Title: A novel decentralised adaptive NN tracking control for double inverted pendulums

Authors: Tieshan Li, Wei Li, Renxiang Bu

Addresses: Navigation College, Dalian Maritime University, 1 Linghai Road, Dalian, 116026, China; School of Naval Architecture, Ocean and Civil Engineering (NAOCE), Shang-hai Jiao Tong University, 800 Dongcuan Road, Shanghai 200240, China. ' Navigation College, Dalian Maritime University, 1 Linghai Road, Dalian, 116026, China. ' Navigation College, Dalian Maritime University, 1 Linghai Road, Dalian, 116026, China

Abstract: Adaptive trajectory-tracking control of double inverted pendulums (DIPs) connected by a spring is considered in this paper. By incorporating |dynamic surface control (DSC)| approach and |minimal learning parameters (MLP)| algorithm, a systematic procedure for the synthesis of a novel decentralised robust adaptive neural control scheme is developed. Two main advantages of the developed scheme are that: 1) The RBF neural networks (NNs) are only used to approximate those unstructured system functions rather than the unknown virtual control gain functions. Consequently, the potential controller singularity problem can be overcome. 2) Only one parameter needs to be updated online for each subsystem, both problems of |dimension curse| and |explosion of complexity| are avoided. The computational burden has thus been greatly reduced. In addition, the stability in the sense of semi-globally uniform ultimate boundedness (SGUUB) of the closed-loop system is established via Lyapunov stability analysis, and the tracking error can be made arbitrarily small. Simulation results for the trajectory tracking of the DIPs are presented to demonstrate the effectiveness and good transient performance of the proposed scheme.

Keywords: double inverted pendulums; DIPs; adaptive control; tracking control; neural networks; NNs; dynamic surface control; DSC; minimal learning parameters; decentralised control; trajectory tracking; robust control; controller singularity; tracking error; simulation.

DOI: 10.1504/IJMIC.2011.041782

International Journal of Modelling, Identification and Control, 2011 Vol.13 No.4, pp.269 - 277

Published online: 21 Mar 2015 *

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