| The output regulation problem is one of the significant research issues in modern control field.In practical engineering systems,the uncertainties caused by measurement errors and other reasons will affect the systems.So these uncertainties need to be taken into account when the model of the system is built.In addition,many practical controlled systems have produced high precision work requirements because of the progress of our society.Thus,it is meaningful for us to research the optimal output regulation problem.This paper investigates the optimal output regulation problem of nonlinear systems with some uncertainties.A new control strategy is designed with the help of inverse optimal control method,the relevant internal model and observer are also established.The concrete contents are as follow:The inverse optimal output regulation problem is researched for nonlinear systems which contain unknown parameter vectors and disturbances.When the state can be measured.Firstly,the output regulation problem becomes a stabilization problem through state transformation.Next,an auxiliary system which is connected with the internal model is constructed for the system.Then by uniting the inverse optimal control method,a new internal model and a state feedback inverse optimal controller are designed according to the auxiliary system.Finally,according to Lyapunov control theory,the stability analysis objective is achieved and the cost functional is also demonstrated to be minimal.When the state is not fully measured directly.A state observer,an internal model and an output feedback inverse optimal controller is designed such that all signals of the closed-loop systems are uniformly ultimately bounded(UUB).Moreover,the optimal objective is achieved by minimizing the newly well defined cost functional.Finally,simulation cases are raised to testify the feasibility of the controller.The finite-time inverse optimal output regulation problem is researched for nonlinear systems with unknown nonlinear functions.The case of unmeasured state is also concerned here.The output regulation problem is converted to a stabilization problem.The fuzzy logic systems(FLSs)are used to approach the unknown nonlinear functions in the controlled systems.Then an auxiliary system and an internal model are established.Next,a fuzzy state observer is designed according to the auxiliary system.An adaptive fuzzy finite-time inverse optimal controller is proposed by employing finite-time stability theory and inverse optimal control method.The controller ensures all signals of the closed-loop system are semi-globally practical finite-time stable(SGPFS),it can also minimize the cost functional.Finally,the validity of the controller is confirmed by a simulation result.The inverse optimal output regulation problem is researched for nonlinear systems with unknown nonlinear functions and unmeasured state.Time-delay is also appeared in the system.Firstly,an internal model is designed based on the immersion system theory and the internal model principle.Next,a high gain state observer which is irrelevant with time-delay is designed.Then time-delay is handled by introducing Lyapunov-Krasovskii functional,while the new controller is designed by incorporating inverse optimal control method.The newly designed control method is able to guarantee that the state of the closed-loop systems is UUB.In addition,a cost functional is designed so that the inverse optimal gain assignment problem can be solved.This cost functional is related to time-delay.Finally,the validity of the controller is confirmed by virtue of a simulation results.For the spacecraft system,the disturbance rejection problem is researched.In particular,the disturbance signals are produced by a nonlinear exosystem.Thus a nonlinear internal model is designed to estimate the external disturbance.Next,by adopting backstepping control technique and inverse optimal control method,a new controller is presented to make the angular velocity and the attitude can reach globally asymptotic stable,the cost functional can be minimized.Finally,the availability of the designed nonlinear internal model and controller is proved by a simulation example. |
