Adaptive control of a nonaffine nonlinear system using self-organising kernel extreme learning machine

Abstract

We propose a self-organising kernel extreme learning machine (KELM) adaptive controller for nonaffine nonlinear systems. Literature survey reveals that neural network (NN) is extensively used to design adaptive controllers for nonlinear systems. When conventional NN, like multilayer feedforward NN and radial basis function NN (RBFNN), is used for controller design, the parameters of these networks converge slowly. Researchers have overcome this shortcoming by using extreme learning machine (ELM). The motivation to use KELM for controller design in our research is to utilise the advantages of ELM and radial basis function kernels. The structure of neural networks is seldom altered during training, resulting in unnecessarily small or large networks. The self-organising nature of our proposed controller caters to solving this problem. The structure of the self-organising KELM updates itself based on a threshold value set for the normalised change in the output weight. In our work, the control input meets three objectives: feedback linearisation, stabilisation of the linearised system and providing immunity to process and measurement noises. The update law for the hidden layer parameters of the KELM is obtained using the Lyapunov technique to ensure the overall stability of the system. A comparative analysis of different performance criteria is performed for trajectory tracking control, in the presence of process and measurement noises, for a numerical example and the Duffing–Holmes chaotic nonlinear system. The simulation results of these analyses demonstrate the superiority of the self-organising KELM compared to ELM and RBFNN based adaptive controllers. The experimental results with a rotary servo system validate the efficacy of the proposed controller in real-time systems. Furthermore, the robustness of the self-organising adaptive controller is verified with the results obtained for the servo system on varying the system parameter and operating condition.