Composite Adaptive Fuzzy Output Feedback Dynamic Surface Control Design for Uncertain Nonlinear Stochastic Systems with Input Quantization

Abstract

In this paper, a composite adaptive fuzzy output feedback control problem is investigated for a class of single-input and single-output stochastic nonlinear systems, where the input signal takes quantized values. In the control design, by using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial-parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and the prediction error between the system states observer model and the serial-parallel estimation model, an adaptive output feedback controller is constructed. The designed fuzzy controller with the composite parameters adaptive laws ensures that all the variables of closed-loop system are bounded in probability, and tracking error converges to a small neighborhood of zero. Two examples are provided to verify the effectiveness of the proposed approach.

Direct Adaptive Fuzzy Backstepping Control for Stochastic Nonlinear SISO Systems with Unmodeled Dynamics

“…Previous references and mainly consider the case of that nonlinear functions g i (·)( i =1,⋯, n ) are identically equal to 1. However, not all the nonlinear functions g i (·) are equal to 1 in some strict‐feedback nonlinear systems.…”

“…However, not all the nonlinear functions g i (·) are equal to 1 in some strict‐feedback nonlinear systems. Therefore, the control methods proposed in and can not be applied for system .…”

“…The main contributions are as follows. A direct adaptive control scheme is obtained to guarantee that the closed‐loop system is ISpS in probability, even though the state observer‐based fuzzy control approaches proposed in and can not be applied in the controller design for the considered system. In the backstepping control design, we utilize FLSs directly to approach unknown control signals, while use FLSs to model the uncertain nonlinear dynamics. Therefore, the proposed direct adaptive scheme eliminates the two reasons which could result in the "explosion of complexity" problem, and makes parameter laws simpler than , because only four adaptive online parameters are needed no matter how many rules in FLSs.…”

“…Meanwhile, some significant results have been made in [31][32][33][34][35][36][37][38] for a class of uncertain nonlinear stochastic systems by combining backstepping technique with fuzzy logic systems (FLSs). For example, two adaptive fuzzy backstepping control approaches are proposed for a class of multi-input and multi-output (MIMO) stochastic nonlinear systems in [31,32].…”

“…The lost dynamic characteristics are called the unmodeled dynamics, which could lead to the system oscillation or divergence, if we ignore it in the controller design. However, unmodeled dynamics are neglected in [25][26][27][28][29][30][31][32][33][34][35][36][37], and unstructured uncertainties g i are identically equal to 1 in [25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”