Mathematics

Research

18 pages, 4696 KiB

Open AccessArticle

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

by Haizhao Liang, Yunhao Luo, Haohui Che, Jingxian Zhu and Jianying Wang

Mathematics 2024, 12(9), 1306; https://doi.org/10.3390/math12091306 - 25 Apr 2024

Viewed by 867

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve [...] Read more.

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

► Show Figures

Figure 1

25 pages, 5960 KiB

Open AccessArticle

Cooperative Guidance Strategy for Active Spacecraft Protection from a Homing Interceptor via Deep Reinforcement Learning

by Weilin Ni, Jiaqi Liu, Zhi Li, Peng Liu and Haizhao Liang

Mathematics 2023, 11(19), 4211; https://doi.org/10.3390/math11194211 - 9 Oct 2023

Cited by 1 | Viewed by 1231

Abstract

The cooperative active defense guidance problem for a spacecraft with active defense is investigated in this paper. An engagement between a spacecraft, an active defense vehicle, and an interceptor is considered, where the target spacecraft with active defense will attempt to evade the [...] Read more.

The cooperative active defense guidance problem for a spacecraft with active defense is investigated in this paper. An engagement between a spacecraft, an active defense vehicle, and an interceptor is considered, where the target spacecraft with active defense will attempt to evade the interceptor. Prior knowledge uncertainty and observation noise are taken into account simultaneously, which are vital for traditional guidance strategies such as the differential-game-based guidance method. In this set, we propose an intelligent cooperative active defense (ICAAI) guidance strategy based on deep reinforcement learning. ICAAI effectively coordinates defender and target maneuvers to achieve successful evasion with less prior knowledge and observational noise. Furthermore, we introduce an efficient and stable convergence (ESC) training approach employing reward shaping and curriculum learning to tackle the sparse reward problem in ICAAI training. Numerical experiments are included to demonstrate ICAAI’s real-time performance, convergence, adaptiveness, and robustness through the learning process and Monte Carlo simulations. The learning process showcases improved convergence efficiency with ESC, while simulation results illustrate ICAAI’s enhanced robustness and adaptiveness compared to optimal guidance laws. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

► Show Figures

Figure 1

17 pages, 1479 KiB

Open AccessArticle

Hybrid Attitude Saturation and Fault-Tolerant Control for Rigid Spacecraft without Unwinding

by Jun Ma, Zeng Wang and Chang Wang

Mathematics 2023, 11(15), 3431; https://doi.org/10.3390/math11153431 - 7 Aug 2023

Cited by 2 | Viewed by 1024

Abstract

This paper tackles the saturation and fault-tolerant attitude tracking problem without unwinding for rigid spacecraft with external disturbances and partial loss of actuator effectiveness faults. A hybrid saturation and fault-tolerant attitude control (HSFC) is proposed. The Lyapunov method is employed to prove that [...] Read more.

This paper tackles the saturation and fault-tolerant attitude tracking problem without unwinding for rigid spacecraft with external disturbances and partial loss of actuator effectiveness faults. A hybrid saturation and fault-tolerant attitude control (HSFC) is proposed. The Lyapunov method is employed to prove that the tracking errors of the spacecraft system tend to the equilibrium point asymptotically with HSFC. The advantages of the HSFC are that it is fault-tolerant, anti-unwinding and explicitly upper bounded a priori which means that both actuator saturation and the unwinding phenomenon can be avoided. Simulations verify the effectiveness of the proposed approach. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

► Show Figures

Figure 1

15 pages, 2597 KiB

Open AccessArticle

Cubature Kalman Filters Model Predictive Static Programming Guidance Method with Impact Time and Angle Constraints Considering Modeling Errors

by Zihan Xie, Jialun Pu, Changzhu Wei and Yingzi Guan

Mathematics 2023, 11(13), 2990; https://doi.org/10.3390/math11132990 - 4 Jul 2023

Cited by 1 | Viewed by 1001

Abstract

This paper proposes a CKF-MPSP guidance method for hitting stationary targets with impact time and angle constraints for missiles in the presence of modeling errors. This innovative guidance scheme is composed of three parts: First, the model predictive static programming (MPSP) algorithm is [...] Read more.

