Research And Implementation Of The Optimal Control Algorithm Based On Hermite-Simpson Discrete Format

Optimal control is to adjust the control variables to achieve a certain performance index while satisfying the state constraints.As the main branch of modern control theory,it is at the forefront of the cross development of mathematics,engineering and computer science,and can be effectively applied in many fields such as system engineering,especially space technology.There are many ways to solve the optimal control problem,in which the analytical method needs to know the specific expression,and the indirect method is more complicated to calculate and solve.The commonly used direct collocation method converts continuous optimal control problems into discrete nonlinear programming problems by discrete control variables and state variables.The Hermite-Simpson method is a kind of direct collocation method.Compared with the gradient method,the solution accuracy is higher.Compared with the Runge-Kutta method and the 5th-order Legendre–Gauss–Lobatto method,it can effectively avoid Runge phenomenon.Software research on optimal control problem solving algorithms has been carried out in China,but mature software is relatively scarce.In response to this situation,the research team developed the solution function for this kind of problem on the system-level integrated design and simulation verification platform Mworks.This thesis focuses on the algorithm and improvement of the Hermite-Simpson method.The main work and contributions of this thesis are:(1)Study and summarize the general form of optimal control problem,design the object system of optimal control problem according to its characteristics,and build the specific framework of problem solving based on Hermite-Simpson method to transform it into nonlinear programming problem(NLP)to replace the original problem,then call the IPOPT tool to solve.(2)Multi-section Hermite interpolation polynomial is used for the optimal control problem.The obtained trajectory is not smooth and can be processed by adding discrete points.This thesis proposes an adaptive mesh refinement strategy based on discrete error.Compared with uniform mesh refinement,it is possible to determine the position and number of nodes,reduce the number of iterations,and improve the accuracy of the solution.The efficiency and accuracy of the calculations using this method have been improved.(3)For the optimal path problem of industrial robots and the maximum range of hang gliders,the optimal control model is established by C++ language,and the Hermite-Simpson algorithm proposed in this thesis is used to solve it,and the adaptive network based on discrete error is applied.The simplification strategy and the solution results verify the feasibility,superiority and efficiency of the method.