Neural Network Backstepping Control For Several Classes Of Underactuated Systems

Underactuated systems are widely used in people’s daily life due to its simple structure,small size,light weight and low power consumption.Although the automatic control problem of underactuated systems has always been a research hotspot in the control field,at present,most of underactuated systems are controled manually,which is time-consuming,laborious and insecure.Therefore,the research and realization of the automatic control method of underactuated systems has important theoretical significance and practical application value.Based on neural network(NN)backstepping control technique and combined with switched control,linear matrix inequality technique and robust backstepping control method,this dissertation mainly studies the control problems of four kinds of different underactuated systems,and these four kinds of underactuated systems increase in order according to the dimension of system degree of freedom,which are two degrees of freedom(2-DOF)underactuated system—rotary inverted pendulum(RIP),three degrees of freedom underactuated system—plane vertical take-off and landing(PVTOL)aircraft,three degrees of freedom(3-DOF)underactuated system—twin-rotor helicopter and six degrees of freedom(6-DOF)underactuated system—quad-rotor unmanned aerial vehicle(UAV).The main research contents of this dissertation are as follows:To solve the swing-up and stbilizaation control problem of a 2-DOF underactuated rotary inverted pendulum system,we first use linearization system and switched control strategy to avoid the problems of underactuation and uncontrollability of the original RIP nonlinear system.Then,robust backstepping method,adaptive NN backstepping method and linear matrix inequality technique are applied to design the state dependent switched swing-up controller and stabilization controller.Finally,Lyapunov stability criterion is used to analyze the stability of the closed-loop RIP system,and uniformly ultimate boundednesss stability of the closed-loop system states is obtained.The effectiveness of the control method is verified by two groups of physical experiments.To solve the position tracking control problem of a 3-DOF underactuated PVTOL aircraft system,we first use intermediate controllers and perturbation of nonlinear terms to avoid underactuation problem of the original system.Then,we propose an improved NN backstepping control method—gradient descent NN backstepping control technique.Two gradient descent NN backstepping controllers are introduced to control the position of the aircraft system,and robust backstepping technique is used to control the roll angle of the system.Finally,Lyapunov stability criterion is used to prove the uniformly ultimate boundednesss stability of the closed-loop system tracking errors,and the effectiveness of the control method is verified by two groups of simulation results.To solve the attitude tracking control problem of a 3-DOF underactuated twin-rotor helicopter system,we first use intermediate controllers to avoid underactuation problem of the original system.Then,gradient descent NN backstepping control technique is applied to design controllers for the three attitude angles of the system,and three gradient descent neural networks are used to deal with perturbations of the system’s three attitude angles.Finally,Lyapunov stability criterion is used to prove the uniformly ultimate boundednesss stability of the tracking errors of the closed-loop system,and the effectiveness of the control method is verified by four groups of physical experiments.To solve the position and attitude tracking control problems of a 6-DOF underactuated quad-rotor UAV system,we first use intermediate controllers and define two subsystems to avoid underactuation problem of the original system.Then,gradient descent NN backstepping control technique is applied to design controllers for the system,and six gradient descent neural networks are used to address perturbations of the system position and attitude.Finally,Lyapunov stability criterion is used to prove the uniformly ultimate boundednesss stability of the closed-loop system tracking errors,and the effectiveness of the control method is verified by two groups of physical experiments.