The miss distance analysis of the first-order Explicit Guidance Law (EGL) is carried out using linearized equation of motion in the normalized form in order to obtain normalized miss distance curves. The initial heading error, constant target, acceleration limit, radome refraction error, and fifth-order binomial control system are considered. Moreover, body rate feedback is added to the Explicit Guidance Law as a well-known classical compensation method of the radome effect as in proportional navigation. The analysis is performed for different values of the power of the alpha function, defined as the time decrease rate of the zero-effort miss to unit control input. As a special case, the EGL with unit power gives the first-order Optimal Guidance strategy for minimizing the integral of the square of the commanded acceleration during the total flight time. For the performance/stability analysis, the rms miss distance versus turning rate time constant and radome slope can be plotted for different values of the power of alpha function.

An Optimal strategy based on minimum effort control and also with terminal positionconstraint is developed for an exoatmospheric interceptor with a fixed- interval Guidance time. It isthen integrated with sliding-mode control theory to drive an Optimal sliding-mode Guidance Law forfixed-interval Guidance time. In addition, this Guidance Law is generalized for intercepting anarbitrarily time-varying target maneuver. Robustness of the new Guidance method againstdisturbances and good miss distance performance are achieved by the second method of Lyapunovand simulation results. The presented Guidance Law is simple to implement in practical applications.

In [1], an Optimal midcourse Guidance Law for close distances, where the difference of gravity for interceptor and ballistic missile is negligible, was introduced. There, a closed form solution, based on an optimization problem, was found, with very good performance for close distances but degraded performance in real problems with unequal gravity for missile and interceptor. In this paper, the difference of gravity is taken into account by considering a spherical gravity model. A new equation to express the relative motion between missile and interceptor is used to derive a "Near Optimal Guidance Law". The results found using the new derivation are similar to those in [1] but it provides a Guidance Law with matrix coefficients. Next, the performance of the Guidance Law is improved using Kepler's algorithm. This modified approach results in an almost perfect intercept, even for large distances between missile and interceptor.

The problem studied in this paper consists of the Optimal launch of a satellite to a circular orbit of the earth. The effect of the air resistance is also taken into consideration. The equations of Optimal launch are first derived and the main problem is converted to a Two-Point Boundary Value Problem (TPBVP). A set of state and co-state variables, corresponding to the ideal case of planar earth with no air resistance, i.e. the case in which the linear tangent Guidance Law is, in fact, Optimal, is used as an initial guess, in order to solve the TPBVP using the shooting algorithm. A gradual or step-by-step introduction of the air resistance effect is shown to make the numerical computations converge, thus, alleviating the problems caused by the shooting algorithm's sensitivity to the initial guess. Simulations reveal that the proposed method also has a satisfactory speed of convergence.

An Explicit Guidance Law is developed for a reentry vehicle. Motion is constrained to a three-dimensional Bezier curve. Acceleration commands are derived by solving an inverse problem that combined with differential flatness approach. Trajectory is related to Bezier parameters. A comparison with pure proportional navigation shows the same accuracy, but a higher capability for Optimal trajectory to some degree. Other advantages such as trajectory representation with minimum parameters, applicability to any reentry vehicle configuration and any control scheme, and Time-to-Go independency make this Guidance approach more favorable.

The problem of cooperative Guidance of two pursuers against an evader equipped with higher maneuverability is investigated. The goal is that the distance between the evader and at least one of the pursuers becomes less than a predetermined threshold at the end of the flight time. To achieve this goal, firstly, the roles of pursuers are divided into two units, which include 1) pursuing the evader 2) Observing the evader’s scape space. Secondly, a novel cooperative Guidance Law based on the Optimal separation of roles of the pursuers is proposed and formulated into a constrained nonlinear Optimal control problem. Thirdly, the problem is solved using the Direct Collocation with Nonlinear Programming (DCNLP) method which is an optimization approach. Finally, several numerical simulations are presented to verify the effectiveness of the proposed cooperative Guidance Law.

In this paper a novel Optimal and robust Guidance Law for three dimensional flying-object system is proposed based on the extended kalman filter. New Guidance Law consists of sliding mode and backstepping Guidance Laws. In this Guidance Law there are some coefficients that must be adjusted. These coefficients are adjusted using Genetic Algorithm (GA). Also system states are estimated by using of Continues Extended Kalman Filter (CEKF). Finally, proposed Guidance Law is compared with Augmented Proportional Navigation Guidance (APNG) Law. Simulation results show that proposed Guidance Law is better than APNG Law.

An Optimal Explicit Guidance Law that maximizes terminal velocity is developed for the reentry of a vehicle to a fixed target. The equations of motion are reduced with differential flatness approach and acceleration commands are related to the parameters of trajectory. An Optimal trajectory is determined by solving a real-coded genetic algorithm. For online trajectory generation, Optimal trajectory is approximated. The approximated trajectory is compared with the pure proportional navigation and genetic algorithm solutions. The near Optimal terminal velocity solution compares very well with these solutions. The approach robustness is examined by Monte Carlo simulation. Other advantages such as trajectory representation with minimum parameters, applicability to any reentry vehicle configuration and any control scheme, and Time-to-Go independency make this Guidance approach more favorable.

In this study, on the basis of proportional navigation strategy, design of Explicit Optimal Guidance Law for missiles tracking maneuvering targets in three-dimensional space using model predictive control is addressed. The model predictive control employs a model to predict the future process behavior and calculates an Optimal control input at each time step through the optimization of an objective function. Generalized model predictive control approach, employed in this study, solves the optimization problem offline to obtain the closed form Optimal control Law. In this paper, firstly, the equations describing the missile-target relative motion kinematics are formulated. Then, the Optimal control Law, as an Explicit function of the state vector is obtained. The evaluation of the proposed scheme is studied by the comparison of the simulation results with the augmented proportional navigation system. Simulation studies, in three different scenarios, demonstrates appropriate performance for the proposed Guidance system specially against maneuvering targets.