Guidance Laws with Finite Time Convergence

Abstract

Conventional guidance laws are designed based on Lyapunov theorems on asymptotic stability or exponential stability. They will guide the line-of-sight angular rate to converge to zero or its small neighborhood, however, only as time approaches infinity. In this paper, new guidance laws with finite convergent time are proposed. The guidance laws are obtained based on new sufficient conditions derived in this paper for the finite time convergence of the line-of-sight angular rate. It is proved that, with the guidance laws, the line-of-sight angular rate will converge to zero or a small neighborhood of zero before the final time of the guidance process. Furthermore, such guidance laws will ensure finite time convergence and finite time stability in both the planar and three-dimensional environments. Simulation results show that the guidance laws are highly effective. Nomenclature a Mr , a M , a M = missile acceleration along the line-of-sight axes a r , a , a = relative acceleration along line-of-sight axes a Tr , a T , a T = target acceleration along line-of-sight axes N = navigation ratio q = line-of-sight angle _ q = derivative of q with respect to time q = second-order derivative of q with respect to time r = relative range _ r = derivative of r with respect to time r = second-order derivative of r with respect to time t = time u = missile acceleration normal to line of sight u r = missile acceleration along line of sight V M = missile velocity V T = target velocity w = target acceleration normal to line of sight w r = target acceleration along line of sight x M , y M , z M = position coordinates of missile in inertial frame x T , y T , z T = position coordinates of target in inertial frame = azimuth = elevation ' M = flight-path angle of missile ' T = flight-path angle of target M = heading angle of missile T = heading angle of target

Integrated Guidance and Control Design for the Near Space Interceptor

“…1, and the kinematical equations are described as follows [24]: The interceptor-target motion in the three-dimensional space can be seen in Fig. 1, and the kinematical equations are described as follows [24 …”

Multiple UAVs Nonlinear Guidance Laws for Stationary Target Observation with Waypoint Incidence Angle Constraint

“…Then, the position of the temporary virtual target can be calculated as (12) where, , and . If the desired heading angle is set as 0 or 180 degrees, then the position of the temporary virtual target should be chosen as (13) To rapidly guide the UAV, the virtual target should be located in front of the temporary virtual target, considering the direction of the movement.…”

“…Time and angle constraints to approach the desired circle path could become important issues for multiple UAVs operation, to avoid them colliding with each other, and to perform the mission effectively. While the time and angle constraints problem has not been treated much in UAV systems, similar problems have been widely studied in missile systems [9][10][11][12]. Impact time and impact angle constraints in missile systems, which have the same meaning of approach time and incidence angle, are very important in This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.…”

Guidance Law for Near Space Interceptor based on Block Backstepping Sliding Mode and Extended State Observer

“…15 (2), 163-172 (2014) solved by introducing first-order low-pass filters [9]. To intercept a larger maneuvering target, some advanced control methods have also been applied to the guidance law, such as the nonlinear H ∞ guidance law [10,11], and sliding mode guidance (SMG) law [12,13]. However, the above methods dealt with the influence of target maneuvers at the price of sacrificing normal guidance performance.…”

“…Moreover, the H ∞ guidance law relies on the solution of the HamiltonJacobi-Isaacs (HJI) partial differential equation, which is difficult to solve, except for simple or special cases. SMG is an efficient method to deal with the influence of the target maneuver and parameter uncertainties, but chattering is an unavoidable problem of engineering application [12]. The saturation function and boundary layer method are often used to alleviate chattering, at the price of disturbance rejection performance.…”