Multi-dimensional Taylor Network Research Articles

Real-Time Updating High-Order Extended Kalman Filtering Method Based on Fixed-Step Life Prediction for Vehicle Lithium-Ion Batteries.

Lithium-ion batteries have become an important power source in low-carbon transportation energy, and the safe operation and remaining useful life prediction are of great significance. Aiming at the shortcomings of existing methods, such as low prediction accuracy and a short prediction period, this paper proposes a real-time update high-order extended Kalman filter method based on fixed-step life prediction for vehicle lithium batteries based on the principle of combining models and data. First, the state model describing the parameters in the dynamic energy attenuation model is established, and the energy attenuation model is regarded as the observation model of the system to meet the requirements of establishing the Kalman filter. Secondly, the multi-step prediction equation of the state model is established by iterative recursion. At the same time, the multi-step prediction equation between the existing energy output value and the future output value is established based on the multi-dimensional Taylor network (MTN). The multiplicative noise term introduced in the dynamic modeling process is regarded as the hidden variable of the system to meet the requirements of establishing the multi-step linear predictive Kalman filter. Finally, the effectiveness of the new method is verified by digital simulation examples.

Integrated fault detection for industrial process monitoring based on multi-dimensional Taylor network

PurposeThis paper aims to provide a novel integrated fault detection method for industrial process monitoring.Design/methodology/approachA novel integrated fault detection method based on the combination of Mallat (MA) algorithm, weight-elimination (WE) algorithm, conjugate gradient (CG) algorithm and multi-dimensional Taylor network (MTN) dynamic model, namely, MA-WE-CG-MTN, is proposed in this paper. First, MA algorithm is taken as data pre-processing. Second, in virtue of approximation ability and low computation complexity owing to the simple structure of MTN, MTN dynamic models are constructed for each frequency band. Furthermore, the CG algorithm is used to discipline the model parameters and the outputs of MTN model of each frequency band are gained. Third, the authors introduce the WE algorithm to cut down the number of middle layer nodes of MTN, reducing the complexity of the network. Finally, the outputs of MTN model for each frequency band are superimposed to achieve outputs of MTN model, and fault detection is proceeded by the residual error generator based on the difference between the output of MTN model and the actual output.FindingsThe novel proposed method is used to perform fault detection for industrial process monitoring effectively, such as the Benchmark Simulation Model 1 wastewater treatment process.Originality/valueThe novel proposed method has generality and provides considerably improved performance and effectiveness, which is used to perform fault detection for industrial process monitoring. The proposed method has good robustness, low complexity and easy implementation.

Predictive Control for Small Unmanned Ground Vehicles via a Multi-Dimensional Taylor Network

Tracking control of Small Unmanned Ground Vehicles (SUGVs) is easily affected by the nonlinearity and time-varying characteristics. An improved predictive control scheme based on the multi-dimensional Taylor network (MTN) is proposed for tracking control of SUGVs. First, a MTN model is used as a predictive model to construct a SUGV model and back propagation (BP) is taken as its learning algorithm. Second, the predictive control law is designed and the traditional objective function is improved to obtain a predictive objective function with a differential term. The optimal control quantity is given in real time through iterative optimization. Meanwhile, the stability of the closed-loop system is proved by the Lyapunov stability theorem. Finally, a tracking control experiment on the SUGV model is used to verify the effectiveness of the proposed scheme. For comparison, traditional MTN and Radial Basis Function (RBF) predictive control schemes are introduced. Moreover, a noise disturbance is considered. Experimental results show that the proposed scheme is effective, which ensures that the vehicle can quickly and accurately track the desired yaw velocity signal with good real-time, robustness, and convergence performance, and is superior to other comparison schemes.

Multi‐dimensional Taylor network‐based control for a class of nonlinear stochastic systems with full state time‐varying constraints and the finite‐time output constraint

AbstractIn this paper, the adaptive multi‐dimensional Taylor network (MTN) control problem is investigated for nonlinear stochastic systems with full state time‐varying constraints and the finite‐time output constraint. By combining the MTN‐based approximation method and the adaptive backstepping control method, a novel adaptive MTN control scheme is provided by constructing the time‐varying barrier Lyapunov function (TVBLF). To implement the finite‐time output constraint, the finite‐time performance function (FTPF) is introduced in the control scheme. The proposed scheme can ensure that the tracking error finally converges to a small neighborhood of the origin in the finite‐time and all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded (SGUUB) in probability. Finally, two simulation examples are presented to show the effectiveness of the provided control scheme.

