By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive...By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.展开更多
In this article,an Enlarged Polygon/Polyhedron(ELP)method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance(CPOA)constraints in trajectory optimization.First,the equi...In this article,an Enlarged Polygon/Polyhedron(ELP)method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance(CPOA)constraints in trajectory optimization.First,the equivalent condition of a point outside the convex set is given and proved rigorously.Then,the ELP condition describing the CPOA constraints equivalently is given without introducing binary variables,and its geometric meaning is explained.Finally,the ELP method is used to transform the CPOA trajectory optimization problem into an optimal control problem without binary variables.The effectiveness and validity of ELP method are demonstrated through simulations with both simple linear dynamic model(unmanned aerial vehicle)and complex nonlinear dynamic model(hypersonic glide vehicle).Comparison indicates the computational time of ELP method is only 1%-20%of that of the traditional Mixed-Integer Programming(MIP)method.展开更多
文摘By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
基金supported by the National Natural Science Foundation of China(No.52232014)the National Natural Science Foundation of China Joint Fund(No.U2241215)。
文摘In this article,an Enlarged Polygon/Polyhedron(ELP)method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance(CPOA)constraints in trajectory optimization.First,the equivalent condition of a point outside the convex set is given and proved rigorously.Then,the ELP condition describing the CPOA constraints equivalently is given without introducing binary variables,and its geometric meaning is explained.Finally,the ELP method is used to transform the CPOA trajectory optimization problem into an optimal control problem without binary variables.The effectiveness and validity of ELP method are demonstrated through simulations with both simple linear dynamic model(unmanned aerial vehicle)and complex nonlinear dynamic model(hypersonic glide vehicle).Comparison indicates the computational time of ELP method is only 1%-20%of that of the traditional Mixed-Integer Programming(MIP)method.