This paper proposes a CKF-MPSP guidance method for hitting stationary targets with impact time and angle constraints for missiles in the presence of modeling errors. This innovative guidance scheme is composed of three parts: First, the model predictive static programming (MPSP) algorithm is used to design a nominal guidance method that simultaneously satisfies impact time and angle constraints. Second, the cubature Kalman filter (CKF) is introduced to estimate values of the influence of the inevitable modeling errors. Finally, a one-step compensation scheme is proposed to eliminate the modeling errors’ influence. The proposed method uses a real missile dynamics model, instead of a simplified one with a constant-velocity assumption, and eliminates the effects of modeling errors with the compensation scheme; thus, it is more practical. Simulations in the presence of modeling errors are conducted, and the results illustrate that the CKF-MPSP guidance method can reach the target with a high accuracy of impact time and angles, which demonstrates the high precision and strong robustness of the method. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

► Show Figures

Figure 1

18 pages, 4491 KiB

Open AccessArticle

Real-Time Trajectory Planning for Hypersonic Entry Using Adaptive Non-Uniform Discretization and Convex Optimization

by Jiarui Ma, Hongbo Chen, Jinbo Wang and Qiliang Zhang

Mathematics 2023, 11(12), 2754; https://doi.org/10.3390/math11122754 - 18 Jun 2023

Cited by 2 | Viewed by 1327

Abstract

This paper introduces an improved sequential convex programming algorithm using adaptive non-uniform discretization for the hypersonic entry problem. In order to ensure real-time performance, an inverse-free precise discretization based on first-order hold discretization is adopted to obtain a high-accuracy solution with fewer temporal [...] Read more.

This paper introduces an improved sequential convex programming algorithm using adaptive non-uniform discretization for the hypersonic entry problem. In order to ensure real-time performance, an inverse-free precise discretization based on first-order hold discretization is adopted to obtain a high-accuracy solution with fewer temporal nodes, which would lead to constraint violation between the temporal nodes due to the sparse time grid. To deal with this limitation, an adaptive non-uniform discretization is developed, which provides a search direction for purposeful clustering of discrete points by adding penalty terms in the problem construction process. Numerical results show that the proposed method has fast convergence with high accuracy while all the path constraints are satisfied over the time horizon, thus giving potential to real-time trajectory planning. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

► Show Figures

Figure 1

16 pages, 801 KiB

Open AccessArticle

Adaptive Trajectory Tracking Algorithm for the Aerospace Vehicle Based on Improved T-MPSP

by Chao Ou, Chengjun Shan, Zhongtao Cheng and Yaosong Long

Mathematics 2023, 11(9), 2160; https://doi.org/10.3390/math11092160 - 4 May 2023

Cited by 3 | Viewed by 1316

Abstract

To deal with the uncertainty and disturbance that exist in the tracking system of an aerospace vehicle, an adaptive trajectory-tracking method based on a novel tracking model predictive static programming (T-MPSP) is proposed. Firstly, to make the proposed method more adaptive to uncertain [...] Read more.

To deal with the uncertainty and disturbance that exist in the tracking system of an aerospace vehicle, an adaptive trajectory-tracking method based on a novel tracking model predictive static programming (T-MPSP) is proposed. Firstly, to make the proposed method more adaptive to uncertain parameter deviations, an extended Kalman filter (EKF) parameter correction strategy is designed. Then, the control constraints are considered to form a novel T-MPSP algorithm. By combining the parameter correction strategy with the improved T-MPSP algorithm, a novel adaptive tracking guidance scheme is presented. Finally, simulations are carried out to demonstrate the effectiveness of the proposed method. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

► Show Figures

Figure 1

15 pages, 2764 KiB

Open AccessArticle

A Novel Fixed-Time Convergence Guidance Law against Maneuvering Targets

by Yaosong Long, Chao Ou, Chengjun Shan and Zhongtao Cheng

Mathematics 2023, 11(9), 2090; https://doi.org/10.3390/math11092090 - 28 Apr 2023

Viewed by 1185

Abstract

In this paper, a new fixed-time convergence guidance law is proposed against maneuvering targets in the three-dimensional (3-D) engagement scenario. The fixed-time stability theory is used to zero the line-of-sight (LOS) angle rate, which will ensure the collision course and the impact of [...] Read more.

