In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training ...In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training a Multilayer Perceptron(MLP)for generating reference sequence and Time of Flight(TOF)to the target,and deriving a system of linear algebraic equations for obtaining the initial costates.To overcome the challenge of generating training samples for the MLP,the backward generation method is proposed to obtain five different training databases.The training database and sample form are determined by analyzing the input and output correlation using the Pearson correlation coefficient.The best-performing MLP is obtained by analyzing the training results with various hyper-parameter combinations.A reference sequence starting from the initial states is obtained by integrating forward with the near-optimal control vector from the output of MLP.Finally,a system of linear algebraic equations for estimating the initial costates is derived using the reference sequence and the necessary conditions for optimality.Simulation results demonstrate that the proposed initial costates solver improves the convergence ratio and reduce the function calls of the shooting function.Furthermore,Monte-Carlo simulation illustrates that the initial costates solver is applicable to different initial velocities,demonstrating excellent generalization ability.展开更多
For the longitudinal midcourse guidance problem of a cruise-glide integrated hypersonic vehicle(CGHV),an analytical method based on optimal control theory is proposed.This method constructs a guidance dynamics model f...For the longitudinal midcourse guidance problem of a cruise-glide integrated hypersonic vehicle(CGHV),an analytical method based on optimal control theory is proposed.This method constructs a guidance dynamics model for such vehicles,using aerodynamic load as the control variable,and introduces a framework for solving the guidance laws.This framework unifies the design process of guidance laws for both the glide and cruise phases.By decomposing the longitudinal guidance task into position control and velocity control,and minimizing energy consumption as the objective function,the method provides an analytical solution for velocity control load through the calculation of costate variables.This approach requires only the current state and terminal state parameters to determine the guidance law solution.Furthermore,by transforming path constraints into aerodynamic load constraints and solving backwards to obtain the angle of attack,bank angle,and throttle setting,this method ensures a smooth transition from the glide phase to the cruise phase,guaranteeing the successful completion of the guidance task.Finally,the effectiveness and practicality of the proposed method are validated through case simulations and analysis.展开更多
This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to...This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.展开更多
The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state space. This paper ...The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state space. This paper presents a so-called Legendre pseudo-spectral (PS) approach for directly estimating the costates of the Bolza problem of optimal control of a set of dynamic equations of the second order. Under a set of closure conditions, it is proved that the Karush-Kuhn-Tucker (KKT) multipliers satisfy the same conditions as those determined by collocating the costate equations of the second order. Hence, the KKT multipliers can be used to estimate the costates of the Bolza problem via a simple linear map- ping. The proposed approach can be used to check the optimality of the direct solution for a trajectory optimization problem involving the dynamic equations of the second order and to remove any conver- sion of the dynamic system from the second order to the first order. The new approach is demonstrated via two classical benchmark problems.展开更多
基金This study was funded by the National Natural Science Foundation of China(Nos.11972077 and 12272039).
文摘In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training a Multilayer Perceptron(MLP)for generating reference sequence and Time of Flight(TOF)to the target,and deriving a system of linear algebraic equations for obtaining the initial costates.To overcome the challenge of generating training samples for the MLP,the backward generation method is proposed to obtain five different training databases.The training database and sample form are determined by analyzing the input and output correlation using the Pearson correlation coefficient.The best-performing MLP is obtained by analyzing the training results with various hyper-parameter combinations.A reference sequence starting from the initial states is obtained by integrating forward with the near-optimal control vector from the output of MLP.Finally,a system of linear algebraic equations for estimating the initial costates is derived using the reference sequence and the necessary conditions for optimality.Simulation results demonstrate that the proposed initial costates solver improves the convergence ratio and reduce the function calls of the shooting function.Furthermore,Monte-Carlo simulation illustrates that the initial costates solver is applicable to different initial velocities,demonstrating excellent generalization ability.
基金supported by the National Natural Science Foundation of China(Grant Nos.62473374,62403487 and U2441243).
文摘For the longitudinal midcourse guidance problem of a cruise-glide integrated hypersonic vehicle(CGHV),an analytical method based on optimal control theory is proposed.This method constructs a guidance dynamics model for such vehicles,using aerodynamic load as the control variable,and introduces a framework for solving the guidance laws.This framework unifies the design process of guidance laws for both the glide and cruise phases.By decomposing the longitudinal guidance task into position control and velocity control,and minimizing energy consumption as the objective function,the method provides an analytical solution for velocity control load through the calculation of costate variables.This approach requires only the current state and terminal state parameters to determine the guidance law solution.Furthermore,by transforming path constraints into aerodynamic load constraints and solving backwards to obtain the angle of attack,bank angle,and throttle setting,this method ensures a smooth transition from the glide phase to the cruise phase,guaranteeing the successful completion of the guidance task.Finally,the effectiveness and practicality of the proposed method are validated through case simulations and analysis.
文摘This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10372039, 10672073)the Innovation Fund for Graduate Students of NUAA (Grant No. 4003-019016)
文摘The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state space. This paper presents a so-called Legendre pseudo-spectral (PS) approach for directly estimating the costates of the Bolza problem of optimal control of a set of dynamic equations of the second order. Under a set of closure conditions, it is proved that the Karush-Kuhn-Tucker (KKT) multipliers satisfy the same conditions as those determined by collocating the costate equations of the second order. Hence, the KKT multipliers can be used to estimate the costates of the Bolza problem via a simple linear map- ping. The proposed approach can be used to check the optimality of the direct solution for a trajectory optimization problem involving the dynamic equations of the second order and to remove any conver- sion of the dynamic system from the second order to the first order. The new approach is demonstrated via two classical benchmark problems.
