Fuzzy Adaptive Optimal Control For Nonlinear Uncertainty Systems

Modern control systems are becoming increasingly complex.Multivariable,strong coupling,uncertain and nonlinear factors seriously affect the performance and quality of systems control,so it is great significant to study optimal control problem of nonlinear uncertain systems.Based on the theoretical framework of adaptive fuzzy control and optimal control,this thesis studies classes of fuzzy adaptive optimal control design schemes,and the stabilities of the corresponding controlled systems are proved.The main research works are stated as follows:(1)For a class of single-input and single-output(SISO)nonlinear systems with unmeasurable states,by using the universal approximation property of fuzzy logic system to deal with the unknown smooth function and cost function,a state observer is established to estimate the unmeasurable states.Under the framework of the backstepping,a feedforward controller is established.Adopting single network adaptive evaluation technique,a feedback optimal controller is designed,and the stability of closed-loop system is proved.The simulation example is provided to show the effectiveness of the approach.(2)For a class of SISO nonlinear systems with actuator faults,adaptive compensation technique is used to solve the problem of actuator faults,the fuzzy logic system is adopted to approximate the unknown cost function.Combining with backstepping technique and optimal control technique,a fuzzy adaptive fault-tolerant optimal controller is established,the state feedback fault-tolerant optimal control problem is solved.Finally,a simulation example is given to validate the feasibility of fault-tolerant optimal control scheme.(3)For a class of SISO nonlinear systems with unmeasurable states and nonlinear function faults,by using the universal approximation property of fuzzy logic system to deal with the unknown smooth function and cost function,a fuzzy state observer is established to estimate the unmeasurable states,a filtered signal is used to circumvent algebraic loop problem.Combining with adaptive fault-tolerant control technique,optimal control technique and adaptive backstepping design technique,an output feedback fault-tolerant optimal controller is established,and the stability of closed-loop system is proved.The numerical simulation is given to validate the rationality of the proposed scheme.(4)For a class of nonlinear interconnected large-scale systems,the fuzzy logic systems are adopted to approximate the unknown smooth function and cost function,by combining with the decentralized control technique,optimal control theory and backstepping design technique,an adaptive fuzzy decentralized optimal controller is designed.Utlizing the Lyapnuov function stability theory,the stability of closed-loop system is proved,the numerical and applied simulation results are given to validate the effectiveness and applicability of the proposed control method.(5)For a class of nonlinear large-scale systems with unmeasurable states,a fuzzy state observer is constructed to estimate unmeasurable states,based on backstepping design technique,an adaptive fuzzy decentralized optimal controller is designed.Using the Lyapnuov function stability theory,the stability of closed-loop system is proved,the numerical simulation result is given to validate the rationality,at the same time,the proposed strategy is applied to a double inverted pendulum system,and the control objective is realized.(6)For a class of nonlinear interconnected large-scale systems with nonlinear function fault,by utlizing the universal approximation property of fuzzy logic system to deal with the unknown smooth function and cost function,a compensation function is introduced to compensate the effect of nonlinear function fault.Combining with Butterworth low-pass filter and adaptive backstepping technique,a feedforward decentralized fault-tolerant controller is designed,by using the single network evaluation technique,a feedback decentralized optimal controller is designed,and the stability of closed-loop system is proved,the simulation example is provided to show the feasibility of the proposed control approach.