Research On Mesh Fine Partitioning Strategy For Dynamic Optimization Problems

Optimal control,also called dynamic optimization,is an important measure to achieve system gain,energy saving and consumption reduction.It is widely used in many fields such as robot control,chemical engineering,clean energy,bioengineering,food engineering and so on.The control vector parameterization method is a mainstream method in direct method for solving dynamic optimization problems.This method divides the whole time domain into several time grids to realize discretization,and then transforms the infinite-dimensional optimal control problem into a non-linear programming problem for solution.In this process,the reasonableness of time gridding has a great influence on the efficiency of solution and the approximation accuracy of the optimal control trajectory.In addition,the reasonableness of the initial value of control variables also affects the efficiency of solution and convergence speed.This research is devoted to solving the contradiction between approximation accuracy and computation time of control vector parameterization method,and improving the efficiency of solution.Thirteen different classical examples are analyzed and verified.On the basis of reading a large number of domestic and foreign literature,this paper carries out the following research:(1)For the research hotspot of control vector parameterization method,the general solution steps of control vector parameterization method are given.Two traditional chemical examples are used to verify the traditional control vector parameterization method.The traditional control vector parameterization is obtained through analysis.The method has disadvantages such as low approximation accuracy,high computational cost,fixed grid,and inaccurate positioning of switching time points.(2)Considering the optimal control problem of Lagrange form and Bolza form with integral term,numerical error will be introduced in the numerical calculation process.In order to reduce the introduction of error amount,both Lagrange form and Bolza form function are converted into Mayer form.Function.For the optimal control problem of the free final value time,introduce a new time variable to map,so that the optimal control problem of the free final value time is transformed into the optimal control problem with fixed final value time.(3)A class of important Bang-Bang optimal control problems are studied.According to the number of control variables,they are divided into single control variable Bang-Bang control problem and multi-control variable Bang-Bang control problem.Then a parameterized solution strategy for variable time scale non-uniform control variables is given.The example calculation shows that the method can not only obtain a good mesh division method,but also solve the defect of grid fixing of the traditional control variable parameterization method.The switching time node can be precisely located.(4)In this paper,a control vector parameterization method based on the slope information on the time scale is proposed.Firstly,the first iteration is carried out with fewer time grids,and the approximate trajectories of control variables are obtained quickly,which provides good initial conditions for the next iteration.Secondly,the time grids are reconstructed,including the elimination of time grids,the refinement of time grids and the displacement of important time switching points.The calculation results show that this method can not only accelerate the convergence speed,reduce the calculation cost,but also obtain more accurate optimization results.(5)In this paper,a dynamic mesh reconstruction strategy for dynamic optimization problem based on Pseudo Wigner-Ville distribution is proposed from another scale——frequency domain scale.Compared with the control vector parameterization method based on slope information,it has fewer iterations,better generality and finer optimization strategy.The results show that the proposed method has better rapidity and accuracy.