Multi-dimensional Taylor Network Research Articles

Multidimensional-Taylor-network-based robust optimal tracking control for MIMO nonlinear discrete-time systems

In practical engineering, system control is indispensable. However, due to the influence of model uncertainty, speed unavailability, input nonlinearity (such as actuator dead zone/fault), and multi-input coupling, the control results are not satisfactory. In this paper, a robust optimal tracking control strategy is proposed for a class of nonlinear multi-input-multi-output discrete-time systems with unknown uncertainties. This control strategy is to minimize the cost function in the process of uncertainty processing and stabilize the closed-loop system by establishing an adaptive controlling approach based on a combination of actor MTN and critic MTN based on the Multi-dimensional Taylor Network (MTN). By using the approximation property of MTN, the optimal control signal is generated by action MTN, which is used to approach the controller, and the cost function is approximated by critic MTN, which is tuned online because the cost function cannot be obtained in hands-on experience. By designing a new cost function, the amount of calculation in the control process is reduced, and the adaptive critic design control idea is integrated into the controller design to deal with the uncertainty of the system. The simulation results verify the effectiveness of the control strategy proposed in the essay.

Adaptive tracking control for a class of stochastic nonlinear systems with input delay using multidimensional Taylor network

AbstractIn this paper, an adaptive tracking control strategy based on multidimensional Taylor network (MTN) is designed for a class of stochastic nonlinear systems with input delay, in which MTN is mainly introduced to approximate uncertain nonlinear functions. Moreover, the effect of input delay is compensated by exploiting an appropriate auxiliary system with the same order as the considered system. By utilizing the backstepping technique and classical adaptive approach, an MTN‐based adaptive tracking control method is proposed, which guarantees that all the signals in the closed‐loop system remain bounded in probability. Furthermore, unlike most existing approaches, the tracking error can be bounded by an explicit expression of design parameters in the mean quartic sense. Finally, two examples are given to verify the validity of the presented scheme.

Adaptive decentralized prescribed performance control for a class of large‐scale stochastic nonlinear systems subject to input saturation and full state constraints

SummaryThis paper focuses on an adaptive decentralized prescribed performance control problem for a class of large‐scale stochastic nonlinear systems with asymmetric input saturation and full state constraints. Firstly, the obstacle of input saturation is overcome by introducing the Gaussian error functions. Secondly, the transient performance of the system output is realized by introducing the asymmetric error transfer functions. Thirdly, the full state constraints are considered in the backstepping control process, and the boundary of state constraints is ensured by constructing barrier Lyapunov functions. Then, the multidimensional Taylor network is employed to approximate the unknown nonlinearity, and an adaptive decentralized controller is designed. Finally, it is shown that the proposed control strategy can ensure that the closed‐loop system is semi‐global ultimately uniformly bounded in probability, and the tracking error of the system can be kept within an adjustable neighborhood of the origin. Two simulation examples are provided to illustrate the feasibility of the proposed control strategy.

Adaptive control for stochastic nonlinear systems with time‐varying delays via multidimensional Taylor network

AbstractControl of stochastic nonlinear systems turns out to be notoriously difficult when stochastic uncertainties and time‐varying delays occur simultaneously. This article presents a tractable adaptive control scheme for the stochastic nonlinear system with time‐varying delays. To mitigate the effects of stochastic uncertainties, an adaptive embedded cubature Kalman filter is developed to realize the robust estimation of the state. Unlike the conventional cubature Kalman filter with fixed construction, a semi‐definite programming is designed to adjust the weights of cubature points dynamically. Such programming guarantees the positive definiteness of the error covariance matrix, which enhances the reliability of the filtering procedure. Based on more accurate state estimations, the multidimensional Taylor network (MTN) is utilized to evaluate the dynamic performance under time‐varying delays and approximate the optimal policy in the deterministic policy gradient framework. Adaptive tracking control with high computational efficiency is achieved due to the concise topological structure of MTN. The exponential convergence of the state estimation error and the semi‐globally uniform ultimate boundness of the tracking error are verified theoretically. The effectiveness of the proposed method is confirmed by a numerical simulation based on a practical electric industrial system.