Time series forecasting based on a multidimensional Taylor network model with clustering of dynamic characteristics

In view of the difficulty of modelling time-varying nonlinear systems, a multidimensional Taylor network (MTN) model based on dynamic characteristic clustering is proposed to establish an online time series forecasting model. The construction method of a MTN, the definitions of the dynamic characteristics, and their similarity criteria are discussed. Specific steps of the MTN online model, based on dynamic clustering, are given. A practical example is presented to demonstrate how the proposed method works in a real application, and its effectiveness is verified.

Adaptive Tracking Control of a Class of Nonlinear Systems with Input Delay and Dynamic Uncertainties Using Multi-dimensional Taylor Network

Adaptive Tracking Control of a Class of Nonlinear Systems with Input Delay and Dynamic Uncertainties Using Multi-dimensional Taylor Network

Novel adaptive controller design for a class of switched nonlinear systems subject to input delay using multi‐dimensional Taylor network

AbstractFor the tracking control problem of a class of switched nonlinear systems with input delay, this article proposes an adaptive tracking control scheme based on multi‐dimensional Taylor network (MTN) approach. First, Padé approximation and Laplace transform are employed to overcome the problem of input delay, and a new variable is introduced. Second, the MTNs are used to approximate the uncertain nonlinear structures in the process of controller design via backstepping. The results show that the controller designed in this article can keep all the signals in the closed‐loop system are bounded, meanwhile, the output tracking error can be converged to arbitrarily small. It should be pointed out that MTN‐based approach is applied to switched nonlinear systems subject to input delay for the first time. Finally, three examples are presented to verify the effectiveness of the proposed control strategy.

Multi-dimensional Taylor network adaptive predictive control for single-input single-output nonlinear systems with input time-delay

In this study, an adaptive predictive control approach based on the multi-dimensional Taylor network (MTN) is proposed for the real-time tracking control of single-input single-output nonlinear systems with input time-delay. Two MTNs are used to implement the accurate tracking control. First, to compensate for the influence of time-delay, MTN is taken as a predictor and the damped recursive least squares algorithm is used as its online learning algorithm. Second, a feed-forward MTN controller is developed on the basis of the proportional–integral–derivative controller, and the closed-loop errors between the reference input and the system output are directly chosen to be the MTN controller’s inputs. The back propagation algorithm is introduced for its learning which can update its weights online at stable learning rate by the errors caused by the system’s uncertain factors. Convergence and stability analysis are given to guarantee the performance of our proposed approach. Finally, two examples are given to verify the effectiveness of the proposed approach.

Design of decentralized adaptive control approach for large-scale nonlinear systems subjected to input delays under prescribed performance

For the first time, the issue of input delay and prescribed performance control is investigated in the same framework for large-scale nonlinear systems in this study, and an original adaptive decentralized control method is proposed by taking advantage of multi-dimensional Taylor network (MTN) method. Firstly, the problem of input delays is solved by introducing new variables, and a new form of coordinate transformation is introduced before controller design, which simplified the control system. Secondly, the problem of prescribed performance control is coped with by integrating the idea of prescribed performance into the Lyapunov functions of first step of backstepping of each subsystem. Thirdly, MTNs are employed to evaluate the combination of unknown functions, and then, a decentralized MTN-based adaptive control scheme is developed by way of backstepping technology. The theoretical analysis indicates that the proposed control scheme can implement the expected tracking goals under the condition of meeting the prescribed performance control. Finally, two examples are given to show the validity and rationality of the proposed control method.

Design Method for a Higher Order Extended Kalman Filter Based on Maximum Correlation Entropy and a Taylor Network System

This paper proposes one new design method for a higher order extended Kalman filter based on combining maximum correlation entropy with a Taylor network system to create a nonlinear random dynamic system with modeling errors and unknown statistical properties. Firstly, the transfer function and measurement function are transformed into a nonlinear random dynamic model with a polynomial form via system identification through the multidimensional Taylor network. Secondly, the higher order polynomials in the transformed state model and measurement model are defined as implicit variables of the system. At the same time, the state model and the measurement model are equivalent to the pseudolinear model based on the combination of the original variable and the hidden variable. Thirdly, higher order hidden variables are treated as additive parameters of the system; then, we establish an extended dimensional linear state model and a measurement model combining state and parameters via the previously used random dynamic model. Finally, as we only know the results of the limited sampling of the random modeling error, we use the combination of the maximum correlation estimator and the Kalman filter to establish a new higher order extended Kalman filter. The effectiveness of the new filter is verified by digital simulation.

