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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]

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]