Multi-dimensional Taylor Network Control Research Articles

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.

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.

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.

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.

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.

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 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 tracking control for a class of switched nonlinear systems with input nonlinearity

In this paper, a multi-dimensional Taylor network (MTN)-based adaptive tracking control approach is proposed for a class of switched nonlinear systems with input nonlinearity. Firstly, the input nonlinearity is assumed to be bounded by a sector interval. Secondly, with the help of MTNs approximating the unknown nonlinear functions, a novel adaptive MTN control scheme has the advantages of low cost, simple structure and real time feature is developed via backstepping technique. It is shown that the tracking error finally converges to a small domain around the origin and all signals in the closed-loop system are bounded. Finally, two examples are given to demonstrate the effectiveness of the proposed control scheme.

Multidimensional Taylor network adaptive control for MIMO time‐varying uncertain nonlinear systems with noises

SummaryIn this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.

Identification and adaptive multi‐dimensional Taylor network control of single‐input single‐output non‐linear uncertain time‐varying systems with noise disturbances

In this paper, an adaptive control approach based on the multi-dimensional Taylor network (MTN) is proposed to control the non-linear uncertain time-varying systems with noise disturbances. MTNs are introduced to formulate adaptive filtering, non-linear identification and optimal control. First, an MTN filter is developed to eliminate the control interference and measurement noise, so that the model output without stochastic disturbance can be obtained. Then, an MTN identifier (MTNI) is so designed as to be capable of dynamic mapping and require fewer weights than traditional neural networks. On the basis of the above, the MTN controller (MTNC) is developed to realise the precise tracking control of the system. The non-linear uncertain time-varying system is identified by MTNI, which then provides sensitivity information of the plant to MTNC to make it adaptive. Furthermore, the skeletonisation algorithm is adopted to remove redundant inputs and redundant regression items from MTNI and MTNC for concise MTNs. Successful convergence and faster learning are guaranteed using the Lyapunov theorem, and the optimal learning rates are identified. Simulation results demonstrate that the proposed approach features its accurate identification, excellent tracking and better anti-interference capability for the adaptive real-time control of uncertain, stochastic and time-varying non-linear systems.

MTN optimal control of MIMO non-affine nonlinear time-varying discrete systems for tracking only by output feedback

In practice, many controlled plants are equipped with MIMO non-affine nonlinear systems. The existing methods for tracking control of time-varying nonlinear systems mostly target the systems with special structures or focus only on the control based on neural networks which are unsuitable for real-time control due to their computation complexity. It is thus necessary to find a new approach to real-time tracking control of time-varying nonlinear systems. In this paper, a control scheme based on multi-dimensional Taylor network (MTN) is proposed to achieve the real-time output feedback tracking control of multi-input multi-output (MIMO) non-affine nonlinear time-varying discrete systems relative to the given reference signals with online training. A set of ideal output signals are selected by the given reference signals, the optimal control laws of the system relative to the selected ideal output signals are set by the minimum principle, and the corresponding optimal outputs are taken as the desired output signals. Then, the MTN controller (MTNC) is generated automatically to fit the optimal control laws, and the conjugate gradient (CG) method is employed to train the network parameters offline to obtain the initial parameters of MTNC for online learning. Addressing the time-varying characteristics of the system, the back-propagation (BP) algorithm is implemented to adjust the weight parameters of MTNC for its desired real-time output tracking control by the given reference signals, and the sufficient condition for the stability of the system is identified. Simulation results show that the proposed control scheme is effective and the actual output of the system tracks the given reference signals satisfactorily.

Adaptive multi-dimensional Taylor network tracking control for a class of nonlinear systems

This paper is concerned with the problem of multi-dimensional Taylor network (MTN) tracking control for a class of nonlinear systems with unknown control direction. By combining MTN' universal approximation ability and adaptive control method in the backstepping recursive design, a new adaptive MTN control approach is presented for the nonlinear system. The computation complexity of the designed controller has significantly reduced thanks to the simple structure of MTN. It is shown that the designed controller can guarantee all the signals in the closed-loop system remain bounded and the tracking error finally converges to a small neighbourhood of the origin. Finally, simulation results demonstrate the effectiveness of the proposed design approach.

Decentralized adaptive multi‐dimensional Taylor network tracking control for a class of large‐scale stochastic nonlinear systems

SummaryThis paper investigates the problem of adaptive multi‐dimensional Taylor network (MTN) decentralized tracking control for large‐scale stochastic nonlinear systems. Minimizing the influence of randomness and complex nonlinearity, which increases computational complexity, and improving the controller's real‐time performance for the stochastic nonlinear system are of great significance. With combining adaptive backstepping with dynamic surface control, a decentralized adaptive MTN tracking control approach is developed. In the controller design, MTNs are used to approximate nonlinearities, the backstepping technique is employed to construct the decentralized adaptive MTN controller, and the dynamic surface control technique is adopted to avoid the “explosion of computational complexity” in the backstepping design. It is proven that all the signals in the closed‐loop system remain bounded in probability, and the tracking errors converge to a small residual set around the origin in the sense of a mean quartic value. As the MTN contains only addition and multiplication, the proposed control method is more simplified and of good real‐time performance, compared with the existing control methods for large‐scale stochastic nonlinear systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this paper has good real‐time performance and control quality, and the dynamic performance of the closed‐loop system is satisfactory.