Adaptive finite-time control for stochastic nonlinear systems using multi-dimensional Taylor network

In this paper, the problem of adaptive finite-time multi-dimensional Taylor network (MTN) control for a class of stochastic nonlinear systems is investigated. By combining the MTN-based approximate method and adaptive backstepping technique, a novel adaptive finite-time MTN control scheme is proposed. In this scheme, the MTNs are used to approximate the unknown nonlinear functions of the systems. The finite-time Lyapunov stability theory is utilized to prove the stability of the close-loop system. The proposed scheme can ensure that all signals in the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood of the origin in a finite time. Three simulation examples are presented to show the effectiveness of the control scheme. It should be pointed that the adaptive MTN controller proposed in this paper has the advantages of fast computational speed and good real-time performance thanks to the simple structure of the MTN.

Adaptive multi-dimensional Taylor network control for nonlinear stochastic systems with time-delay

In this article, the problem of adaptive multi-dimensional Taylor network control for strict-feedback nonlinear stochastic systems with time-delay is investigated. To overcome the control degradation resulting from the delay terms, the appropriate integral-type Lyapunov–Krasovskii functions are introduced. A novel adaptive multi-dimensional Taylor network control scheme is provided via backstepping technique. The proposed adaptive multi-dimensional Taylor network controller can ensure that all signals in the closed-loop system are bounded in probability and the tracking error eventually converges to a small neighborhood of the origin. Three simulation examples are given to demonstrate the effectiveness of the proposed control scheme.

Adaptive control of a class of stochastic nonlinear systems with full state constraints and input saturation using multi‐dimensional Taylor network

AbstractIn the paper, a new control algorithm to realize the tracking control for a class of stochastic nonlinear systems with both full state constraints and input saturation is put forward using multi‐dimensional Taylor network (MTN) approach. By introducing a continuous function, the input saturation is converted into a linear model with bounded error. With the help of approximation properties of MTN, by proposing barrier Lyapunov functions (BLFs) and involving the idea of state‐constrained control into backstepping technique, a simple and efficient control scheme is developed. The proposed control scheme can guarantee the system states fall in the given constrained bounds as well as keeping the resulting control system stable. The effectiveness of the proposed control method is demonstrated through two examples.

Adaptive decentralized control for large‐scale nonlinear systems with finite‐time output constraints by multi‐ dimensional Taylor network

AbstractThis paper investigates the adaptive decentralized control problem for a class of large‐scale nonlinear systems with finite‐time output constraints. In order to ensure that the tracking errors are constrained within a predefined boundary in finite time, a novel adaptive barrier Lyapunov function (BLF) control method is proposed by combining the modified finite‐time performance function (FTPF) in the first step of backstepping process. Besides, the mean value theorem and regulating functions are employed to handle the difficulties caused by interconnection functions in large‐scale systems. Subsequently, with the approximation performance of multi‐dimensional Taylor network (MTN), a MTN‐based adaptive decentralized tracking control scheme is developed to guarantee that the tracking errors satisfy the prescribed performance and all signals of the closed‐loop systems are bounded. Finally, the stability theory analysis and simulation results demonstrate the effectiveness of the proposed method.

Adaptive multi‐dimensional Taylor network funnel control of a class of nonlinear systems with asymmetric input saturation

SummaryIn view of the result and performance of control are affected by the existence of input constraints and requirements, adaptive multi‐dimensional Taylor network (MTN) funnel control problem is studied for a class of nonlinear systems with asymmetric input saturation in this paper. Firstly, the effect of asymmetric input saturation can overcome by introducing the Gaussian error function, namely, the asymmetric saturation model is represented as a simple linear model with a bounded disturbance. Secondly, MTNs are employed to approximate the unknown functions in the controller design. Then, an adaptive MTN tracking controller is developed by blends the idea of funnel control into backstepping, which can guarantee that the tracking error always meets the given prescribed performance regarding the transient and steady state responses as well as the output of system tracks the give continuous reference signal. Finally, the effectiveness of the proposed control is demonstrated using two examples.

