In this paper we present a new method combining interior and exterior approaches to solve linear programming problems. With the assumption that a feasible interior solution to the input system is known, this algorithm...In this paper we present a new method combining interior and exterior approaches to solve linear programming problems. With the assumption that a feasible interior solution to the input system is known, this algorithm uses it and appropriate constraints of the system to construct a sequence of the so called station cones whose vertices tend very fast to the solution to be found. The computational experiments show that the number of iterations of the new algorithm is significantly smaller than that of the second phase of the simplex method. Additionally, when the number of variables and constraints of the problem increase, the number of iterations of the new algorithm increase in a slower manner than that of the simplex method.展开更多
This paper considers the stochastic linear quadratic regulation （LQR） problem for Ito stochastic systems with multiple input controllers. The explicit controllers are given in terms of two Riccati equations by intro...This paper considers the stochastic linear quadratic regulation （LQR） problem for Ito stochastic systems with multiple input controllers. The explicit controllers are given in terms of two Riccati equations by introducing one new costate and establishing the homogeneous relationship be- tween the state and the new costate. More importantly, it is more computation saving for the derived Riccati equations than the one derived by augmentation technique.展开更多
An optimal motion planning of a free-falling cat based on the spline approximation is investigated.Nonholonomicity arises in a free-falling cat subjected to nonintegrable velocity constraints or nonintegrable conserva...An optimal motion planning of a free-falling cat based on the spline approximation is investigated.Nonholonomicity arises in a free-falling cat subjected to nonintegrable velocity constraints or nonintegrable conservation laws.The equation of dynamics of a free-falling cat is obtained by using the model of two symmetric rigid bodies.The control of the system can be converted to the motion planning problem for a driftless system.A cost function is used to incorporate the final errors and control energy.The motion planning is to determine control inputs to minimize the cost function and is formulated as an infinite dimensional optimal control problem.By using the control parameterization,the infinite dimensional optimal control problem can be transformed to a finite dimensional one.The particle swarm optimization(PSO) algorithm with the cubic spline approximation is proposed to solve the finite dimension optimal control problem.The cubic spline approximation is introduced to realize the control parameterization.The resulting controls are smooth and the initial and terminal values of the control inputs are zeros,so they can be easily generated by experiment.Simulations are also performed for the nonholonomic motion planning of a free-falling cat.Simulated experimental results show that the proposed algorithm is more effective than the Newtoian algorithm.展开更多
文摘In this paper we present a new method combining interior and exterior approaches to solve linear programming problems. With the assumption that a feasible interior solution to the input system is known, this algorithm uses it and appropriate constraints of the system to construct a sequence of the so called station cones whose vertices tend very fast to the solution to be found. The computational experiments show that the number of iterations of the new algorithm is significantly smaller than that of the second phase of the simplex method. Additionally, when the number of variables and constraints of the problem increase, the number of iterations of the new algorithm increase in a slower manner than that of the simplex method.
基金supported by the Taishan Scholar Construction Engineering by Shandong Governmentthe National Natural Science Foundation of China under Grant Nos.61120106011,61403235,61573221 and 61633014+2 种基金the Natural Science Foundation of Shandong Province under Grant No.ZR2014FQ011the China Postdoctoral Science Foundation under Grant No.2014M561929the Special Funds for Postdoctoral Innovation Project of Shandong Province under Grant No.201402032
文摘This paper considers the stochastic linear quadratic regulation （LQR） problem for Ito stochastic systems with multiple input controllers. The explicit controllers are given in terms of two Riccati equations by introducing one new costate and establishing the homogeneous relationship be- tween the state and the new costate. More importantly, it is more computation saving for the derived Riccati equations than the one derived by augmentation technique.
基金supported by the National Natural Science Foundation of China (Grant No. 11072038)the Municipal Key Programs of Natural Science Foundation of Beijing,China (Grant No. KZ201110772039)
文摘An optimal motion planning of a free-falling cat based on the spline approximation is investigated.Nonholonomicity arises in a free-falling cat subjected to nonintegrable velocity constraints or nonintegrable conservation laws.The equation of dynamics of a free-falling cat is obtained by using the model of two symmetric rigid bodies.The control of the system can be converted to the motion planning problem for a driftless system.A cost function is used to incorporate the final errors and control energy.The motion planning is to determine control inputs to minimize the cost function and is formulated as an infinite dimensional optimal control problem.By using the control parameterization,the infinite dimensional optimal control problem can be transformed to a finite dimensional one.The particle swarm optimization(PSO) algorithm with the cubic spline approximation is proposed to solve the finite dimension optimal control problem.The cubic spline approximation is introduced to realize the control parameterization.The resulting controls are smooth and the initial and terminal values of the control inputs are zeros,so they can be easily generated by experiment.Simulations are also performed for the nonholonomic motion planning of a free-falling cat.Simulated experimental results show that the proposed algorithm is more effective than the Newtoian algorithm.
