Intelligent Adaptive Finite-time And Optimal Control For Uncertain Nonlinear Systems

With the development of science and technology,the actual engineering system is becoming more and more complex.In order to meet the needs of engineering,many complex practical systems always expect the shortest convergence time or the best performance index.Therefore,compared with the control problems of infinite-time or not meeting the performance index,the research of the finite-time and optimal control have the higher theoretical and engineering application value.In this paper,under the framework of fuzzy or neural network intelligent control,and based on adaptive control theory,finite-time control approach and optimal control theory,a series of intelligent adaptive finite-time and optimal control strategies are proposed for several kinds of uncertain nonlinear systems,and the theoretical proofs of convergence and stability for the plant systems are given.The main research contents are as follows:(1)A fuzzy finite-time adaptive control strategy with state constraints and power exponents is presented for nonlinear systems.During the design of control strategy,fuzzy logic system(FLS)is used to identify unknown dynamics.Based on backstepping design technology,power integral control method and finite-time barrier Lyapunov theory,a finite-time control approach is constructed.It is proved that all the states of the plant system do not violate the boundary and all the signals converge to a small region near the origin in finite-time.Finally,a second-order numerical system illustrates the validity of the proposed scheme.(2)A fuzzy finite-time adaptive control strategy under arbitrary switching signals is constructed for nonlinear system with the power exponent contains switching behavior.During the control design process,the FLS is used to deal with the unknown dynamics.Combined with the adding one power integral method and backstepping design technology,the fuzzy actual finite-time controller is constructed.On this basis,the main idea of inverse optimization theory is used to devise the finite-time optimal controller with the minimum performance index function.Moreover,under the perspective of finite-time common Lyapunov stability theory,the semi-globally practically finite-time stable and optimal properties of the plant system are proved,respectively.Finally,both numerical example and actual inverted pendulum system are carried out to verify the effectiveness of the proposed approach.(3)A decentralized fuzzy finite-time fault-tolerant tracking control strategy is presented for interconnected nonlinear large-scale systems with power exponents and actuator faults.During the design of control strategy,FLS is carried out to cope with the unknown dynamics.Combined with backstepping decentralized control design technology,power integral method and fault-tolerant control technique,a decentralized finite-time adaptive control approach is constructed.Moreover,the stability of the plant system is analyzed by finite-time Lyapunov function theory.Finally,a second-order interconnected large-scale numerical system is given to illustrate the validity of the proposed scheme.(4)A adaptive neural network(NN)tracking optimal control problem is investigated for stochastic nonlinear systems which contain uncertain dynamics and state constraints.During control design process,firstly,to avoid the violation of state constraints in achieving optimal control,the novel barrier optimal performance index functions for subsystems are developed.Further,under the framework of identifier-actor-critic,the virtual and actual optimal controllers are presented based on backstepping technique,in which,the unknown nonlinear dynamics are learned by the NN approximators.Moreover,the quartic barrier Lyapunov functions are constructed to ensure the stability of the systems with stochastic disturbance.Finally,a second-order numerical system and a third-order practical electromechanical system are carried out to verify the validity of the presented optimal scheme.