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

• Published in: International journal of adaptive control and signal processing Vol. 33; no. 4; pp. 664 - 683
• Main Authors: Yan, Hong‐Sen, Han, Yu‐Qun
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.04.2019
• Subjects: Adaptive control; Complexity; Computation; Computer simulation; Control methods; Control systems design; Controllers; decentralized tracking control; dynamic surface control; large‐scale stochastic nonlinear systems; Lyapunov stability theorem; Multiplication; multi‐dimensional Taylor network; Nonlinear systems; Nonlinearity; Randomness; Stochastic systems; System effectiveness; Tracking control; Tracking errors
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.2978

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.