This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be dir...This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.展开更多
In this paper,we consider optimal control of stochastic differential equations subject to an expected path constraint.The stochastic maximum principle is given for a general optimal stochastic control in terms of cons...In this paper,we consider optimal control of stochastic differential equations subject to an expected path constraint.The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs.In particular,the compensated process in our adjoint equation is deterministic,which seems to be new in the literature.For the typical case of linear stochastic systems and quadratic cost functionals(i.e.,the so-called LQ optimal stochastic control),a verification theorem is established,and the existence and uniqueness of the constrained reflected FBSDEs are also given.展开更多
蚁群算法拥有良好的全局性、自组织性、鲁棒性,但传统蚁群算法存在许多不足之处。为此,针对算法在路径规划问题中的缺陷,在传统蚁群算法的状态转移公式中,引入目标点距离因素和引导素,加快算法收敛性和改善局部最优缺陷。在带时间窗的...蚁群算法拥有良好的全局性、自组织性、鲁棒性,但传统蚁群算法存在许多不足之处。为此,针对算法在路径规划问题中的缺陷,在传统蚁群算法的状态转移公式中,引入目标点距离因素和引导素,加快算法收敛性和改善局部最优缺陷。在带时间窗的车辆路径问题(vehicle routing problem with time windows,VRPTW)上,融合蚁群算法和遗传算法,并将顾客时间窗宽度以及机器人等待时间加入蚁群算法状态转移公式中,以及将蚁群算法的解作为遗传算法的初始种群,提高遗传算法的初始解质量,然后进行编码,设置违反时间窗约束和载重量的惩罚函数和适应度函数,在传统遗传算法的交叉、变异操作后加入了破坏-修复基因的操作来优化每一代新解的质量,在Solomon Benchmark算例上进行仿真,对比算法改进前后的最优解,验证算法可行性。最后在餐厅送餐问题中把带有障碍物的仿真环境路径规划问题和VRPTW问题结合,使用改进后的算法解决餐厅环境下送餐机器人对顾客服务配送问题。展开更多
Aerocapture is one of the key technologies for low-cost transportation,with high demands of autonomy,accuracy,and robustness of guidance and control,due to its high reliability requirements for only one chance of tryi...Aerocapture is one of the key technologies for low-cost transportation,with high demands of autonomy,accuracy,and robustness of guidance and control,due to its high reliability requirements for only one chance of trying.A unified numerical predictor-corrector guidance method based on characteristic models for aerocapture is proposed.The numerical predictor-corrector guidance method is used to achieve autonomy and high accuracy,and the characteristic model control method is introduced to achieve robustness.At the same time,by transforming path constraints,characteristic model equations including apogee deviation and altitude differentiation are established.Based on the characteristic model equations,a unified guidance law which can satisfy path constraints and guidance objectives simultaneously is designed.In guidance problems,guidance deviation is not directly obtained from the output of the dynamics at present,but is calculated through integral and algebraic equations.Therefore,the method of directly discretizing differential equations cannot be used to establish characteristic models,which brings great difficulty to characteristic modeling.A method for characteristic modeling of guidance problems is proposed,and convergence analysis of the proposed guidance law is also provided.Finally,a joint numerical simulation of guidance and control considering navigation deviation and various uncertainties is conducted to verify the effectiveness of the proposed method.The proposed unified method can be extended to general aerodynamic entry guidance designs,providing theoretical and methodological support for them.展开更多
基金Supported by the National Natural Science Foundation of China(U1162130)the National High Technology Research and Development Program of China(2006AA05Z226)Outstanding Youth Science Foundation of Zhejiang Province(R4100133)
文摘This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.
基金Ying Hu is partially supported by Lebesgue Center of Mathematics“Investissements d’avenir”Program(Grant No.ANR-11-LABX-0020-01)ANR CAESARS(Grant No.ANR-15-CE05-0024)+6 种基金ANR MFG(Grant No.ANR-16-CE40-0015-01)Shanjian Tang is partially supported by the National Science Foundation of China(Grant Nos.11631004 and 12031009)Zuo Quan Xu is partially supported by NSFC(Grant No.11971409)Research Grants Council of Hong Kong(GRF,Grant No.15202421)PolyU-SDU Joint Research Center on Financial MathematicsCAS AMSS-POLYU Joint Laboratory of Applied MathematicsHong Kong Polytechnic University.
文摘In this paper,we consider optimal control of stochastic differential equations subject to an expected path constraint.The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs.In particular,the compensated process in our adjoint equation is deterministic,which seems to be new in the literature.For the typical case of linear stochastic systems and quadratic cost functionals(i.e.,the so-called LQ optimal stochastic control),a verification theorem is established,and the existence and uniqueness of the constrained reflected FBSDEs are also given.
文摘蚁群算法拥有良好的全局性、自组织性、鲁棒性,但传统蚁群算法存在许多不足之处。为此,针对算法在路径规划问题中的缺陷,在传统蚁群算法的状态转移公式中,引入目标点距离因素和引导素,加快算法收敛性和改善局部最优缺陷。在带时间窗的车辆路径问题(vehicle routing problem with time windows,VRPTW)上,融合蚁群算法和遗传算法,并将顾客时间窗宽度以及机器人等待时间加入蚁群算法状态转移公式中,以及将蚁群算法的解作为遗传算法的初始种群,提高遗传算法的初始解质量,然后进行编码,设置违反时间窗约束和载重量的惩罚函数和适应度函数,在传统遗传算法的交叉、变异操作后加入了破坏-修复基因的操作来优化每一代新解的质量,在Solomon Benchmark算例上进行仿真,对比算法改进前后的最优解,验证算法可行性。最后在餐厅送餐问题中把带有障碍物的仿真环境路径规划问题和VRPTW问题结合,使用改进后的算法解决餐厅环境下送餐机器人对顾客服务配送问题。
基金The National Key R&D Program of China(2018YFA0703800)。
文摘Aerocapture is one of the key technologies for low-cost transportation,with high demands of autonomy,accuracy,and robustness of guidance and control,due to its high reliability requirements for only one chance of trying.A unified numerical predictor-corrector guidance method based on characteristic models for aerocapture is proposed.The numerical predictor-corrector guidance method is used to achieve autonomy and high accuracy,and the characteristic model control method is introduced to achieve robustness.At the same time,by transforming path constraints,characteristic model equations including apogee deviation and altitude differentiation are established.Based on the characteristic model equations,a unified guidance law which can satisfy path constraints and guidance objectives simultaneously is designed.In guidance problems,guidance deviation is not directly obtained from the output of the dynamics at present,but is calculated through integral and algebraic equations.Therefore,the method of directly discretizing differential equations cannot be used to establish characteristic models,which brings great difficulty to characteristic modeling.A method for characteristic modeling of guidance problems is proposed,and convergence analysis of the proposed guidance law is also provided.Finally,a joint numerical simulation of guidance and control considering navigation deviation and various uncertainties is conducted to verify the effectiveness of the proposed method.The proposed unified method can be extended to general aerodynamic entry guidance designs,providing theoretical and methodological support for them.
