Approximation-Based Quantized State Feedback Tracking of Uncertain Input-Saturated MIMO Nonlinear Systems with Application to 2-DOF Helicopter

Byung Mo Kim,Sung Jin Yoo

doi:10.3390/math9091062

Abstract

This paper addresses an approximation-based quantized state feedback tracking problem of multiple-input multiple-output (MIMO) nonlinear systems with quantized input saturation. A uniform quantizer is adopted to quantize state variables and control inputs of MIMO nonlinear systems. The primary features in the current development are that (i) an adaptive neural network tracker using quantized states is developed for MIMO nonlinear systems and (ii) a compensation mechanism of quantized input saturation is designed by constructing an auxiliary system. An adaptive neural tracker design with the compensation of quantized input saturation is developed by deriving an augmented error surface using quantized states. It is shown that closed-loop stability analysis and tracking error convergence are conducted based on Lyapunov theory. Finally, we give simulation and experimental results of the 2-degrees-of-freedom (2-DOF) helicopter system for verifying to the validity of the proposed methodology where the tracking performance of pitch and yaw angles is measured with the mean squared errors of 0.1044 and 0.0435 for simulation results, and those of 0.0656 and 0.0523 for experimental results.

Highlights

El-NabulsiIn industrial systems, the operating ranges of actuators are restricted because of the physical limitation and specification [1]
We propose a quantized-states-based adaptive neural control design for uncertain multiple-input multiple-output (MIMO) nonlinear systems subject to input saturation that overcomes the above restrictions (I) and (II)
We show that the proposed adaptive quantized state feedback tracker achieves the robust tracking in the presence of state quantization and the quantized input saturation of the MIMO nonlinear system (34)

Summary

Introduction

El-NabulsiIn industrial systems, the operating ranges of actuators are restricted because of the physical limitation and specification [1]. First-order-filter-based auxiliary systems were introduced to analyze the effect of input saturation in uncertain nonlinear systems such as nonlinear strict-feedback systems [4] and nonlinear stochastic systems [5]. Auxiliary systems using high-order filters were constructed to design adaptive controllers for input-saturated nonlinear systems with model uncertainties such as nonlinear stochastic systems [6] and nonlinear strict-feedback systems [7]. By combining these approaches using auxiliary systems with the function approximation technique, some study results were recently developed for various uncertain nonlinear systems in strict-feedback and purefeedback forms. A robust adaptive control approach was proposed for stateconstrained nonlinear systems with input saturation and unknown control direction [10]

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