Research On The Estimation Problem Of Discrete Time Interval Type-2 T-S Fuzzy Systems

With the rapid development of automation technology,there are a lot of complex nonlinear systems in many fields such as aerospace,communication,medical treatment and chemical industry.The type-1 T-S fuzzy system model has the capability to effectively approximate or fit a wide category of smooth complex non-linear systems,which is realized by weighted sum of a succession of partial linear subsystem models exploiting fuzzy membership functions.The interval type-2 T-S fuzzy system model,as an extension of type-1 T-S fuzzy system,which can cope with nonlinearities,also deal with modeling uncertainties by means of the upper and lower membership functions.In many engineering applications,the actual state information of equipment is often not available.State estimation has important theoretical and practical significance as the research basis of system reconstruction,state feedback control,process monitoring and fault diagnosis.In addition,the existence of unknown input,bounded disturbance,parameter mutations and uncertainties will affect the accuracy of system state estimations,thus affect the control performance of the system.In this study,based on the interval type-2 T-S fuzzy model,the problem of state estimation for uncertain discrete complex nonlinear systems subject to unknown inputs or bounded disturbances is studied,which improves the existing research results and reduces the conservatism of the design.The specific research questions are as follows:1.This study proposes a novel unknown input functional observer design approach towards discrete-time interval type-2 T-S fuzzy system models subject to measurable and immeasurable premise variables.By constructing a new state vector that contains both the unknown inputs and the system states,functional observers are proposed for the cases with measurable and immeasurable premise variables to estimate this new state vector for unknown input and/or state estimation.The observers design problem is converted into the solvability issue of a linear matrix equation involving observer gain matrices,the existence conditions of the observers are explicitly obtained based on matrix rank analysis.Meanwhile,instead of solving the intricate Sylvester equation directly,the solution of the simplified matrix equation is employed to derive the observer gains.2.In this study,the state estimator design problem of interval type-2 Takagi-Sugeno fuzzy systems suffering from bounded disturbances is studied.To enhance the resilience of the observer,a non-fragile design scheme is proposed to tackle the observer gain variations.Meanwhile,an event-triggered communication mechanism is introduced for relieving the transmission burden over networks.To settle down the non-fragile observer design issue subject to bounded disturbances and event-induced error,we propose a new definition of quadratic boundedness via the multiple Lyapunov functions.Based on this definition,a novel co-design method of observer and event generator for fuzzy system models in the presence of both measurable and immeasurable premise variables is presented.In virtue of quadratic boundedness framework,less conservative conditions of the existence and quadratic stability of the fuzzy observer s are obtained,the upper bound of estimation error is given explicitly.The desired observer gains are determined by convex optimization technique using slack matrices.3.This study addresses a novel fuzzy observer synthesis method toward discrete time interval type-2 T-S fuzzy systems,which involve measurable/immeasurable premise variables and bounded disturbances within ellipsoids.For keeping resilience to the potential gain variations,a nonfragile observer design strategy is adopted to handle with random gain perturbations.A simplified adaptive event-triggered communicating mechanism with online dynamically adjustable threshold is proposed for alleviating the network transmitting pressure and energy consumption.To design the observer and the event generator parameters simultaneously,a new definition of stochastic quadratic boundedness employing multiple Lyapunov functions is proposed.Resorting to this definition,stochastically quadratic boundedness of the observation error systems is guaranteed.The parameters of both the desired observer and event generator are co-designed by the slack-variable and convex optimization techniques,the corresponding upper bounds on observation errors are provided explicitly.The feasibility and superiority of the proposed method are validated through a continuously stirred tank reactor system and a tunnel diode circuit.