Event-triggered adaptive multi-dimensional Taylor network tracking control for stochastic nonlinear systems

For a class of stochastic nonlinear systems, this paper proposes a novel event-triggered adaptive control scheme by means of multi-dimensional Taylor network (MTN) approach for the first time, which has the advantages of alleviating computational burden and reducing communication frequency. In addition, the event-triggered control (ETC) strategy can effectively save network resource by alleviating the computational burden and reducing the communication frequency. Therefore, the proposed control approach can not only reduce communication frequency but also further alleviate computational burden, thereby saving network resource to a greater extent. The proposed control scheme ensures that all signals of the system are semi-global uniformly ultimately bounded (SGUUB) in probability and the tracking error can be made arbitrarily small by choosing appropriate design parameters. Meanwhile, Zeno behavior can be avoided. Finally, two simulation results are given to illustrate the effectiveness of the proposed scheme.

A novel network-based controller design for a class of stochastic nonlinear systems with multiple faults and full state constraints

In this paper, the control issue of adaptive fault-tolerant is studied for a class of stochastic nonlinear systems with multiple faults and full state constraints, with multiple faults including the actuator faults and the external system fault. The problem with full state constraints are solved by constructing a logarithmic barrier Lyapunov functions (BLFs). By integrating multi-dimensional Taylor network (MTN) technology into the backstepping process, a new adaptive MTN-based fault-tolerant controller is designed. On the basis of considering multiple faults, the proposed control strategy can ensure that all signals in the closed-loop system are semi-global ultimately uniformly bounded (SGUUB) in probability, and all states of the system are constrained within the given boundary. Finally, three simulation examples are given to illustrate the effectiveness and practicability of the proposed control strategy.

A Backpropagation Multidimensional Taylor Network Model for Measured 3-D Data Fitting

A Backpropagation Multidimensional Taylor Network Model for Measured 3-D Data Fitting

Contraction-based model predictive control for stochastic nonlinear discrete-time systems with time-varying delays via multi-dimensional Taylor network

For stochastic nonlinear systems with time-varying delays, the existing robust control approaches are unnecessarily conservative in most practical scenarios. Within this context, a mathematically rigorous and computationally tractable tube-based model predictive control scheme is proposed in the framework of contraction theory. A contraction metric is systematically constructed via convex optimization by forming a differential LyapunovKrasovskii function on tangent space. It guarantees the perturbed actual solution trajectories to be contained within a robust positive invariant tube centered along the reference trajectories and results in an explicit exponential bound on the deviation. The application scenarios of the control contraction metric controller are extended from constant delay systems into time-varying delay systems thereby. Compared with the existing robust mechanism for time-delay systems based on min-max optimization formulation with a linear feedback controller, the proposed scheme greatly reduces the design conservativeness and yields a larger region of attraction. A sparse multi-dimensional Taylor network (MTN) is designed to parameterize the family of the geodesic. Compared to conventional NNs and MTN surrogates, sparse MTN features a more concise topology that enhances its computational efficiency conspicuously. Results of the numerical simulations verify the effectiveness of the proposed method.

Fault diagnosis of HVAC AHUs based on a BP-MTN classifier

HVAC Air Conditioning Units (AHU) adjust and deliver air to rooms through fans and ducts to meet human comfort needs. Fault diagnosis of AHUs helps to reduce energy consumption and meet human comfort needs, and thus is significant. As a network, the Multi-dimensional Taylor Network (MTN) approximates a nonlinear function with a polynomial network. It is suitable for embedding in a control system since it has a much simpler structure than a neural network while having high accuracy. However, the traditional MTN is usually used for model fitting but not for classification. To solve this problem, a Back Propagation Multi-dimensional Taylor Network (BP-MTN) classifier is proposed in this paper to diagnose the faults of AHUs. This BP-MTN classifier has three main features: 1) a fully connected layer is added after the output layer of the traditional MTN to solve the mismatch between the dimensionality of fault features and the number of categories; 2) the softmax layer is added in the traditional MTN to realize the classification; 3) ReLU function is added in the traditional MTN to improve the classification accuracy and reduce the model complexity; 4) the Back-Propagation (BP) algorithm based on the small batch gradient descent algorithm is used to train the BP-MTN classifier rather than the nonlinear least square used in the traditional MTN. Additionally, this paper explores the selection of polynomial orders and activation functions of BP-MTN through extensive experiments. The experimental results show that the BP-MTN can achieve the accurate classification of AHU faults effectively.

