| Optimal control is one of the important branches of modern control theory.Optimal control methods are widely used in guidance and control,power systems,path planning,aerospace and other industrial fields.At present,a number of numerical solvers for optimal control problems have been developed at home and abroad,and the dynamic equations of the control optimization problems handled are all expressed explicitly.However,with the increasing complexity of engineering problems and the application of visual modeling,the processing of implicit dynamic equations has become a key obstacle to solving optimal control problems.Aiming at how to efficiently solve the optimal control problem with implicit dynamic equations,this paper studies the processing of implicit dynamic equations based on MWORKS-NSOCP,an integrated platform for visual modeling,solving and postprocessing of optimal control problems independently developed by the research group Method and its realization.The main work and contributions in the paper are as follows:(1)In-depth analysis of JModelica technology and its tools,research based on JModelica optimal control problem solving method,focusing on the realization of the automatic conversion algorithm of the MWorks-NSOCP platform visual control optimization model to JModelica,which well solves the implicit dynamic equations Optimal control problem,and tested the feasibility and effectiveness of the method with examples.(2)Through the analysis and research on the structure of explicit and implicit dynamic equations,as well as the in-depth analysis of the model exchange function of the FMI standard,the processing method of implicit dynamic equations based on FMI is proposed and implemented.This method uses the FMI model exchange function and numerical differential technology to directly solve the optimal control problem with implicit dynamic equations.Tested by examples,this method is simple and convenient when solving complex control optimization problems.(3)Aiming at the problem of low optimization speed based on FMI processing implicit equation method,an explicit method of dynamic equation based on RSM(quadratic response surface)model is proposed and implemented.This method uses the explicit dynamic equations of the hierarchical RSM model to replace the implicit dynamic equations of the original model.In order to obtain a high-precision hierarchical RSM model,a response surface adaptive partitioning criterion based on Sobol sensitivity index combined with local space length is explored.Tested by examples,this method has a higher optimization solution efficiency. |
