This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the ty...This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.展开更多
For air-to-air missiles, the terminal guidance’s preci-sion is directly contingent upon the tracking capabilities of the roll-pitch seeker. This paper presents a combined non-singular fast terminal sliding mode contr...For air-to-air missiles, the terminal guidance’s preci-sion is directly contingent upon the tracking capabilities of the roll-pitch seeker. This paper presents a combined non-singular fast terminal sliding mode control method, aimed at resolving the frame control problem of roll-pitch seeker tracking high maneu-vering target. The sliding mode surface is structured around the principle of segmentation, which enables the control system’s rapid attainment of the zero point and ensure global fast conver-gence. The system’s state is more swiftly converged to the slid-ing mode surface through an improved adaptive fast dual power reaching law. Utilizing an extended state observer, the overall disturbance is both identified and compensated. The validation of the system’s stability and its convergence within a finite-time is grounded in Lyapunov’s stability criteria. The performance of the introduced control method is confirmed through roll-pitch seeker tracking control simulation. Data analysis reveals that newly proposed control technique significantly outperforms existing sliding mode control methods by rapidly converging the frame to the target angle, reduce the tracking error of the detec-tor for the target, and bolster tracking precision of the roll-pitch seeker huring disturbed conditions.展开更多
针对高速飞行情况下倾斜转弯(Bank To Turn,BTT)飞行器编队控制问题,基于一种制导控制一体化(Integrated Guidance and Control,IGC)理论提出一种分布式编队系统建模与控制器设计方法。通过坐标变换,将双积分系统模型与BTT飞行器动力学...针对高速飞行情况下倾斜转弯(Bank To Turn,BTT)飞行器编队控制问题,基于一种制导控制一体化(Integrated Guidance and Control,IGC)理论提出一种分布式编队系统建模与控制器设计方法。通过坐标变换,将双积分系统模型与BTT飞行器动力学模型相结合,得到了IGC模型;在反演控制框架下,采用一致性理论与神经网络自适应滑模变结构理论设计了编队控制器;进行严格的理论分析并证明了闭环系统的稳定性和收敛特性;在高速情况下进行了六自由度数学仿真,仿真结果表明了IGC设计方法的有效性,以及较传统设计方法的优越性。展开更多
基金co-supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF21-BJ-J-1180)。
文摘This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.
文摘For air-to-air missiles, the terminal guidance’s preci-sion is directly contingent upon the tracking capabilities of the roll-pitch seeker. This paper presents a combined non-singular fast terminal sliding mode control method, aimed at resolving the frame control problem of roll-pitch seeker tracking high maneu-vering target. The sliding mode surface is structured around the principle of segmentation, which enables the control system’s rapid attainment of the zero point and ensure global fast conver-gence. The system’s state is more swiftly converged to the slid-ing mode surface through an improved adaptive fast dual power reaching law. Utilizing an extended state observer, the overall disturbance is both identified and compensated. The validation of the system’s stability and its convergence within a finite-time is grounded in Lyapunov’s stability criteria. The performance of the introduced control method is confirmed through roll-pitch seeker tracking control simulation. Data analysis reveals that newly proposed control technique significantly outperforms existing sliding mode control methods by rapidly converging the frame to the target angle, reduce the tracking error of the detec-tor for the target, and bolster tracking precision of the roll-pitch seeker huring disturbed conditions.
文摘针对高速飞行情况下倾斜转弯(Bank To Turn,BTT)飞行器编队控制问题,基于一种制导控制一体化(Integrated Guidance and Control,IGC)理论提出一种分布式编队系统建模与控制器设计方法。通过坐标变换,将双积分系统模型与BTT飞行器动力学模型相结合,得到了IGC模型;在反演控制框架下,采用一致性理论与神经网络自适应滑模变结构理论设计了编队控制器;进行严格的理论分析并证明了闭环系统的稳定性和收敛特性;在高速情况下进行了六自由度数学仿真,仿真结果表明了IGC设计方法的有效性,以及较传统设计方法的优越性。
