Fuzzy Adaptive Output Feedback Control For Uncertain Nonlinear Systems

As is known to all,many practical engineering systems have unmodeled dynamics,time delay,unknown control gain and other phenomena,which become an important factor leading to the instability of the controlled system.With the development of science and technology faster and faster,many industrial areas of the control system control quality requirements are more and more high,they not only require the controlled system is stable,but also hope that the controlled system can have a certain robustness,which makes the theoretical research of the controlled system more practical significance.Therefore,in recent years,the field of control has gradually strengthened the exploration of robust control of nonlinear systems on the basis of the study of system stability.In this paper,based on the fuzzy adaptive Backstepping design,the robust control design problem of several kinds of strict feedback nonlinear systems with unknown nonlinear gain is studied under the premise that the system state is unmeasured,and the stability and convergence of the system are analyzed and proved.The main contents are as follows:(1)For strict feedback nonlinear systems with unknown state delays,when the nonlinear control gain and the system states are unknown,the Lyapunov-krasovskii function addressed the problem of the unknown state time-delay.The unknown nonlinear dynamics will be approximated by the fuzzy logic system,and the state observer is constructed to solve the problem of the ummeasured states.Inspired by Backstepping design ideas,an intelligent adaptive output feedback control scheme is designed,and the stability of the controlled system in the sense of Lyapunov function is proved.In the end,the effectiveness of the proposed control method is verified by numerical simulation results.(2)For a class of strict feedback nonlinear systems whose states are not measurable,when the control gains in the system are assumed to be unknown nonlinear functions,the problem that the system state cannot be measured is solved by building a state observer,and then the fuzzy logic system is used to identify unknown nonlinear dynamics.In addition,the problem of “computational inflation” inherent in traditional Backstepping control method is also solved by introducing dynamic surface control technology,and an intelligent adaptive dynamic surface control approach is proposed and its stability is proved.The designed control method avoids repeated differentiation of the virtual controller,reduces the complexity of system calculation and reduces the calculation time.At last,the simulation result can proof the availability of the designed scheme.(3)For the strict feedback nonlinear system with unmodeled dynamic,when the control gains in the system are assumed to be unknown nonlinear functions and the state is not completely measurable,dynamic signal method is used to deal with the unmodeled dynamic disturbance,and logarithmic Lyapunov function is constructed according to the design idea of bounded control.By constructing logarithmic Lyapunov function and combining projection operator technique,the designed controller is guaranteed to be bounded.Based on Backstepping control design technology,give the fuzzy adaptive robust control design method and its stability analysis.In the end,the simulation results can proof the availability of the presented scheme.(4)The robust control issue for a class of multi-input multi-output strict feedback nonlinear systems with input delay is studied.When the control gains in the system are assumed to be unknown nonlinear functions and the state is not completely measurable,the problem that the state of the system cannot be measured is addressed by building a state observer.Then the fuzzy logic system is used to identify the unknown nonlinear dynamics.Based on Backstepping control technology,give a fuzzy adaptive output feedback control algorithm and its stability analysis.Eventually,the simulation results can proof the validity of the presented approach.(5)For a class of uncertain nonlinear switched systems with ummeasured states,when the control gain in the system is assumed to be unknown nonlinear function,the control problem of input saturation is further considered.By using the mean value theorem,the saturated function of the input is transformed into a bounded function.Thus,the problem of saturated input is effectively solved.Moreover,in order to address the inherent“computational inflation” issue of the conventional Backstepping control scheme,the command filter not only overcomes the repeated differentiation of the virtual controller,but also considers the filtering error of the filter,and introduces the error compensation signal to suppress the filtering error.Under the framework of fuzzy control and Backstepping control,an intelligent adaptive output feedback control method and stability proof are presented.At last,a simulation example is proposed to proof the effectiveness of the presented control approach.