Integrated Guidance and Control of Missiles with Θ-D Method

A new suboptimal control method is proposed in this study to effectively design an integrated guidance and control system for missiles. Optimal formulations allow designers to bring together concerns about guidance law performance and autopilot responses under one unified framework. They lead to a natural integration of these different functions. by modifying the appropriate cost functions, different responses, control saturations (autopilot related), miss distance (guidance related), etc., which are of primary concern to a missile system designer, can be easily studied. A new suboptimal control method, called the θ-D method, is employed to obtain an approximate closed-form solution to this nonlinear guidance problem based on approximations to the Hamilton-Jacobi-Bellman equation. Missile guidance law and autopilot design are formulated into a single unified state space framework. The cost function is chosen to reflect both guidance and control concerns. The ultimate control input is the missile fin deflections. A nonlinear six-degree-of-freedom (6-DOF) missile simulation is used to demonstrate the potential of this new integrated guidance and control approach

Finite-Horizon Robust Integrated Guidance-Control of A Moving-Mass Actuated Kinetic Warhead

A game-theoretic approach to the design of robust integrated guidance-control system for a moving-mass actuated kinetic warhead is presented. Feedback linearized form of the kinetic warhead dynamics and a high-order target model are used in the formulation. Nonlinear feedback solution to the robust finite-horizon target interception problem is derived using the recently developed multi-stepping algorithm. Due to its computational efficiency, the multi-stepping algorithm is suitable for real-time implementation. Interception of targets in the presence of modeling uncertainties is demonstrated in nonlinear engagement simulations

Guidance Law Design for Missiles with Reduced Seeker Field-Of-View

In this paper, a missile guidance law is designed to address the reduced seeker field-of-view constraint that is required in the low cost weapon system. The guidance problem is formulated as a nonlinear optimal control problem in the polar coordinates such that the line-of-sight (LOS) can be explicitly controlled. A closed-form guidance law is obtained by employing the θ − D nonlinear control technique. By virtue of state dependent weighting functions, impact angle requirement for increasing weapon lethality can also be met while satisfying reduced seeker field-of-view constraint. A missile attacking a stationary target is considered in this study. The simulation demonstrated favorable results compared with the classical proportional navigation law in terms of satisfying both reduced seeker field-of-view constraint and the terminal impact angle requirement

Midcourse Guidance Law with Neural Networks

A dual neural network \u27adaptive critic approach\u27 is used in this study to generate midcourse guidance commands for a missile to reach a predicted impact point while maximizing its final velocity. The adaptive critic approach is based on approximate dynamic programming. The first network, called a \u27critic\u27, network, outputs the Lagrangian multipliers arising in an optimal control formulation while the second network, called an \u27action\u27 network, outputs the optimal guidance/control. While a typical adaptive critic structure consists of a single critic and a single controller, the midcourse guidance problem needs indexing in terms of the independent variable and therefore there is a cascade of critics and controllers each set for a different index. Every controller learns from the critic at the previous stage. Though the networks are trained off-line, the resulting control is in a feedback form. A midcourse guidance problem is the first testbed for this approach where the input is vector-valued. The numerical results for a number of scenarios show that the network performance is excellent. Corroboration for optimality is provided by comparisons of the numerical solutions using a shooting method for a number of scenarios. Numerical results demonstrate some attractive features of the adaptive critic approach and show that this formulation works very well in guiding the missile to its final conditions from an envelope of initial conditions. This application also demonstrates the use of adaptive critics as a tool to solve a class of \u27free final time\u27 problems in optimal control, which are usually very difficult

Nonlinear Missile Autopilot Design with Θ - D Technique

In this paper, a new nonlinear control method is used to design a full-envelope, hybrid bank-to-turn (BTT)/skidto- turn (STT) autopilot for an air-breathing air-to-air missile. Through this new approach, called the θ − D method, we find approximate solutions to the Hamilton- Jacobi-Bellman (HJB) equation. An interesting and important feature of this new technique is that the nonlinear feedback law can be expressed in a closed form. In this autopilot design, a θ − D outer-loop and inner-loop controller structure is adopted. A hybrid BTT/STT autopilot command logic is used to convert the commanded accelerations from the guidance laws to reference angle commands for the autopilot. The outerloop θ − D controller converts the angle-of-attack, the sideslip, and the bank angle commands to body rate commands for the inner loop. An inner-loop θ − D nonlinear controller converts the body rate commands to fin commands. The nonlinear design is evaluated using a detailed six-degrees-of-freedom simulation. Simulation results show that the new controllers achieve excellent tracking performance and exhibit insensitivity to parameter variations over a wide flight envelope

Nonlinear Bank-To-Turn / Skid-To-Turn Missile Outer-Loop / Inner-Loop Autopilot Design with Θ - D Technique

In this paper, a new nonlinear control method is used to design a full-envelope, hybrid bank-to-turn (BTT)/skid-to-turn (STT) autopilot for an air-breathing air-to-air missile. Through this new approach, called the θ − D method, we find approximate solutions to the Hamilton- Jacobi-Bellman (HJB) equation. An interesting and important feature of this new technique is that the nonlinear feedback law can be expressed in a closed form. In this autopilot design, a θ − D outer-loop and inner-loop controller structure is adopted. A hybrid BTT/STT autopilot command logic is used to convert the commanded accelerations from the guidance laws to reference angle commands for the autopilot. The outerloop θ − D controller converts the angle-of-attack, the sideslip, and the bank angle commands to body rate commands for the inner loop. An inner-loop θ − D nonlinear controller converts the body rate commands to fin commands. The nonlinear design is evaluated using a detailed six-degrees-of-freedom simulation. Simulation results show that the new controllers achieve excellent tracking performance and exhibit insensitivity to parameter variations over a wide flight envelope