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Archimedean Spiral-Based Intercept Angle Guidance

JOURNAL OF GUIDANCE control AND DYNAMICS 2019年第5期42卷 1105-1115页

作者： Tripathy, Twinkle Shima, Tal Technion Israel Inst Technol Fac Aerosp Engn IL-3200003 Haifa Israel

This paper focuses on designing an intercept angle guidance law for the planar interception of a stationary target. The underlying geometrical rule is based on an Archimedean spiral, which allows a pursuer to enforce a desired intercept angle or time by generating an appropriate spiral trajectory. An inherent advantage of using the proposed geometrical rule is that the required lateral acceleration to ensure interception is bounded throughout the engagement. The applicability of the geometrical rule is also analyzed against nonmaneuvering moving targets. The geometrical rule is implemented using a sliding-mode control-based nonlinear and robust guidance law. Using the proposed guidance law, the desired intercept angle is achieved in finite time. The theoretical results are validated through numerical simulations. The interception of the target with a specified intercept angle from different initial conditions and with various intercept angles from a given initial condition are shown. The robustness of the controller against disturbances and heading errors is also evaluated.

关键词： Guidance Laws Terminal Sliding Mode Numerical Simulation Intercept Angle Guidance Law Heading Angle linear quadratic control problem Cartesian Coordinate System Proportional Navigation Engagement Kinematics Nonlinear control Theory

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Elliptic Guidance

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JOURNAL OF GUIDANCE control AND DYNAMICS 2018年第11期41卷 2435-2444页

作者： Livermore, Riley Tsalik, Ronny Shima, Tal Technion Israel Inst Technol Dept Aerosp Engn IL-32000 Haifa Israel

A new three-point guidance concept for imposing a launch angle, impact angle, and intercept time against a stationary target is proposed. The guidance concept is based on the defining geometric rule of an ellipse. This rule states that, for every point along an ellipse, the sum of the distances to the two focal points is constant. A general method for finding the desired elliptical trajectory that achieves a desired launch angle, impact angle, and intercept time is presented. Once the elliptical trajectory is determined, the sum of the distances between the interceptor and the two foci is the only information required for implementation. The interceptor's equations of motion are linearized around the desired elliptical trajectory, and a proportional-integral-derivative controller is used to implement the elliptical geometric rule. Nonlinear simulations are performed for an interceptor imposing different impact angles with the same intercept time as well as different intercept times at the same impact angle, both against a stationary target. The effects of initial heading errors and first-order interceptor dynamics are also examined.

关键词： Proportional Integral Derivative Guidance Laws Flight Path Angle linear quadratic control problem Three Degrees of Freedom Proportional Navigation Eccentric Anomaly Nonlinear Systems Autopilot Hypersonic Vehicles

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A GENERAL STOCHASTIC MAXIMUM PRINCIPLE FOR A MARKOV REGIME SWITCHING JUMP-DIFFUSION MODEL OF MEAN-FIELD TYPE

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SIAM JOURNAL ON control AND OPTIMIZATION 2018年第4期56卷 2563-2592页

作者： Zhang, Xin Sun, Zhongyang Xiong, Jie Southeast Univ Sch Math Nanjing 211189 Jiangsu Peoples R China Qufu Normal Univ Sch Stat Qufu 273165 Shandong Peoples R China Southern Univ Sci & Technol Dept Math Shenzhen 518055 Peoples R China

In this paper, we develop a global form stochastic maximum principle for a Markov regime switching mean-field model driven by Brownian motions and Poisson jumps. The form of the maximum principle turns out to be quite different from the classical one in the sense that here the first order adjoint process is defined as a solution to a certain jump-diffusion mean-field backward stochastic differential equation (BSDE), but the second order adjoint equation is still a classical BSDE. As an application, we apply the main results to study a linear quadratic stochastic control problem of mean-field type.

关键词： stochastic maximum principle regime switching mean-field type model jump-diffusion mean-field BSDE linear quadratic control problem

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Planar Proportional Navigation Equation Solutions for Periodic Inputs

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JOURNAL OF GUIDANCE control AND DYNAMICS 2019年第9期42卷 2093-2097页

作者： Markham, Keith C. Chepstow Wales NP16 7HX United Kingdom*Retired Aerospace Engineer.