In this paper, a new fixed-time convergence guidance law is proposed against maneuvering targets in the three-dimensional (3-D) engagement scenario. The fixed-time stability theory is used to zero the line-of-sight (LOS) angle rate, which will ensure the collision course and the impact of the target. It is proven that the convergence of the LOS angle rate can be achieved before the final impact time of the guidance process, regardless of the initial conditions. Furthermore, the convergence rate is merely related to control parameters. In theoretical analysis, the convergence rate and upper bound are compared with that of other laws to show the potential advantages of the proposed guidance law. Finally, simulations are carried out to illustrate the effectiveness and robustness of the proposed guidance law. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

► Show Figures

Figure 1

13 pages, 1342 KiB

Open AccessArticle

Three-Dimensional Path Planning of UAV Based on Improved Particle Swarm Optimization

by Lixia Deng, Huanyu Chen, Xiaoyiqun Zhang and Haiying Liu

Mathematics 2023, 11(9), 1987; https://doi.org/10.3390/math11091987 - 23 Apr 2023

Cited by 15 | Viewed by 2035

Abstract

The traditional particle swarm optimization algorithm is fast and efficient, but it is easy to fall into a local optimum. An improved PSO algorithm is proposed and applied in 3D path planning of UAV to solve the problem. Improvement methods are described as [...] Read more.

The traditional particle swarm optimization algorithm is fast and efficient, but it is easy to fall into a local optimum. An improved PSO algorithm is proposed and applied in 3D path planning of UAV to solve the problem. Improvement methods are described as follows: combining PSO algorithm with genetic algorithm (GA), setting dynamic inertia weight, adding sigmoid function to improve the crossover and mutation probability of genetic algorithm, and changing the selection method. The simulation results show that the improved PSO algorithm solves better route results and is faster and more stable. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

► Show Figures

Figure 1

14 pages, 410 KiB

Open AccessArticle

Finite-Time Contractive Control of Spacecraft Rendezvous System

by Jing Sheng, Yunhai Geng, Min Li and Baolong Zhu

Mathematics 2023, 11(8), 1871; https://doi.org/10.3390/math11081871 - 14 Apr 2023

Cited by 1 | Viewed by 1389

Abstract

In this paper we investigate the problem of a finite-time contractive control method for a spacecraft rendezvous control system. The dynamic model of relative motion is formulated by the C-W equations. To improve the convergent performance of the spacecraft rendezvous control system, a [...] Read more.

In this paper we investigate the problem of a finite-time contractive control method for a spacecraft rendezvous control system. The dynamic model of relative motion is formulated by the C-W equations. To improve the convergent performance of the spacecraft rendezvous control system, a finite-time contractive control law is introduced. Lyapunov’s direct method is employed to obtain the existence condition of the desired controllers. The controller parameter can be obtained with the help of the cone complementary linearization algorithm. A numerical example verifies the effectiveness of the obtained theoretical results. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

► Show Figures

Figure 1

22 pages, 4316 KiB

Open AccessArticle

Improved Thrust Performance Optimization Method for UAVs Based on the Adaptive Margin Control Approach

by Yeguang Wang, Honglin Liu and Kai Liu

Mathematics 2023, 11(5), 1176; https://doi.org/10.3390/math11051176 - 27 Feb 2023

Viewed by 1676

Abstract

This study proposes a strategy for improving the thrust performance of fixed-wing UAV turbine engines from the perspective of aircraft/engine integration. In the UAV engine control process, the inlet distortion caused by the angle of attack change is taken into account, the inlet [...] Read more.

This study proposes a strategy for improving the thrust performance of fixed-wing UAV turbine engines from the perspective of aircraft/engine integration. In the UAV engine control process, the inlet distortion caused by the angle of attack change is taken into account, the inlet distortion index is calculated in real time by predicting the angle of attack, and the influence of the inlet distortion on the engine model is analyzed mechanically. Then, the pressure ratio command is adjusted according to the new compressor surge margin requirement caused by the inlet distortion to finally improve the engine thrust performance. To verify the effectiveness of the algorithm, an adaptive disturbance rejection controller is designed for the flight control of a fixed-wing UAV to complete the simulation of horizontal acceleration. The simulation results show that, with this strategy, the UAV turbofan engine can improve the turbofan engine thrust performance by more than 8% under the safety conditions. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Advanced Guidance and Control of Flight Vehicle: Theory and Application

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (10 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI