nonlinear Systems With Input Delay Using Multidimensional Taylor Network

For nonlinear systems with stochastic uncertainties and input delay, the existing control approaches based on the robust mechanism are generally conservative in most practical scenarios. Within this context, a stochastic model predictive control (MPC) scheme based on uncertainty contraction is proposed here to reduce conservativeness and improve real-time performance. In terms of the Lyapunov-Razumikhin theorem, a robust variational controller (RVC) is deduced as the primary controller for the variational dynamic with input delay. A variational vector field in Wasserstein metric space is constructed to detect the minimum geodesic between the uncertainty distribution and the desired one. Integrating RVC along the minimum geodesic, the modified auxiliary controller is developed for tracking the nominal trajectory with less conservatism. Subsequently, the chance constraints of stochastic states are transformed into the deterministic quantile constraints of nominal states. The sparse multi-dimensional Taylor network based on Bayesian compressive sensing is designed to parameterize the ambiguity set in Wasserstein metric space for higher computational efficiency.A tractable MPC scheme is then formulated to achieve the reference index with an improved trade-off between robustness and real-time performance.The stochastic input-to-state stability of the considered system is verified theoretically by the Lyapunov-Krasovskii theorem. The effectiveness of the proposed scheme is confirmed by a numerical simulation derived from a practical industrial process.

Adaptive Multi-Dimensional Taylor Network Tracking Control for a Class of Nonlinear Strict Feedback Systems

Nonlinear systems are very common in real life, but because they are not superposed and homogeneous, there are many difficulties in controlling nonlinear systems. Therefore, an adaptive control method based on a multi-dimensional Taylor network (MTN) is proposed for a class of nonlinear systems with strict feedback so that the output of the system can track the given signal. In order to achieve the control effect, we define a new state variable and transform the strict feedback system. After transformation, the original feedback system has a standard form, and two parameters to be identified are obtained. Then, the state observer is designed, and the two parameters are identified via the approximation of the MTN. On this basis, the controller design and a system stability analysis are completed. The lemma is introduced, and the stability condition is established by using this low-pass filter to ensure that all closed-loop signals are semi-globally uniform and finally bounded and the output tracking error converges to the residual set near zero. Finally, a numerical simulation of a hydraulic system is carried out to verify the effectiveness of the proposed method. Under the three indexes, the proposed method has obvious advantages.

Adaptive tracking control for stochastic nonlinear state-constrained systems with input delay based on multi-dimensional Taylor network

In this paper, an adaptive tracking control strategy based on multi-dimensional Taylor network (MTN) is proposed for a class of stochastic nonlinear state-constrained systems with input delay. Firstly, to avoid constraint violation, the adaptive backstepping approach and barrier Lyapunov function (BLF) are combined in a unified framework. Then, a suitable auxiliary system with the same order as the considered system is constructed to deal with the effect of input delay. In addition, MTN is used to estimate unknown nonlinear functions during the design of the controller. Furthermore, with the help of the Lyapunov stability theorem, the controller presented in this paper can guarantee that all the closed-loop signals are bounded in probability, the system states remain in the defined compact sets, the output signal can track the reference signal successfully, and the tracking error is bounded by the expected bound. Finally, two examples are given to verify the effectiveness of the designed scheme.

Adaptive Robust Control of an Industrial Motor-Driven Stage with Disturbance Rejection Ability Based on Multidimensional Taylor Network

Linear motors are widely used in practical engineering fields, but it is difficult to achieve accurate position control because of model uncertainty, external interference, input nonlinearity and other factors. In this paper, a multidimensional Taylor network (MTN) controller with flexible learning robustness is proposed to realize tracking control and make the motor have excellent antijamming ability. The controller is composed of a robust feedback part, a parameter adaptive part and a multidimensional Taylor network control part. This strategy has good track tracking performance and anti-interference ability. In this control strategy, the input of the multidimensional Taylor network is determined only by the referable trajectories, and no model information is required. In addition, the designed multidimensional Taylor network can accurately describe the relationship between state variables and any complex disturbance, which is the basis of disturbance suppression. Finally, the stability of the controller is proved by the Lyapunov theorem. The unknown interference comparison experiment and numerical simulation experiment are carried out on the industrial linear motor platform, respectively. Experimental results show that compared with NNPID, the proposed algorithm has smaller overshoot and better performance under various error statistical dimensions.

Recursive d-step-ahead predictive control of MIMO nonlinear systems with input time-delay via multi-dimensional Taylor network extended from PID

In this paper, a recursive d-step-ahead predictive control scheme based on multi-dimensional Taylor network (MTN) is proposed for the real-time tracking control of multiple-input multiple-output (MIMO) nonlinear systems with input time-delay. The MTN predictive model is designed using a recursive approach to compensate the influence of time-delay, and an extended Kalman filter (EKF) is applied as its learning algorithm. An MTN controller is developed based on a proportional–integral–derivative (PID) controller where the closed-loop errors between the reference input and the system output are set as the MTN controller’s inputs. Then, a back propagation (BP) algorithm, designed to update its weights according to errors caused by system uncertainty, is used as a learning algorithm for the MTN controller. Meanwhile, the convergence of the MTN predictive model and the stability of the closed-loop system are evaluated. Two numerical examples and a practical example – continuous stirred tank reactor (CSTR) process are presented to verify the superiority of the proposed scheme. The experimental results and the computational complexity analysis show that the proposed scheme is effective, promising its desirable robustness, anti-disturbance, tracking and real-time performance.