Optimal Guidance Law with Impact-Angle Constraint and Acceleration Limit for Exo-Atmospheric Interception

Abstract

This paper aims to develop an optimal guidance law for exo-atmospheric interception, in which impact-angle constraint and acceleration limit are considered. Firstly, an optimal control problem with constraints on terminal miss and impact-angle is formulated, in which the control energy performance index is weighted by a power function of the time-to-go. The closed-loop guidance command, which is expressed as a linear combination of zero-effort miss distance and the zero-effort angle error, is derived using a traditional order reduction transformation. Then, an analytical solution to the maximal acceleration during the flight is obtained by analyzing the boundary points and critical points of the guidance command curve. It is found that the maximal acceleration is a function of the weighted gain in the performance index. Therefore, the maximal acceleration can be efficiently limited by using the variable weighted gain. Furthermore, the relationship between the total control energy and the weighted gain is studied. As a result, a systematic method is proposed for selecting the weighted gain so as to meet the constraint of the acceleration while the total control energy is minimal. Nonlinear simulations have been carried out to test the performance of the proposed method. The results show that this method performs well in intercepting the maneuvering target with a negligible miss distance and intercept angle error. And it can tolerate a stricter acceleration limit in comparison with the typical method.

Design of Convergent and Accurate Guidance Law with Finite Time in Complex Adversarial Scenarios

“…The LOS angle acceleration x 2 is required in both the Sliding Mode Equation ( 17) and the Guidance Law Equation (26), and x 2 can be replaced by Equation (11). In the actual process of terminal guidance, target acceleration is not available.…”

“…The above references are based on traditional guidance laws for attack and propose anti-interference algorithms based on the algorithm of the seeker head, without using more robust and accurate modern guidance laws for simulation verification. Currently, various modern control methods are applied in the field of flight vehicle guidance, such as sliding mode control [5][6][7], finite-time control [8][9][10], optimal control [11][12][13], etc. However, many modern guidance laws are designed based on asymptotic stability.…”

Obstacle Avoidance Trajectory Planning for Autonomous Vehicles on Urban Roads Based on Gaussian Pseudo-Spectral Method

“…In recent years, optimal control has gradually been applied in fields such as aerospace [12][13][14], transportation [15], and chemical industry [16]. The trajectory planning of aircraft and vehicles is the most widely used area of optimal control.…”

Terminal Impact Angle Control Guidance Law Considering Target Observability

“…Reference [7] proposed an optimal-control-based guidance law considering the field-of-view constraint for the practical implementation of impact angle control guidance. Reference [8] designed an optimal guidance law with a constraint on the impact angle and acceleration limit.…”