Adaptive Neural Network-based Optimal Control Of Nonlinear Strict Feedback System

Recently,with the increasingly prominent problems of energy crisis and environmental pollution,the investigation on optimal control plays an important role.Strict feedback nonlinear system is a very representative modeling form of modeling in practical engineering systems,and the optimal control of such systems has attracted the attention of scholars in the field of control.Theoretically,the optimal solution of a nonlinear system can be obtained by solving HJB equation.However,the equation has strong nonlinear characteristics,so that its analytical solution is found very difficult or even impossible.In order to solve this problem,adaptive neural network approximation based RL is usually considered to achieve optimized control.However,in real-world systems,it is necessary to consider the control gain function and most system states are difficult to collect.In addition,traditional RL optimization methods are complex and computationally expensive,which makes them difficult to expand and apply.Therefore,this thesis mainly considers the problems of unmeasured state,unknown gain function and complex calculation in the optimized control of strict feedback nonlinear system by using backstepping control technology and adaptive neural network.The main work is as follows:(1)A new adaptive state observer control method is proposed for a class of strict feedback nonlinear systems with unmeasurable states.Because the observer method can be performed with the relaxed condition because it does not require the design parameters to satisfy the Hurwitz equation,therefore it can be more easily applied and extended to serve for nonlinear system control than the existing observer methods.Finally,by integrating the observer dynamic into the backstepping design,the adaptive tracking control is achieved.(2)Based on the design idea of OB technique,an optimized control method is proposed for a class of strict feedback nonlinear systems containing the unknown control gain function.OB technique requires to deal with the actual and virtual controls of backstepping as the optimized solutions of corresponding subsystems so that the entire backstepping control is optimized.In the work,for achieving the optimization control,RL of critic-actor structure is constructed in every backstepping step on the basis of the neural network approximation of the HJB equation’s solution.The proposed RL is with the simple training laws,it can greatly alleviate the algorithm complexity for the optimized control.(3)An OB control method is proposed for a class of strict feedback nonlinear systems by combining DS technique with RL.However,the original design of OB still needs to repeatedly calculate the derivative of virtual control,as a result,it will inevitably cause the problem of “differential explosion”.In order to alleviate the phenomenon,DS technique is combined with RL in this OB control.Furthermore,OB control needs to conduct RL in every backstepping step,hence simplifying the algorithm of RL is very necessary and substantive for achieving the combination of this two techniques.Furthermore,OB control needs to conduct RL in every backstepping step,hence simplifying the algorithm of RL is very necessary and substantive for achieving the combination of this two techniques.Because the optimized control derives both critic and actor training laws from a simple positive function,it can obviously simplify the RL algorithm compared with the traditional optimizing methods.