Research On Computational Method Based On Multiple Shooting For Path Constrained Optimal Control Problems

Optimal control is an important part of modern control theory and has become an important tool for solving industrial problems.Nowadays,it has been widely used in the fields of aircraft trajectory optimization,economic management,Chemical medicine,energy and power,and has brought huge economic benefits,so that it has attracted widespread attention and research from scholars at home and abroad.However,in actual industrial problems,path constraints closely related to engineering safety have brought many difficulties to the solving of optimal control problems.Aiming at how to solve the optimal control problem containing path constraints with high precision and efficiency,this paper studies the processing of path constraints based on the MWorks-NSOCP,which is a platform developed by the research group.The main work of this paper is as follows:(1)Focus on multiple shooting method,after studying the influence of path constraints on gradient and analyzing the influence of auxiliary variables on the convergence of the algorithm,an adaptive meshing method including grid node optimization and target segment optimization is proposed.Testing of examples denotes that the method is proved to reduce the computational cost of solving the optimal control problem including inequality path constraints.(2)Research on methods of processing equality path constraints with solving differential-algebraic equations,this paper analyzes the influence of the transform method on the computational cost,proposes a method based on the Functional Mock-up Interface.In addition,the advantages and disadvantages of these methods are comprehensively discussed,and selection criteria of methods to process the equation path constraint is proposed.What’s more,examples are tested to verify that the method can improve computing efficiency.(3)Based on the research of the equality path constraints,this paper studies on the slack variable method which is used to processing inequality path constraints,and find that the cost of time the method will sharply increase as a price of high precision.To deal with the problem,this paper research on the difference of gradient between state variables and path constraints,and proposes a pseudo-relaxation variable method that transforms inequality path constraints into the constraints of state variable.Meanwhile,the efficiency of the method is verified through example tests.At the end of this paper,the multiple method with improved adaptive meshing and the methods used to process path constraints are implemented,and proved to be efficient through solving practical problems in industry.