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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. [ABSTRACT FROM AUTHOR]

In this paper, a multi-dimensional Taylor network (MTN) output feedback tracking control of nonlinear single-input single-output (SISO) systems in discrete-time form is studied. To date, neural networks are generally used to identify unknown nonlinear systems. However, the neuron of neural networks includes the exponential function, which contributes to the complexity of calculation, making the neural network control unable to meet the real-time requirements. In order to identify the controlled object whose model is unknown, the MTN, which requires only addition and multiplication, is utilized for successful real-time control of the SISO nonlinear system based on only its output feedback. Lyapunov analysis proves that output signals in the closed-loop system remain bounded and the tracking error converges to an arbitrarily small neighbourhood around the origin. In contrast to the back propagation (BP) neural network self-adaption reconstitution controller, the edge of the scheme is that the MTN optimal controller promises desirable response speed, robustness and real-time control. [ABSTRACT FROM AUTHOR]

In this paper, the problem of multi-dimensional Taylor network (MTN) decentralised adaptive output-feedback tracking control is investigated for large-scale stochastic nonlinear systems. MTNs are used to approximate the unknown nonlinear functions, and a MTN state observer is designed for estimating the unmeasured states. Based on the designed MTN state observer, and by combining the backstepping technique with dynamic surface control (DSC), an adaptive MTN decentralised output-feedback tracking control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability, and the tracking errors converge to an arbitrarily small neighbourhood around the origin in the sense of mean quartic value. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and the simulation results demonstrate that the proposed method promises desirable real-time performance and tracking control. [ABSTRACT FROM AUTHOR]

Summary This 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. [ABSTRACT FROM AUTHOR]

The randomness and nonlinearity of stochastic nonlinear systems increase computational complexity and impede their tracking performance. However, randomness and nonlinearity are inevitable in practical applications, and the existing methods can hardly achieve the desirable control effect, especially in real-time control. For this end, a new network control strategy based on multi-dimensional Taylor network (MTN), whose design depends only on the system output, is put forward to solve the optimal output-feedback tracking problem of the SISO stochastic nonlinear systems. The network structure of the MTN is given first, and its approximation properties are proven. Based on the quadratic cost function design learning algorithm, the tracking error is minimized to update the controller parameters, and the desired tracking performance is obtained. Using the Lyapunov stability theorem, it is proved that the corresponding closed-loop system is bounded in the sense of probability and it can be ensured that the output tracking error converges to a small residual set around the origin in the sense of probability. An example is provided to illustrate the effectiveness of the proposed design approach. Comparative simulation study reveals that the proposed solution promises desirable real-time dynamic performance. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]