Fuzzy Adaptive Inverse Optimal Control For Nonlinear Systems

This thesis studies the fuzzy adaptive inverse optimal control problems for classes of uncertain strict feedback nonlinear systems,and the stability and optimization performance analysis of the closed-loop system are given.The main contents are as follows:(1)For a class of standard nonlinear systems,the fuzzy adaptive inverse optimal state feedback and output feedback control problems are studied,respectively.(1)The case of measurable system states is considered.Firstly,the FLSs are utilized to modify the unknown nonlinear dynamics,then,an equivalent system and its auxiliary system are established.Based on the auxiliary system and backstepping design algorithm,fuzzy adaptive inverse optimal control methods are developed,respectively.The proposed control schemes can guarantee that the auxiliary systems are asymptotically stable,which makes the controlled systems are input to state stable and the inverse optimal gain assignment problems are solvable.Furthermore,the inverse optimal control objectives are achieved,that is to ensure that the cost functionals are minimized.(2)The case of immeasurable system states is considered.Since controlled systems contain unknown nonlinear dynamics,firstly,the FLSs are utilized to approximate the unknown nonlinear function,and the auxiliary systems of the controlled systems are constructed.Then,based on the auxiliary systems,two fuzzy state observers are established to estimate the immeasurable states,respectively.By combining with the inverse optimal control principle and adaptive backstepping design technology,observer-based fuzzy adaptive inverse optimal output feedback control schemes are proposed,respectively.The proposed control methods ensure that all signals of the closed-loop system are bounded,so that the inverse optimal gain assignment problems of the controlled systems are solvable,and the inverse optimal control goals are achieved,that is to ensure that the cost functionals are minimized.Finally,two simulation examples are given to illustrate the validity of the proposed control method,respectively.(2)For two classes of nonlinear systems with full-state constraints and partial state constraints,the fuzzy adaptive inverse optimal state feedback and output feedback control methods are developed,respectively.Firstly,based on the control scheme in the previous chapter,by constructing the log-type Lyapunov functions and combining with the inverse optimal control principle and adaptive backstepping design technology,the fuzzy adaptive inverse optimal state feedback control problem is addressed for the closed-loop system,and the stability and optimization performance of the system are guaranteed.And it is proved to guarantee that the full state constraints are not overstepped.Meanwhile,this theory is extended to the study of output feedback control.The fuzzy adaptive inverse optimal output feedback control scheme is presented,so that the inverse optimal gain assignment problems of the controlled systems are solvable,and the inverse optimal control goals are achieved.Furthermore,the limited state does not violate the constrained bound.Finally,two numerical simulation examples are given to verify the effectiveness of the proposed method.(3)Based on the control schemes proposed in the previous two chapters,firstly,by considering the measurable and unmeasurable states of the system respectively,the control problems are studied for a class of quarter-vehicle active suspension systems with electromagnetic actuator.The fuzzy adaptive inverse optimal state feedback and output feedback control schemes are presented.Then,this theory is extended to the study for active suspension systems with full-state constraints and partial state constraints.Finally,the simulation studies are given in the cases of both bump road and sinusoid road displacement input,and the simulation results show the validity of the proposed control method.