MTN Optimal Tracking Control of SISO Nonlinear Time-Varying Discrete-Time Systems without Mechanism Models

Nonlinear time-varying systems without mechanism models are common in application. They cannot be controlled directly by the traditional control methods based on precise mathematical models. Intelligent control is unsuitable for real-time control due to its computation complexity. For that sake, a multidimensional Taylor network (MTN) based output tracking control scheme, which consists of two MTNs, one as an identifier and the other as a controller, is proposed for SISO nonlinear time-varying discrete-time systems with no mechanism models. A MTN identifier is constructed to build the offline model of the system, and a set of initial parameters for online learning of the identifier is obtained. Then, an ideal output signal is selected relative to the given reference signal. Based on the system identification model, Pontryagin minimum principle is introduced to obtain the numerical solution of the optimal control law for the system relative to the given ideal output signal, with the corresponding optimal output taken as the desired output signal. A MTN controller is generated automatically to fit the numerical solution of the optimal control law using the conjugate gradient (CG) method, and a set of initial parameters for online learning of the controller is obtained. An adaptive back propagation (BP) algorithm is developed to adjust the parameters of the identifier and controller in real time, and the convergence for the proposed learning algorithm is verified. Simulation results show that the proposed scheme is valid.

Adaptive multi‐dimensional Taylor network tracking control for SISO uncertain stochastic non‐linear systems

In this study, the problem of adaptive multi-dimensional Taylor network (MTN) control for single-input single-output (SISO) uncertain stochastic non-linear systems is investigated. How to minimise the influence of randomness and uncertain non-linearity for less complex computation, and how to improve the real-time performance of the controller are of great significance. To this end, a control approach based on MTN is proposed for tracking control of stochastic non-linear systems. MTNs are used to approximate the non-linearities, and the backstepping technique is employed to construct the MTN controller (MTNC). MTNC involves only addition and multiplication, featuring desirable simplicity and real-time performance. Stability of the system is guaranteed via Lyapunov approach, and it is proved that the proposed controller can guarantee that all signals of the closed-loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighbourhood around the origin. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this study has good real-time performance and control quality.

Adaptive Multi-Dimensional Taylor Network Tracking Control for a Class of Stochastic Nonlinear Systems With Unknown Input Dead-Zone

In this paper, a multi-dimensional Taylor network (MTN) tracking control scheme is proposed for a class of stochastic nonlinear systems with unknown input dead-zone. The MTNs are used to approximate the nonlinearities, and then, an adaptive MTN controller is constructed via a backstepping technique. It is proved that the design MTN controller ensures that all signals of the closed-loop system remain bounded in probability, and the tracking error eventually converges to an arbitrarily small neighborhood around the origin in the sense of a mean quartic value. Finally, two numerical examples and one practical example are given to demonstrate the effectiveness of the proposed design method.

Stability analysis and dynamic regulation of multi-dimensional Taylor network controller for SISO nonlinear systems with time-varying delay

Though many studies are focused on the stabilization of nonlinear systems with time-varying delay, they fail to involve the dynamic regulation without on-line optimization commonly. For this sake, feedback linearization, Lyapunov-Razumikhin theorem and polynomial approximation theorem are employed here to verify that the multi-dimensional Taylor network (MTN) controller can stabilize the single input single output (SISO) nonlinear time-varying delay systems through dynamic regulation of the system output with no need for on-line optimization. Here, the design of the controller is transformed into a convex optimization problem, which is tackled by means of the appropriate optimization method. Like its PD-like controller peers, the MTN controller functions well in eliminating the dependence on the system model. The effectiveness of the proposed approach is demonstrated and confirmed via two examples.

Asymptotic tracking and dynamic regulation of SISO non‐linear system based on discrete multi‐dimensional Taylor network

For non-linear control, it is important to secure a generally structured controller that promises wide application and desirable performance. This study deals with the problem of asymptotic tracking and dynamic regulation of single-input single output (SISO) non-linear systems via output feedbacks by the discrete multi-dimensional Taylor network (MTN) controller, a novel controller with fixed structure and sampled-data control mechanism. For verification of its validity, differential geometry and polynomial approximation are adopted. Using the emulation technique and regional pole assignment, the asymptotic tracking and dynamic regulation without online optimisation of the system by discrete MTN controller is tested. With the dynamic change of error signals, the dynamic regulation by given index is realised. As a convex optimisation problem, the controller parameters can be acquired by parametric learning. Based on the delta operator model, the procedure of the controller design is given in detail. Simulation results confirm the feasibility and effectiveness of the proposed approach.