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New Impact Time and Angle Guidance Strategy via Virtual Target Approach

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JOURNAL OF GUIDANCE control AND DYNAMICS 2018年第8期41卷 1755-1765页

作者： Hu, Qinglei Han, Tuo Xin, Ming Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China Univ Missouri Dept Mech & Aerosp Engn Columbia MO 65211 USA

In this paper, a new guidance strategy is proposed for intercepting stationary and constant-velocity moving targets with desired impact time and angle via a virtual target approach, subject to nonlinear engagement kinematics and lateral-acceleration limits. The guidance procedure is divided into two stages by introducing a virtual target. Specifically, for the first stage, the nonsingular terminal sliding-mode guidance law is employed to intercept the virtual target with a specified impact angle in finite time. Furthermore, to achieve the desired impact angle on the real target, the proportional navigation guidance law is used in the second stage to keep the missile traveling with invariant flight-path angle. The impact time and angle on the real target are simultaneously controlled by selecting a proper guidance parameter whose optimal value is obtained via an optimization routine with a small number of iterations. This technique is user/designer-friendly in that it does not involve the time-to-go estimation procedure. In addition, less control energy is required in the overall guidance process. Numerical simulations with comparisons are conducted to validate the effectiveness and feasibility of the proposed guidance strategy in different engagement scenarios.

关键词： Flight Path Angle Guidance Laws Terminal Sliding Mode Engagement Kinematics Proportional Navigation Numerical Simulation Flight Trajectory Autopilot linear quadratic control problem Warship

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Optimal Boundary control for Selective Catalytic Reduction Distributed Parameter Model

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IFAC-PapersOnLine 2018年第32期51卷 286-291页

作者： Aksikas, Ahmed Aksikas, Ilyasse Hayes, Robert E. Forbes, Fraser J. Department of Chemical and Materials Engineering University of Alberta Edmonton Canada Department of Mathematics Statistics and Physics Qatar University Doha Qatar

This paper is devoted to design a model-based boundary optimal controller for selective catalytic reduction system. The mathematical model consists of coupled parabolic-hyperbolic PDEs with an ODE. The main objective is to manipulate the ammonia gas at the inlet of the SCR in order to reduce the amount of NOx and ammonia slip as much as possible. The augmented infinite-dimensional state space representation has been used in order to solve the corresponding linear-quadratic control problem. The dynamical properties of both the linearized system and its augmented version have been studied. Under some technical conditions, it has been shown that the augmented system generates an exponentially stabilizable and detectable C0-semigroups. The linear-quadratic control problem has been solved for the augmented system. A decoupling technique has been implemented to decouple and solve the corresponding Riccati equation. An algorithm has been developed to describe the steps of solving the Riccati equation. Numerical simulations for the closed-loop system have been implemented to show the controller performances. © 2018

关键词： Selective catalytic reduction Ammonia Closed loop systems controllers Distributed parameter control systems linear control systems Riccati equations State space methods Boundary controls Distributed parameter systems Distributed parameter model linear quadratic control problem Optimal controls Partial differential equations (PDE) Selective catalytic reduction systems State space representation

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Stochastic linear-quadratic control with State Dependent Fractional Brownian Noise and Stochastic Coefficients

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IFAC-PapersOnLine 2017年第2期50卷 199-202页

作者： Duncan, T.E. Pasik-Duncan, B. Department of Mathematics University of Kansas LawrenceKS66045 United States

Stochastic linear-quadratic control problems for bilinear equations with some stochastic coefficients and driven by fractional Brownian motions with the Hurst parameters H (½,1) are formulated and solved. The family of admissible controls is the collection of linear feedback controls. An optimal control in this family is not optimal in the admissible family of all adapted controls. However an optimal linear feedback control obtained in this paper can be relatively easily implemented whereas an optimal control in the family of adapted controls has a term that predicts the future noise so it is more difficult to implement. An optimal control is determined from the solution of a Riccati equation which differs from the Riccati equation for the linear-quadratic control problem with a Brownian motion replacing the noise term. Since the Riccati equation has some stochastic coefficients it is solved as a backward stochastic differential equation. Given the solution of the stochastic Riccati equation, a direct method is used to determine the optimal linear feedback control. © 2017

