Research And Application Of Optimal Control Algorithm Based On MATLAB

With the continuous development of modern science and technology and the improvement of production requirements,the theoretical application of optimal control is becoming more and more extensive in various fields such as transportation,national defense and aerospace.In the research process of optimal control algorithm,the theory of variational method,target method and pseudo-spectral method has been formed.There are many related methods which can solve the target problem,but most of them are deficient in the refinement of grid,and it is often difficult to obtain the optimal solution quickly.Therefore,based on the pseudo-spectral method,this paper has a research on the optimal control algorithm,and constructs an improved mesh refinement algorithm which comprehensively considers the dynamic error and path constraint error.And combined the data preprocessing module with this mesh refinement algorithm to improve the computational efficiency of the numerical solver.The pseudo-spectral method mentioned in this paper uses interpolation instead of integral,translate the continuous optimal control problem into a very sparse problem of nonlinear programming(NLP)with appropriate discrete point set,the speed go faster with sparse nonlinear programming algorithm.When the constraint error did not meet the requirements in the interval sampling point,generally we have to refine the grid,the most commonly used method is to adjust the grid adaptively,to increase the number interval polynomial or grid refinement,with fewer discrete points to obtain higher accuracy.In some extent,the adaptive grid optimizationalso has certain limitation: when a grid constraint tolerance does not meet the requirements and to take a particular optimization strategy(For example,mesh refinement in multiple subintervals),is still possible to have too much discrete points in the target segmnent that adds difficulty in solving the problem.Therefore,this paper proposes a improved method based on adaptive pseud-spectrum method,Take the maximum dynamic error and path constraint error as the standard to mesh optimization,using fewer encryption grid point to improve the precision as much as possible,thus it can reduce the number of iterations and scale,improve the efficiency of the follow-up to solve.In addition,based on the pseudo spectrum method solving tool GPOPS,this article made a improvement on relevant algorithms,optimizing data preprocessing with automatic dimensionless method,taking hand of the dependent variables in the process of solving problems,so it can remove unnecessary partial derivative calculation process,save calculation time and computer memory space.Finally,based on the above improvements,several engineering problems are modeled and solved under Matlab,and the feasibility of solving the optimal control problem is illustrated.The results in this article show that data preprocessing and the improvement of adaptive pseudo spectrum method which can not only solve the general optimal control problem,it can also has good effect in solving path constraint and multistage complex issues.It provides a basis for the efficient solution of the optimal control problem in engineering and has certain practical engineering significance.