Multi-dimensional Taylor network modelling and optimal control of SISO nonlinear systems for tracking by output feedback

Abstract

Abstract 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.