Numerical Solution Of Optimal Control For A Class Of LPV Systems

The limit acceleration of aero-engine is an important index of aircraft take-off performance.Under the condition of safety,it is an important research subject of engine control system to make the acceleration process as short as possible.The acceleration control of an aeroengine is essentially a nonlinear control theory,usually using a nonlinear mathematical optimization analysis.In order to solve the optimization problem of general linear parameter varying(LPV)system,this paper uses the difference sorting mutation whale optimization algorithm(RWOA)to solve the problem.Examples show that RWOA has the characteristics of high precision and fast convergence speed.The main research contents of this paper are as follows:1.For linear variable parameter LPV system,this paper mainly studies its optimal control problem and gives the related description.Because it is relatively difficult to calculate the optimal control with the gradient-based optimization algorithm,this paper presents an intelligent whale optimization algorithm for this problem,it has the characteristics of simple frame,few parameters to be operated,and easy to be solved by programming.The research on WOA is still in the stage of fumbling,and the algorithm still has many shortcomings: the precision of the solution is not up to the requirement,the convergence speed is slow and the optimal solution is likely to be local,etc.2.In view of the slow convergence speed of whale optimization algorithm,this paper adopts the method of combining the difference sorting mutation strategy with whale optimization algorithm,and then the difference sorting mutation whale optimization algorithm(RWOA)is proposed.The position of each whale is changed by the differential sorting strategy,and then it is updated by the previous algorithm,which makes the convergence speed of the whale optimization algorithm faster.Numerical examples are given to illustrate the effectiveness of the proposed algorithm in solving optimal control problem of LPV systems,and the algorithm is also applicable to general LPV systems.3.In LPV systems,for constrained optimal control problems,two LPV systems(dynamic system and constrained system)which share the same scheduling parameters need to be solved together,this will make the problem more meaningful in practical application.The algorithm steps of the whale optimization algorithm using the differential sorting mutation strategy are also given,and its validity is proved by the numerical examples.