MTN output feedback tracking control for MIMO discrete-time uncertain nonlinear systems

An adaptive controller is developed that is based on the multidimensional Taylor network (MTN). This controller is used for multi-input and multi-output (MIMO) uncertain discrete-time nonlinear systems. This newly developed MTN is dissimilar with the neural network, in which only multiplication and addition are needed for this controller. Thus, real-time control is more easily to be achieved. The theoretical analysis shows that the output errors of the system are convergent and the output signals are semi-globally, uniformly and ultimately bounded. To illustrate the validity of MTN-based adaptive controller (MTNAC), a numerical example is given. The simulation data demonstrate that this MNTAC has better real-time performance and higher robustness compared with neural networks.

Multi-dimensional Taylor network-based adaptive control for nonlinear systems with unknown parameters

This paper presents an adaptive multi-dimensional Taylor network (MTN) control approach for a class of nonlinear systems with unknown parameters. MTN is employed to identify unknown nonlinear characteristics existing in the system, and then a novel adaptive MTN tracking control method is proposed, via backstepping technique. In the controller design, double adaptive laws are designed and appropriate Lyapunov functions are chosen to overcome the difficulties caused by the unknown parameters. The designed controller can guarantee that all the variables in the closed-loop systems are bounded and the tracking error can be arbitrarily small. Finally, simulation results are presented to verify the effectiveness of the proposed approach.

Adaptive tracking control for a class of stochastic non‐linear systems with input delay: a novel approach based on multi‐dimensional Taylor network

In this study, by means of the techniques of adaptive multi-dimensional Taylor network (MTN) control, the tracking problem of a class of stochastic non-linear systems with input delay is studied. Firstly, based on the Pade approximation method, a new variable is employed to overcome the problem of input delay, and MTNs are applied to estimate the non-linear functions in the design of the controller. Secondly, an adaptive MTN controller design scheme is developed in the framework of backstepping. Thirdly, the stability of the closed-loop system is analysed using Lyapunov's stability theory. Finally, the effectiveness of the proposed design approach is demonstrated by two examples.

Adaptive multi-dimensional Taylor network dynamic surface control for a class of strict-feedback uncertain nonlinear systems with unmodeled dynamics and output constraint

Unmodeled dynamics and output constraint are very often experienced in many physical applications, while few studies on them simultaneously are constructed. This study concentrates on the problem of adaptive multi-dimensional Taylor network dynamic surface control (MTN-DSC) for a class of strict-feedback uncertain nonlinear systems subjected to unmodeled dynamics and output constraint. The purpose is to make this study more practical, and design a controller with simple structure to improve the system performance. A barrier Lyapunov function is used to restrict the system output to within the prescribed constraint. At each step during the backstepping design process, an MTN is applied to approach the generated unknown composite function stemming from the unknown functions and uncertain disturbances, rather than individually; this simplifies the structure and reduces the complexity of the controllers. Meanwhile, the computational burden is further reduced, as only one parameter is adjusted online, which has the minimum number of parameters to be adjusted. Additionally, DSC technique is introduced to eliminate the inherent “explosion of complexity” problem in traditional backstepping design procedure. Furthermore, it is proved that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, and that the output constraint is never violated. The validity of the proposed control scheme is illustrated through the numerical and applied simulation examples.

Adaptive sliding mode robust control based on multi‐dimensional Taylor network for trajectory tracking of quadrotor UAV

In this study, multi-dimensional Taylor network (MTN) inspired sliding mode robust control theory based adaptation laws are proposed to realise trajectory tracking for a quadrotor unmanned aerial vehicle. Compared with existing methods, the composite disturbance considered in this study includes external multiple interference and fuselage parameter perturbation, which is more in accord with reality. Through a linear state transformation, the uncertain coefficients and unknown external disturbances are grouped together and the original kinetic model is decoupled into two subsystems of position and attitude that make the control design become feasible. MTNs are used to compensate the lumped non-linearities, and the adaptive sliding mode technique is employed to construct the controller. Different from the controllers based on neural networks, MTN contains only addition and multiplication, which greatly lessens the computational complexity and improves the real-time performance. By the Lyapunov theory, the position tracking error, attitude tracking error and fuselage load identification error are bounded in probability have been proved and the stability of the system is guaranteed. Simulation studies demonstrate the effectiveness and superiority of the proposed trajectory tracking control scheme.