关键词： Stochastic control systems Brownian movement Discrete time control systems Feedback control linear control systems Riccati equations Stochastic models Stochastic systems Backward stochastic differential equations control strategies Fractional brownian motion linear quadratic control problem linear quadratic stochastic control State dependent noise Stochastic linear quadratic control Stochastic linear quadratic control problems

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Impact-Time-control Guidance with Generalized Proportional Navigation Based on Nonlinear Formulation

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JOURNAL OF GUIDANCE control AND DYNAMICS 2016年第8期39卷 1885-U266页

作者： Jeon, In-Soo Lee, Jin-Ik Tahk, Min-Jea Agcy Def Dev Antiship Syst Dept Daejeon 305152 South Korea Korea Adv Inst Sci & Technol Sch Aerosp Engn Taejon 305701 South Korea

A new quite accurate higher-order time-to-go estimate of proportional navigation guidance (PNG) for a fixed target was proposed. The study begins with nonlinear formulation of the homing problem of multiple missiles against a single target, subject to constraints on the impact time. Next, a feedback control is obtained from an optimal homing guidance problem for reducing the miss distance. In derivation of the feedback control, the closed-form solution of PNG as a base trajectory of impact-time-control guidance (ITCG) is investigated. By using more accurate higher-order terms of time-to-go estimates of PNG than the previous one, it could be seen that the proposed law can accomplish accurate impact-time-control covering large initial heading angle or error in initial impact time. In addition, the new-form of ITCG for a nonmaneuvering moving target was introduced, and some convincing results from numerical simulations were presented for its feasibility.

关键词： control Guidance Proportional Navigation Predicted Impact Point Heading Angle Sliding Mode control Flight Path Angle linear quadratic control problem Feedback control Homing Guidance Nonlinear control Theory

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Attractive Sets to Unstable Orbits Using Optimal Feedback control

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JOURNAL OF GUIDANCE control AND DYNAMICS 2016年第12期39卷 2725-2739页

作者： Bando, Mai Scheeres, Daniel J. Kyushu Univ Dept Aeronaut & Astronaut Nishi Ku 744 Motooka Fukuoka 8190395 Japan Univ Colorado Aerosp Engn Sci Boulder CO 80309 USA

This paper investigates the combination of optimal feedback control with the dynamical structure of the three-body problem. The results provide new insights for the design of continuous low-thrust spacecraft trajectories. Specifically, the attracting set of an equilibrium point or a periodic orbit (represented as a fixed point) under optimal control with quadratic cost is obtained. The analysis reveals the relation between the attractive set and original dynamics. In particular, it is found that the largest dimensions of the set are found along the stable manifold and the least extent is along the left eigenvector of the unstable manifold. The asymptotic behavior of the structure of the attractive set when time tends to infinity is analytically revealed. The results generalize the use of manifolds for transfers to equilibrium points and periodic orbits in astrodynamic problems. The result is theoretical and developed for a linearized system, but it can be extended to nonlinear systems in the future.

关键词： Feedback control linear quadratic control problem Astrodynamics Spacecraft Trajectories Nonlinear Systems linear Time Invariant System Halo Orbit Libration Points Earth Optimization Algorithm

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Impact Time and Angle control Based on Constrained Optimal Solutions

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JOURNAL OF GUIDANCE control AND DYNAMICS 2016年第10期39卷 2445-U2451页

作者： Erer, Koray S. Tekin, Raziye Roketsan Missiles Inc TMS Guidance Syst Design Dept TR-06780 Ankara Turkey Aselsan Inc MGEO Nav & Guidance Syst Design Dept TR-06750 Ankara Turkey

A study proposes a technique which differs in that the problem of trajectory shaping is addressed by considering the full extent of the available resources in the form of look angle and acceleration constraints. This is made possible by the use of the nonlinear optimal control framework where the cost function is made up of an endpoint cost aiming to extremize the impact time or the impact angle against a stationary target. Based on the constrained optimal control solutions obtained in this way, practical guidance laws to control the impact time or the impact angle without violating the constraints are derived by realizing that optimality, which dictates the familiar PN guidance law with specific values of the navigation gain.

关键词： Guidance Laws Sliding Mode control linear quadratic control problem Autopilot Proportional Navigation Terminal Guidance Feedback linearization Guidance Algorithms MATLAB

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