Fuzzy model-based stabilization control and state estimation of nonlinear systems

Abstract With the increasing demand for automation and accuracy in industry, the control objective has been expanded from simple linear systems to complex nonlinear systems. To mitigate fluctuations in nonlinear systems due to external disturbances and enhance the accuracy of state variable estimation, this study employs fuzzy theory. The study introduces a time-delay-dependent Lyapunov asymptotic stability criterion and optimizes the affiliation function in type II fuzzy mathematics to establish a sedimentation model. A state estimation model is optimized based on the unscented Kalman filter method with an extended kernel risk-sensitive loss function and a deep residual network. The experimental results show that when <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>μ</m:mi> </m:math> \mu takes the value of 0.2, the maximum time-delay allowed upper bound obtained by the calming model is 2.2143, which is at the highest value. The state estimation model used in the study fits the true value curve better, and the error percentages are within 0.01%. This indicates that the model has better convergence accuracy and stability control performance.