Dynamic Optimization Of Differential-Algebraic Systems With Inequality Path Constraints Research

Dynamic optimization,as an effective tool to solve various difficult problems in the actual industrial process of production,now has been widely used in power systems,petrochemicals,bioengineering,clean energy and other fields to achieve the goal of energy saving,consumption reduction,efficiency,etc.Because of its great practical application value,it has attracted extensive attention and extensive in-depth research by many famous experts and scholars at home and abroad.Control vector parameterization is the mainstream calculation method to solve the dynamic optimization problem directly.Using this method to discretize the original problem,the mathematical programming problem after conversion is small and easy to solve,as well as the solution accuracy is high.But at the same time,there are still some deficiencies and difficulties in the control vector parameterization:(1)The division of the time grid can only be artificially set before the problem is solved,and will not change during the problem solving process;(2)It is difficult to deal with inequality path constraints;(3)The existence of equality path constraints may lead to higher-order problems of differential algebraic equations,which are difficult to solve.The segmentation approximation strategy of the control variables and the degree of density of the meshing will directly affect the approximation degree of the solution results to the optimal control trajectory.In general,the more flexible the segmentation approximation strategy of the control variables and the finer the time meshing are,the better the approximation of the optimal control trajectory is.But at the same time it can greatly increase the dimensionality of the problem and the time of solution,thus leading to poor efficiency.Aiming at these problems,this paper firstly uses the control vector parameterization method to transform the infinite dimensional dynamic optimization problem into a dynamic optimization problem with limited decision variables and infinite constraints,and then uses the pointwise discretization method to deal with inequality path constraints,to study its dynamic optimization.The research content and innovation points summarized are as follows:(1)For differential-algebraic equations with inequality path constraints,the differential algebraic equations are directly solved by backward differentiation formula.Then,a dynamic optimization algorithm for dealing with differential algebraic systems with inequality path constraints is proposed utilizing pointwise discretization method.The algorithm obtains the optimal solution after a finite number of iterations and can guarantee that the violation of the path constraint satisfies the accuracy specified by the user.Finally,in order to verify the effectiveness of the algorithm,three classical test cases are simulated and compared with the methods in the literature.The simulation results show the effectiveness of the proposed method.(2)On this basis,a linear continuous approximation strategy is adopted for the CVP constant approximation strategy and the equal time period,and the time nodes are adaptively updated based on the linear continuous strategy.Firstly,the linear continuous approximation strategy is used to replace the single constant approximation strategy to approximate the control variables to study the dynamic optimization of differential algebraic systems with inequality path constraints.The two similar strategies are compared by simulation in the classic DAE chemical case.The simulation results illustrate the advantages of the linear continuous approximation strategy.Then,for the problem of equal time period,the adaptive optimization vector parameterized differential algebraic system dynamic optimization of linear continuous approximation strategy is proposed.Finally,the simulation results are verified by DAE example.The simulation results verify the effectiveness of the proposed method.