Finite-time Optimal Control For Uncertain Nonlinear Systems

With the rapid development of science and technology,many technical fields not only require the controlled systems refer to the stability within a finite-time,but also need the optimal performance index.Therefore,the study of finite-time optimal control problems has important theoretical and practical significance.This thesis addresses the finite-time optimal control problem for classes of nonlinear systems whose powers are positive odd rational numbers,and provides stability analyses for the closed-loop systems.The specific contents are as follows:(1)A finite-time controller is developed for a class of strict feedback nonlinear lower triangular systems with unknown dynamics.Throughout the design process,the homogeneous system theory is used to deal with the nonlinear unknown functions,and a finite-time control law is developed based on the nested saturation control theory,adding one power integrator technique and the backstepping control method.The stability and convergence of the closed-loop system are proved based on the stability theory of finite-time Lyapunov.Finally,the feasibility and effectiveness of the proposed control strategy are verified by numerical example and application example.(2)Under the unknown arbitrary switchings signals,a finite-time optimal control strategy is proposed for a class of non-strict feedback nonlinear switched systems whose powers have switching signals.Firstly,the unknown nonlinear functions are processed by using the homogeneous system theory.Then,the Lyapunov functions are constructed via the adding one power integrator technique,and a global nested saturation finite-time control law is designed by backstepping control method.Then,based on the optimal control principle and global finite-time controller,a global finite-time optimal controller is constructively devised by adjusting parameters to minimize the cost function.Based on the finite-time Lyapunov stability theory,it has been shown that all the closed-loop signals converge to zero in finite-time.Finally,simulation examples are provided to validate the effectiveness of the proposed control scheme.(3)An adaptive neural network finite-time optimal control strategy is proposed for a class of non-strict feedback nonlinear systems with measurable states.The neural networks are used to approximate the unknown nonlinear functions.A nested saturation finite-time optimal control scheme is proposed via backstepping control method and optimal control theory.Based on the finite-time Lyapunov stability and inverse optimal theory,the stability analysis of the closed-loop system is performed to prove the controlled system is semi-globally practically finite-time stable and optimal properties.Finally,a numerical simulation example is given to further validate the feasibility and effectiveness of the proposed optimal control strategy.(4)A fixed-time fault tolerant control scheme is proposed for a class of non-strict feedback switched nonlinear systems under the unknown arbitrary switchings signals.Throughout the design process,the fixed-time fault tolerant control strategy is proposed using the backstepping control method and adding one power integrator technique.Based on the Lyapunov stability theorem,it is proved that all signals tend to stability at fixed-time for the closed-loop systems.Finally,a numerical simulation example is given to illustrate the effectiveness of the proposed control strategy.(5)A finite-time optimal control design method is proposed for a class of nonlinear interconnected large systems in non-strict feedback.Firstly,a semi-global finite-time controller is established via the theory of homogeneous systems,adding one power integrator technique,and backstepping control method.Then,a global finite-time optimized controller is given to minimize the cost function using the nested saturation control theory,optimal control theory,and the semi-global finite-time controller.According to the finite-time Lyapunov stability theorem,the convergence and stability of the closed-loop system are proved.Finally,a numerical simulation example is given to illustrate the effectiveness of the proposed control strategy.