Optimal guidance laws providing the specified impact angle as well as zero terminal miss distance are generalized for arbitrary missile dynamics. The optimal guidance command is represented by a linear combination of the ramp and the step responses of the missile’s lateral acceleration. Optimal guidance laws in the form of the state feedback for the lag-free and the first-order lag system are derived, and their characteristics are investigated. Practical timeto-go calculation methods, which are important for the implementation of the optimal guidance laws, are proposed to consider the path curvature. Nonlinear and adjoint simulations are performed to investigate the performance of the proposed laws.

Optimal Guidance Laws with Terminal Impact Angle Constraint

Missile guidance and pursuit

New missile guidance law is proposed via variable structure control. The acceleration command is determined considering the target acceleration information as uncertainty. Target and missile are assumed to be point masses moving in the two dimensional plane. According to the property of the missile acceleration command, the proposed guidance laws are classified into IPN type and RTPN type. Moreover, it is shown that the conventional proportional guidance laws can be derived from the proposed guidance law. Numerical simulation results show that the proposed guidance law exhibits better performance compared to the conventional proportional guidance laws.

Design of Missile Guidance Law via Variable Structure Control

A new adaptive nonlinear guidance law is proposed here. The fourth order state equation for integrated guidance and control loop is formulated taking into consideration the target uncertainties and control loop dynamics. The state equation is further changed into the normal form by nonlinear coordinate transformation. Using the normal form of state equation, an adaptive nonlinear guidance law is proposed to compensate for the uncertainties in both target acceleration and control loop dynamics. The proposed law adopts the sliding mode control approach with adaptation for unknown bound of uncertainties. The present approach can effectively solve the existing guidance problem against target maneuver and the limited performance of control loop. We have provided the stability analyses and performed simulations comparing favorably our approach to the state of the art.

Adaptive nonlinear guidance law considering control loop dynamics

Design of Time-constrained Guidance Laws via Virtual Leader Approach

Modern guidance law for high-order autopilot

Explicit formulas of optimal guidance for a linear, time-invariant, arbitrary-order, and acceleration constrained missile are derived. These formulas are given in terms of the missile's transfer function and acceleration constraint. Optimal, full-state feedback guidance laws are synthesized and compared to first-order approximation and the proportional navigation for minimum and nonminimum missile dynamics. Simulations on a third-order missile model show the relative gain from using the full-order guidance law vs the acceleration constraint as well as some robustness tests. HE optimal control theory has been used to derive modern/optimal guidance laws which have improved performance. The improved performance of these homing laws is achieved by a consideration of the detailed dynamics of the threat (target) and the interceptor (missile). However, it comes at the expense of increased complexity in realization (cost), sensitivity to knowledge of various parameters, etc. An extensive study of literature on guidance laws in general, and optimal guidance laws in particular, is performed by Pastrick et al.1 In various references,2'6 optimal guidance laws are derived for first- and second-order missiles, respectively. In our previous paper,7 the structure of optimal guidance laws for a linear, arbitrary high-order missile was considered. Mainly, we derived the closed-loop, general structure formulas of the guidance law. Further, we studied the behavior of the gains for minimum and nonminimum phase missiles and compared the performance of some sub-optimal approximations of the guidance laws. The effect of the acceleration constraint, which is imposed by the structural or aerodynamic limitations, on guidance laws and performance for a first-order missile is systematicall y treated by Anderson.8 In this paper we derive an optimal/moder n guidance law, on collision course, for a linear, time-invariant, arbitrary order and acceleration constrained missile. It is shown that, for a minimum phase missile, the optimal guidance law is the guidance law for an unconstrained missile with saturation on the commanded acceleration. However, for a nonminimum phase missile, this is only a suboptimal guidance law, and the optimal controller is more complicated. In the paper comparison of the proportional navigation, first-order approximation, and full-order guidance laws is performed on a third-order minimum and nonminimum phase model of a missile. The comparison is performed on a common basis. Moreover, the robustness of these guidance laws is subject to an analysis, namely, the sensitivity to uncertainty/ variation in parameters, radome refraction slope, and acceleration constraint is checked for minimum and nonminimum phase air frames. The main conclusions are that, for a minimum phase missile, the full-order guidance law does not give improved performance with respect to the first-order approximation,

Optimal Guidance for High-Order and Acceleration Constrained Missile

Explicit formulas of optimal guidance laws for an acceleration-constrained, arbitrary-order missile and maneuvering target are derived. These formulas are given in terms of the transfer function and acceleration constraint of the missile and the transfer function/shaping filter of the target. Optimal full-state feedback guidance law is synthesized against a target performing a barrel roll maneuver, and compared with the performance of proportional navigation (PN) for minimum and nonminimum phase missile. Simulation of a third-order missile shows the relative gain from using the full-order guidance law. >

Optimal guidance for acceleration constrained missile and maneuvering target

Excplicit formulas of optimal guidance law for acceleration constrained arbitrary order missile and maneuvering target are derived. These formulas are given in terms of the missile's transfer function and acceleration constraint, and the transfer function/shaping filter of the target. Optimal, full state feedback guidance law is synthesized against a target performing a barrel roll maneuver, and compared to the performance of the Proportional Navigation for minimum and non-minimum missile. Simulation of a 3rd order missile show the relative gain from using the full order guidance law for several acceleration constraints.

Optimal Guidance for Acceleration Constrained Missile and Maneuvering Target

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Modern guidance law for high-order autopilot

Optimal Guidance for High-Order and Acceleration Constrained Missile

Optimal guidance for acceleration constrained missile and maneuvering target

Optimal Guidance for Acceleration Constrained Missile and Maneuvering Target