Research Of Sliding Mode Control For Interval Type-2 Fuzzy Systems And Its Applications

This paper explores the problem of sliding mode control and synthesis for several classes of continuous-time complex nonlinear systems based on interval type-2 fuzzy model method.Compared with the classical T-S fuzzy method which is studied more,the interval type-2 fuzzy model method can deal with nonlinearity and at the same time tolerate parameter uncertainties in modeling.For the modeling also give full consideration to the realistic effects of the external environment,such as the unknown system state,measurement uncertainty,multi-time scale and external disturbance,etc,and strive to make the established system model is closer to reality.In addition,the whole research is put forward under the framework of networked control,to explore the effects of the network environment brings to the control strategy,including the network transmission delay,limited network bandwidth resources,etc.On the research content,with the aid of the interval type-2 fuzzy set theory,sliding mode control theory,and Lyapunov method,etc,in view of the complex nonlinear systems,under the different aspects of unlimited time and limited time,the corresponding stability criterion and the sliding mode controller design scheme are put forward using advanced mathematical processing technology to reduce the conservatism of the results.The control strategy is proved by numerical and practical simulation examples.This work extends the research field of sliding mode control for nonlinear systems based on fuzzy model,and the concrete research content is as follows:1.The problem of designing sliding mode controller for a class of interval type-2fuzzy systems with unmeasurable state information is studied in a given finite-time interval.Aiming at the nonlinear characteristic with parameter uncertainty in modeling,the interval type-2 fuzzy method is used to model the nonlinear system.Considering the designed flexibility,an observer model with mismatched premise structure based on nonparallel distributed compensation idea is designed to obtain the state information of the controlled object.Then,using sliding mode control theory and Lyapunov functional method,the reach stage,sliding mode stage and whole stage of the whole sliding mode control process are analyzed theoretically in a finite-time interval.Some sufficient criteria are established to ensure the finite-time boundedness of the closed-loop system at different stages and the whole stage based on Lyapunov functional method.Finally,numerical example and classical mass-spring-damper system model are used to test the proposed control strategy.2.The design of extended dissipative sliding mode controller for a class of nonlinear systems with the phenomenon of uncertain measurement is studied.The nonlinear characteristics of the system are modeled by using the interval type-2 T-S fuzzy modeling method.In addition,considering the inevitable phenomenon of uncertain measurement in practice,the Bernoulli distribution is used to describe this phenomenon.On account of solving the issue of bandwidth usage,the event detection method is used.Then,the stateobserver based sliding mode controller is designed according to the non-parallel distributed compensation scheme.Some stability conditions for the closed-loop system with extended dissipative performance are established based on Lyapunov functional method.Finally,a set of numerical examples are used to verify the proposed method.3.The design of sliding mode controller for a class of nonlinear systems with multiple time scale effects is studied.Firstly,the system is modeled as an interval type-2fuzzy singularly perturbed system model.Then,a disturbance observer model is constructed to suppress the existence of external disturbance.To further reduce the bandwidth usage,an event-triggered protocol with dynamic threshold parameters is adopted,whose threshold can be adjusted with the change of system states.On this basis,a non-parallel distributed compensation scheme-based fuzzy sliding mode controller with higher flexibility is designed.In the stability analysis,using the singular perturbation parameter dependent-Lyapunov function method and membership function dependent analysis method,the lower conservative stability results are obtained.Finally,the two classical examples,circuit model and the model of inverted pendulum are generalized to interval type-2 T-S fuzzy method,to prove the rationality and potential applicability of the proposed method.