On The Method Solving Finite Time Constraint Optimal Contorl Problem Based On Generating Functions

As an important part of modern control theory,optimal control has been greatly applied and developed in all major engineering fields.However,with the improvement of system complexity and the constraint of parameters caused by various conditions,the method has been difficult to solve such control problems.The numerical algorithm for optimal control of nonlinear systems with constraints is studied in this paper.According to the numerical algorithm,the paper is divided into two parts: the first part is to consider constrained nonlinear system optimal control problem in the framework of constructing numerical algorithms for Hamiltonian systems;The second part is the applications of the algorithm proposed in this paper on the optimal control law design for the nonlinear system model with constraints.First,this paper analyzes the development of nonlinear optimal control problem and the research status of our country and abroad,the derivation of the optimal control problem to the two-point boundary value problem is introduced,based on this,the optimal control problem with state or control constraints is studied.The difficulty of solving this kind of constrained problems is that they include continuous inequality constraints of state parameters and control parameters in time interval,.To deal with this kind of problem,this paper uses the interior point penalty function idea to transform it into an unconstrained optimal control problem.At last,based on the idea of generating function algorithm,the double generating function is used to realize the optimal approximation of the two-point boundary value problem,and the simulation is realized.The theoretical results of the numerical algorithm for the constrained nonlinear optimal control problem,this paper applies it to the control of the gantry lifting system and the separation of spacecraft modules in the near earth orbit.Both of them are constrained optimal control problem for six order system,this paper carries on the simulation analysis based on both nonlinear model approximation,the simulation results show that the proposed method can satisfy the small swing angle limitation during the lifting process and the small thrust constraint conditions of the spacecraft.