Adaptive finite-time control for switched nonlinear systems subject to multiple objective constraints via multi-dimensional Taylor network approach

The finite-time control of switched nonlinear systems subject to multiple objective constraints is investigated in this article. Firstly, with the aim of dealing with the major challenge brought by multiple objective constraints, the time-varying and asymmetric barrier function is designed, which transforms multiple objective constrained systems into unconstrained systems. Secondly, the dynamic surface control technique is introduced into the backstepping design process, and the error generated in the filtering process is reduced by constructing the error compensation systems. Then, an adaptive finite-time controller based on multi-dimensional Taylor network (MTN) is proposed. The controller proposed in this article can avoid the “singularity” problem and ensure that the objective functions never violate constraints. Finally, the effectiveness of the finite-time control strategy proposed in this article is verified by the aircraft system simulation.

Controller design for nonlinear systems subject to both input saturation and asymmetry time‐varying state constraints: A novel network‐based approach

SummaryIn this article, the issues of asymmetric input saturation and asymmetric time‐varying state constraints are integrated into nonlinear systems for the first time, and a new adaptive tracking control strategy is proposed based on the multi‐dimensional Taylor network (MTN) method. Firstly, by introducing a continuous auxiliary function, the input saturation is transformed into a smooth model with bounded error. Secondly, MTNs are employed to estimate nonlinear functions, asymmetric barrier Lyapunov functions (ABLFs) are constructed to make all state variables meet asymmetric constraints, and then a novel control scheme with simple structure is developed via backstepping. Thirdly, according to the Lyapunov stability theory, it is proved that all signals in the closed‐loop systems are bounded, and all state variables do not violate the constraints. Finally, three examples show the effectiveness of the proposed scheme.

Data-Driven Forecasting of Nonlinear System with Herding via Multi-Dimensional Taylor Network

This work focuses on developing a forecasting model for the nonlinear system with herding. Firstly, for clear presentation of the mechanism of herding behavior, a concept called intermittent positive feedback is defined. The mathematical expression of intermittent positive feedback is formulated in terms of dead-zone functions with the beginning and ending thresholds in the positive and negative directions. Then a dynamic surrogate based on the intermittent positive feedback multi-dimensional Taylor network is established, and a method for identifying its parameters is proposed. Multi-dimensional Taylor network module simulates the long-term trends of time series. Subsequently, an optimization model based on the alternating iteration of the parameters is developed to enhance the forecast accuracy of the intermittent positive feedback part. Simulation results demonstrate that the forecasting effect of the proposed modeling method is superior to that of conventional non-mechanism data-based surrogates for herding behavior.

Adaptive Decentralized Tracking Control for a Class of Large-Scale Nonlinear Systems with Dynamic Uncertainties Using Multi-dimensional Taylor Network Approach

Adaptive Decentralized Tracking Control for a Class of Large-Scale Nonlinear Systems with Dynamic Uncertainties Using Multi-dimensional Taylor Network Approach

Asymptotic Tracking and Dynamic Regulation of MIMO Nonaffine Nonlinear System With Actuator Saturation via Multidimensional Taylor Network Controller

