Adaptive Backstepping Control For Strict Nonlinear Systems With State Constraints

Adaptive control of the nonlinear system is widely applied in various industry environments.Due to the limitation of physical devices and performance/safety requirements of the actual system,most practical systems have input,output or state constraints.Meanwhile,time delay is also an inherent characteristic in many engineering systems and it is also frequently encountered in many practical systems,such as long pipe feeding or belt transmission,slow process or complex online analyzer.In addition,various uncertainties(such as parameter uncertainty,model function uncertainty and structure uncertainty)are inevitable in nonlinear systems.Therefore,in this paper,a series of methods,such as nonlinear system theory,adaptive control,neural network,fuzzy logic system,are synthetically used to study the adaptive control method for a class of uncertain strict feedback nonlinear systems with time delay and state constraints.The research topics of this paper are as follows:An adaptive neural network control method is proposed for the strict feedback nonlinear system with both unknown gain function(known symbol)and state constraints.By introducing iBLF in every step of the Backstepping method,the problems of unknown control gain and full state constraint are solved.The neural network(NNs)is used to estimate the unknown system function.At the same time,Pade estimation and coordinate transformation are used to deal with the input delay.Then a novel control method is proposed to ensure the boundedness of all signals in the closed-loop system,and all state variables are in constraints.On this basis,a feasible condition test is proposed to obtain the optimal control parameters.A fuzzy control method is proposed for the strict feedback nonlinear system with time-varying control gain(unknown symbol)and state constraints.By constructing the bounded Lyapunov method(BLF),the problem of all state constraints is solved.The unknown system function is estimated by using fuzzy logic system.At the same time,for the unknown time-varying control gain and input delay,Laplace transform and Pade approximation technique are used to transform the system model.On this basis,Nussbaum function method is applied to realize the state constraint control of nonlinear system with both input delay and unknown gain function.The boundedness of all signals in the closed-loop system is guaranteed,and the signal tracking is realized.Meanwhile,the simulation results show that the proposed control method is robust to time-varying input delay.A fuzzy control method is proposed for the strict feedback nonlinear system with both state delay and unknown time-varying control gain(unknown symbol).Different from the above,Lyapunov Krasovskii universal function method(LKFs)is used to eliminate the influence of unknown time-varying delay.Furthermore,the boundedness of all signals in the closed-loop system is guaranteed,and all state variables do not violate the constraints.The effectiveness of the proposed method is verified by a simulation in MATLAB environment.