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
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
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.
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.