Control input acting on the system in the form of nonlinear implicit tends to exert great impacts on the dynamic behavior of the multiple-input–multiple-output (MIMO) nonaffine nonlinear system with actuator saturation, posing a great challenge to its tracking control and dynamic regulation. Performance optimization and design simplicity are hardly taken simultaneously into account by existing controllers. For this sake, the multidimensional Taylor network (MTN) controller, which involves both transient improvement and design simplicity, is proposed here. The MTN controller, as a novel one with a fixed structure, is capable of making the proposed system asymptotically track the reference with no need of system information except for the control direction. A performance index related to the transient improvement by dynamic regulation is established. Parameters of the MTN controller are adapted for the optimization problem in line with this performance index of the arbitrary approximation by the polynomial function. The existence and the realizability of the solution to the optimization problem are demonstrated. Specific steps of the controller design are given. The effectiveness of the proposed controller is confirmed by its theoretical analysis as well as its application to a two-link manipulator system.

Tracking control for large‐scale switched nonlinear systems subject to asymmetric input saturation and output hysteresis: A new adaptive network‐based approach

AbstractFor large‐scale switched nonlinear systems subject to asymmetric input saturation and output hysteresis, an adaptive control strategy is put forward by using a novel neural network, that is, multi‐dimensional Taylor network (MTN), which can effectively cope with the output tracking problem of this system. Firstly, asymmetric input saturation is expressed as the combination of a linear function and a bounded error function. Then, the modified Bouc‐Wen hysteresis model is employed to solve the nonlinear problem caused by output hysteresis. Afterwards, based on the approximation ability of MTN, a novel adaptive decentralized control method is designed by combining Lyapunov stability theory with adaptive backstepping technology, which realizes the stability and boundedness of the controlled systems. It should be noted that the asymmetric input saturation, the output hysteresis, large‐scale nonlinear systems and switched nonlinear systems appear in the same framework for the first time. Finally, a practical example and a numerical example are given to verify the availability of the proposed control strategy.

MTN-based recursive d-step-ahead predictive control of MIMO nonlinear systems with unknown input time-delay in industrial process

PurposeThis paper aims to provide a precise tracking control scheme for multi-input multi-output “MIMO” nonlinear systems with unknown input time-delay in industrial process.Design/methodology/approachThe predictive control scheme based on multi-dimensional Taylor network (MTN) model is proposed. First, for the unknown input time-delay, the cross-correlation function is used to identify the input time-delay through just the input and output data. And then, the scheme of predictive control is designed based on the MTN model. It goes as follows: a recursive d-step-ahead MTN predictive model is developed to compensate the influence of time-delay, and the extended Kalman filter (EKF) algorithm is applied for its learning; the multistep predictive objective function is designed, and the optimal controlled output is determined by iterative refinement; and the convergence of MTN predictive model and the stability of closed-loop system are proved.FindingsSimulation results show that the proposed scheme is of desirable generality and capable of performing the tracking control for MIMO nonlinear systems with unknown input time-delay in industrial process effectively, such as the continuous stirred tank reactor (CSTR) process, which provides a considerably improved performance and effectiveness. The proposed scheme promises strong robustness, low complexity and easy implementation.Research limitations/implicationsFor the limitations of proposed scheme, the time-invariant time-delay is only considered in time-delay identification and control schemes. And the CSTR process is only introduced to prove that the proposed scheme can adapt to practical industrial scenario.Originality/valueThe originality of the paper is that the proposed MTN control scheme has good tracking performance, which solves the influence of time-delay, coupling and nonlinearity and the real-time performance for MIMO nonlinear systems with unknown input time-delay.

Adaptive multi‐dimensional Taylor network tracking control for nonlinear systems with input saturation and full state time‐varying constraints

SummaryIn this article, an adaptive multi‐dimensional Taylor network (MTN) control approach is developed for nonlinear systems subject to input saturation and full state time‐varying constraints. Using the function approximation property of MTN, an adaptive tracking control method is developed by incorporating the concept of time‐varying state constraints into the construct of barrier Lyapunov functions. The proposed approach not only ensures all closed‐loop system signals are bounded but also that all states of the system never violate the given time‐varying constraints. The most important advantage of the proposed control strategy is that it can obtain satisfactory control effects with low computational cost. Finally, two examples are given to validate the effectiveness of the proposed method.

