Trajectory Optimization Based on Multi‐Interval Mesh Refinement Method

Referring to the optimal tracking guidance of aircraft, the conventional time based kinematics model is transformed into a downrange based model by independent variable replacement. The deviations of in-flight altitude and flight path angle are penalized and corrected to achieve high precision tracking of reference trajectory. The tracking problem is solved as a linear quadratic regulator applying small perturbation theory, and the approximate dynamic programming method is used to cope with the solving of finite-horizon optimization. An actor-critic structure is established to approximate the optimal tracking controller and minimum cost function. The least squares method and Adam optimization algorithm are adopted to learn the parameters of critic network and actor network, respectively. A boosting trajectory with maximum final velocity is generated by Gauss pseudospectral method for the validation of guidance strategy. The results show that the trained feedback control parameters can effectively resist random wind disturbance, correct the initial altitude and flight path angle deviations, and achieve the goal of following a given trajectory.

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“…The general equations of motion in the longitudinal plane for an aircraft [33], assumed as point mass, are given bẏ…”

Section: Problem Formulationmentioning

confidence: 99%

Finite‐Horizon Optimal Tracking Guidance for Aircraft Based on Approximate Dynamic Programming

Wan

Chang

et al. 2019

Mathematical Problems in Engineering

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“…In recent years, many scholars have carried out extensive research on it and greatly developed its related theory and application [26][27][28][29][30]. Li et al [31,32] apply the adaptive hp method to the field of trajectory optimization, which effectively solve this kind of complex nonlinear optimization problem, and obtain satisfactory solution accuracy. By improving the mesh refinement process, some effective variants of the hp method are proposed in [33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

“…Although the aforementioned works [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] on the adaptive hp method has made great progress, there still are several issues that need further consideration.…”

Section: Introductionmentioning

confidence: 99%

An Improved Adaptive hp Mesh Refinement Method in Solving Optimal Control Problems

Luo¹,

Li²,

Zhou³

et al. 2021

Preprint

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The adaptive hp pseudospectral method is an effective choice in solving the optimal control problem. In order to improve the computing efficiency of the adaptive hp method, an improved adaptive hp mesh refinement method is proposed in this paper. There are two main cores in this method. The first is to refine the mesh in advance based on the change rate of the control, so that the algorithm can more efficiently deal with the optimal control problem with discontinuous control. And the second is to based on the accumulation of curvature values to ensure that those positions that need to be refined more can be quickly allocated to more mesh points. These two are combined with each other to improve the solving efficiency of the algorithm proposed in this paper, which shortens the required computing time. In addition, the convergence of the algorithm is proved in this paper. The simulation results show the effectiveness and superiority of the algorithm proposed in this paper.

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“…e direct shooting method (DSM) [14], particle swarm optimization algorithm [15], genetic algorithm [16], and symplectic iterative algorithm [17,18] achieve satisfying results for the specific missions. Different from other direct methods, the Gauss pseudospectral method (GPM) has obtained great attention for fast convergence, global optimization, and extensive applications in the aerospace field recently by means of approximating the control and state variables with polynomials [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Trajectory Optimization Method and Tracking Guidance for Variable-Sweep Missiles

Wei

Cheng²,

Xiangxiang³

et al. 2021

Mathematical Problems in Engineering

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In this paper, an offline hybrid trajectory optimization approach is proposed for variable-sweep missiles to explore the superiority in the diving phase. Aiming at the maximal terminal velocity with the impact angle constraint, the trajectory optimization model is formulated under multiple constraints, and the aerodynamic analysis in different sweep angles is discussed. Unlike only the attack angle used for the optimization process traditionally, the two-variable optimization scheme on both the attack angle and sweep angle is investigated for variable-sweep missiles. Then, the trajectory optimization problem is transformed into the nonlinear programming problem via a hybrid optimization strategy combining the Gauss pseudospectral method and direct shooting method to obtain the high precision and fast convergence solution. Finally, to verify the feasibility of the optimal trajectory under uncertainties, the tracking guidance law is designed on basis of the gain scheduled linear quadratic regulator control. Numerical simulation results reveal not only of the proposed hybrid optimization strategy but also of the superiority of variable-sweep missiles compared with traditional missiles.

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Trajectory Optimization Based on Multi‐Interval Mesh Refinement Method

Cited by 9 publications

References 17 publications

Finite‐Horizon Optimal Tracking Guidance for Aircraft Based on Approximate Dynamic Programming

Finite‐Horizon Optimal Tracking Guidance for Aircraft Based on Approximate Dynamic Programming

An Improved Adaptive hp Mesh Refinement Method in Solving Optimal Control Problems

Hybrid Trajectory Optimization Method and Tracking Guidance for Variable-Sweep Missiles

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