Study On Time Delay And Packet Dropout In Nonlinear Systems Via Fuzzy Control Approach

Takagi-Sugeno (T-S) fuzzy models can approximate any smooth nonlinear functionto any specified accuracy within any compact set, and the parallel distributed compensa-tion scheme is also an approximation of nonlinear controllers. T-S fuzzy models providea way to convert the problem of analysis and synthesis of nonlinear systems into that of aset of local linear models in a kind, which makes the application of fruitful results in linearcontrol field on complex nonlinear systems possible. The sharp development of controlscience pushes the introduction of communication networks into control loops. Comparedwith the traditional communication architecture, networks have many advantages. How-ever, due to the time sharing nature of communication networks, various communicationissues are introduced into the control loops, such as data packet dropout and transmis-sion delay, which are the main sources of degraded systems'performance. It is worthmentioning that most of present available results on data packet dropout are concerninglinear systems, and few systematic results has been worked out for nonlinear systems. Al-though problems on delayed fuzzy systems based on the transmission delay backgroundhave been addressed by many researchers, there still leaves much room for further de-velopment. The attention of this thesis is to propose new approaches based on T-S fuzzymodels to analyze and synthesize nonlinear systems with data packet dropout and timedelay, and some of the obtained results will be applied to fuzzy control of the complexnonlinear overhead crane system with input delay.Chapter 2 proposes a new approach for solving the problem of stability analysis andstabilization for continuous delayed T-S fuzzy systems by extending a delay partitioningidea into the construction of basis-dependent Lyapunov functional. The obtained delay-dependent stability condition is much less conservative than most of the existing results.Based on that, the problem of stabilization via the so-called parallel distributed compen-sation scheme is also solved. Both the stability and stabilization results are extended todelayed fuzzy systems with norm bounded uncertainties, and new criteria of robust sta-bility and stabilization of the uncertain delayed fuzzy system are obtained. The method isfurther used for H∞controller design for delayed T-S fuzzy systems. Chapter 3, focusedon interval uncertainties which often appear in complex nonlinear systems, presents the results on guaranteed cost control of retarded T-S fuzzy systems and the optimal guar-anteed cost controller is obtained. The results in this part are more advanced than mostexisting results and the advantages lie especially in the reduced conservatism and over de-sign, and the method for retarded fuzzy systems'study will be utilized for fuzzy controlof the overhead carne in Chapter 8.Chapter 4 investigates the problem of H∞control of T-S fuzzy systems with datapacket dropout. The T-S fuzzy model is to represent a nonlinear system. The commu-nication links, existing between the plant and controller, are assumed to be imperfect(that is, data packet dropouts occur intermittently), and independent stochastic variablessatisfying the Bernoulli random binary distribution are utilized to model the unreliablecommunication links. The closed-loop is then converted to a stochastic fuzzy model.H∞performance of the closed-loop system is analyzed based on the second Lyapunovfunction approach. Two approaches, quadratic Lyapunov function and basis-dependentLyapunov function approaches are developed to obtain the H∞controller design methodswith various conservatism and computational cost. With the help of the mathematicalproblem formulation in Chapter 4, Chapter 5 studies the T-S fuzzy model based predic-tive controller design in virtue of a piecewise Lyapunov function method. The obtainedresults in this part have both theoretical and practical meaning for nonlinear systems withdata packet dropout.Chapter 6 investigates the problem of H∞filtering for continuous T-S fuzzy systemswith an interval time-varying delay in the state. The delay partitioning idea, which isusually used for solving the problem of stability analysis for linear systems in literaturesis extended to solving the problem of filtering for time-varying delayed fuzzy systems.Sufficient conditions of existence of the H∞filter are obtained. This part addresses theopen filtering problem of fuzzy systems with interval time delay, and the results also canbe regarded as an improvement of the existing results on filtering for time-varying delayedfuzzy systems.Chapter 7 is concerned with the problems of H∞filtering and fault detection of T-Sfuzzy systems with intermittent measurements. The T-S fuzzy model is used to representa nonlinear plant. The measurement transmission from the plant to the filter is assumed tobe imperfect and a stochastic variable satisfying the Bernoulli random binary distributionis utilized to model the phenomenon of the measurements missing. The filtering error system is converted to a stochastic fuzzy model. Sufficient conditions of existence of anH∞filter are obtained based on the fuzzy basis-dependent Lyapunov function approach.By introducing some slack matrix variables, the coupling between the Lyapunov matrixand the system matrices is eliminated, which greatly facilitates the filter design proce-dure. The developed theoretical results contributes to the fault detection technology, sothe fault detection problem of T-S fuzzy systems with missing measurements is further in-vestigated, and sufficient conditions of existence of the fault detection filter are obtained.This part provide a theoretical base for filtering and fault detecting for real systems innetwork environment.Chapter 8 first gives the fuzzy modelling process of a complex nonlinear dynamicsystem of the crane with actuator saturation, which is modelled as a 3-rules'T-S fuzzymodel. When transmission delay occurs between the plant and controller, according tothe method in solving problems of delayed fuzzy systems in Chapter 2, a state feedbackcontroller is designed guaranteeing the load to be placed in a desired position in a shorttime by the crane with a much suppressed swing angle. At the same time, actuator sat-uration is considered and delay-dependent conditions are established for determining ifan ellipsoid is contractively invariant. Compared with the structure variable control, theadvantages of the fuzzy control are the more suppressed swing angle and less control cost.This part constitutes an attempt of applying the T-S fuzzy model based control to practicalengineering problems, which extends the T-S fuzzy model based control and provides adesign example for practical engineers's reference as well.