Adaptive tracking control for stochastic nonlinear systems with time-varying delays using multi-dimensional Taylor network

For stochastic nonlinear systems (SNSs) perturbed by compound uncertainties, the conventional model-based control approaches assume that the evolution behavior of uncertain variables is known. Unfortunately, such approaches are often conservative for most practical scenarios with the slow convergence speed and unsatisfactory anti-interference performance. For this sake, an adaptive control scheme based on deep deterministic policy gradient (DDPG) and multi-dimensional Taylor network (MTN) is proposed here to address the tracking problem for a category of SNSs subject to fast time-varying uncertainties, stochastic disturbance and unknown time-varying delays. The effect of time delay is embedded in the reproducing kernel Hilbert space through the error coordinate transformation. In the framework of DDPG, the MTN-based surrogate is utilized to construct the online network and target network via the temporal-difference method, which promises more desirable real-time performance due to its concise structure than conventional NN-based surrogates. In order to enhance the robustness of the system under fast time-varying uncertainties, a novel persistent excitation (PE) mechanism is designed to ensure that the control policy is appropriately rewarded or punished. Based on the PE condition, weights of MTNs converge exponentially and animate the system to evolve towards the target persistently. The tracking error and closed-loop state signals are proved theoretically to be uniformly ultimately bounded (UUB) via Lyapunov–Krasovskii functional. A numerical simulation from the process industry verifies the effectiveness of the proposed method.

Data-based modeling and identification for general nonlinear dynamical systems by the multidimensional Taylor network

PurposeThe present study is intended to develop an effective approach to the real-time modeling of general dynamic nonlinear systems based on the multidimensional Taylor network (MTN).Design/methodology/approachThe authors present a detailed explanation for modeling the general discrete nonlinear dynamic system by the MTN. The weight coefficients of the network can be obtained by sampling data learning. Specifically, the least square (LS) method is adopted herein due to its desirable real-time performance and robustness.FindingsCompared with the existing mainstream nonlinear time series analysis methods, the least square method-based multidimensional Taylor network (LSMTN) features its more desirable prediction accuracy and real-time performance. Model metric results confirm the satisfaction of modeling and identification for the generalized nonlinear system. In addition, the MTN is of simpler structure and lower computational complexity than neural networks.Research limitations/implicationsOnce models of general nonlinear dynamical systems are formulated based on MTNs and their weight coefficients are identified using the data from the systems of ecosystems, society, organizations, businesses or human behavior, the forecasting, optimizing and controlling of the systems can be further studied by means of the MTN analytical models.Practical implicationsMTNs can be used as controllers, identifiers, filters, predictors, compensators and equation solvers (solving nonlinear differential equations or approximating nonlinear functions) of the systems of ecosystems, society, organizations, businesses or human behavior.Social implicationsThe operating efficiency and benefits of social systems can be prominently enhanced, and their operating costs can be significantly reduced.Originality/valueNonlinear systems are typically impacted by a variety of factors, which makes it a challenge to build correct mathematical models for various tasks. As a result, existing modeling approaches necessitate a large number of limitations as preconditions, severely limiting their applicability. The proposed MTN methodology is believed to contribute much to the data-based modeling and identification of the general nonlinear dynamical system with no need for its prior knowledge.

Tracking control for switched nonlinear systems subject to output hysteresis via adaptive multi-dimensional Taylor network approach

For switched nonlinear systems with output hysteresis, by working on multi-dimensional Taylor network (MTN), an adaptive control strategy is put forward, which can effectively solve the tracking control problem. Firstly, the modified Bouc–Wen hysteresis model is employed to cope with the nonlinear problem caused by output hysteresis. Secondly, the Nussbaum function is introduced into the control design process, and MTN is used to approach nonlinear structures. Thirdly, a novel network adaptive control strategy is constructed with the help of a common Lyapunov function, which can realize the tracking control and stability of the system simultaneously. It is worth noting that as a new type of neural network, MTN is first used for control of switched systems with output hysteresis. Finally, two simulation examples show that the proposed control strategy is effective.