Fuzzy Adaptive Control For Stochastic Nonlinear Large-Scale Systems And Stability Analysis

In this thesis, For a class of dynamic uncertainly stochastic nonlinear large-scale systems,fuzzy logic systems are used to the system model, based on adaptive fuzzy Backsteppingdesign technique and decentralized control theory, by combining It stochastic differentialequation, and dynamic surface control, etc. It is proved that the closed-loop systems are stablein probability. The detailed content of dissertation is as following:(1) For a class of uncertain stochastic nonlinear large-scale systems, with unknownnonlinear functions, unknown control direction and unmeasurable state variables. Fuzzy logicsystems are used to approximate the unknown nonlinear functions, and a fuzzy filter observeris designed for estimating the unmeasured states. To solve the problem of the unknowncontrol direction in decentralized control design, Nussbaum-type functions are introduced andnew property on Nussbaum-type function is proved. Based on the backstepping recursivedesign technique, a new robust adaptive decentralized fuzzy output feedback control approachis developed. It is proved that the proposed control approach can guarantee that all the signalsof the resulting closed–loop system are bounded in probability. A simulation example isprovided to show the effectiveness of the proposed approach.(2) For a class of uncertain stochastic large-scale nonlinear systems with unknownnonlinear functions, unknown dead-zones, unmodeled dynamics and unmeasurable statevariables. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions,and a fuzzy state observer is established to estimate the unmeasurable states. Based on thebackstepping design and the supply changing function technique, a robust adaptive fuzzydecentralized output feedback control approach is developed. It is proved that proposedcontrol approach can ensure the closed-loop system to be input-state-practically stable (ISpS)in probability, and accommodate the unmodeled dynamics and unknown dead-zones as well.The effectiveness of the proposed control approach is illustrated by a simulation example.(3) For a class of pure-feedback large-scale stochastic nonlinear systems with unknowndead-zone. Fuzzy logic systems are used to approximate the unknown nonlinear functions,and a k-filter observer is designed for estimating the unmeasured states. A robust adaptivefuzzy decentralized output feedback control approach is constructed via the backsteppingrecursive design technique. It is shown that the proposed control approach can guarantee thatall the signals of the resulting closed–loop system are semi-globally uniformly ultimatelybounded (SGUUB) in probability, and the observer errors and the output of the system can beregulated to a small neighborhood of the origin by choosing design parameters appropriately.A simulation example is provided to show the effectiveness of the proposed approach. (4) For a class of unknown stochastic nonlinear strict-feedback systems with actuatorfaults, unknown functions, unmodeled dynamics and without the direct measurements of statevariables. Fuzzy logic systems are employed to identify the unknown stochastic nonlinearsystems, and a fuzzy state observer is established for estimating the immeasurable states. Thedynamic surface design approach (DSC) based on the backstepping technique is presented todesign adaptive decentralized tracking fault-tolerant controller. It is proved that proposedcontrol approach guarantees that all the variables of the closed-loop system are bounded inprobability, and also that the tracking errors converge to an adjustable neighborhood of theorigin regardless of actuator faults and unmodeled dynamics. The simulation results areprovided to illustrate the effectiveness of the proposed control approach.(5) For a class of uncertain stochastic multi-input and multi-output (MIMO) nonlinearsystems in pure-feedback form, with unknown nonlinear functions, input saturation andimmeasurable states. Fuzzy logic systems are used to identify the uncertain nonlinear system,and the input saturation is approximated by a smooth function, a fuzzy state observer isdesigned for estimating the unmeasured states, based on the backstepping recursive designtechnique, an adaptive fuzzy output feedback tracking control approach is developed. It isshown that the proposed control approach can guarantee that all the signals of the resultingclosed–loop system are semi-globally uniformly ultimately bounded (SGUUB) in the sense ofprobability, and the observer errors and tracking errors can be regulated to a smallneighborhood of the origin by choosing design parameters appropriately. A simulationexample is provided to show the effectiveness of the proposed approach.