Research Of Optimal Strategy Based On Multiple Shooting With Time Grid Refinement

Optimal control,also known as dynamic optimization,is a vital component of modern control theory.It has been applied successfully in various fields,such as aerospace engineering,petrochemical industry,biomedical engineering,and so on.Optimal operation strategies of controlled systems can be obtained by implementing optimal control algorithms.Furthermore,such objectives as energy saving,cost reducing,potential mining and efficiency improving can be achieved.A common class of computation method for optimal control problems is the direct methods,which transform infinite-dimensional optimal control problems to finite-dimensional static optimization ones.Multiple shooting,as a representative method,can solve those optimal control problems with highly nonlinear dynamic equations.Also,multiple shooting method has advantages of high precision,easy implementation and so on.However,numerical calculation of multiple shooting method may be confronted with the contradiction between solution accuracy and computational costs,and the difficulties to handle path constraints.In this thesis,terms of settlement are come up.Modified multiple shooting method with time grid refinement is realized.Several typical optimal control problems are tested in this framework-The main work and contributions of this thesis are as follows:(1)Contraposing the time consuming differential equations solver,Runge-Kutta formula is introduced for fast calculation,which implements numerical integration computation on discretization time grid.It saves time costs and guarantees accuracy simultaneously.(2)To conquer the difficulties brought by inequality path constraints,smoothed penalty function method is applied to handle them.Inequality path constraints are approximated by smoothing functions.Then,these functions are added to the objective as penalty terms.Cases show the validity of this method.(3)To balance the contradiction of grid resolution and computational costs,a slope-based time grid refinement strategies is proposed.It adaptively adjusts time grid partition according to the different contributions to approximation accuracy of different time nodes.(4)Contraposing the drawback of fixed time grid,a modified multiple shooting method with variable time nodes is proposed.Optimal time grid partition is obtained during the optimization procedure.The results are also compared with Time-Scaling method.