An L₁ adaptive closed-loop guidance law for an orbital injection problem

Abstract

The current paper presents the determination of a closed-loop guidance law for an orbital injection problem using two different approaches and, considering the existing time-optimal open-loop trajectory as the nominal solution, compares the advantages of the two proposed strategies. In the first method, named neighbouring optimal control (NOC), the perturbation feedback method is utilized to determine the closed-loop trajectory in an analytical form for the non-linear system. This law, which produces feedback gains, is in general a function of small perturbations appearing in the states and constraints separately. The second method uses an L1 adaptive strategy in determination of the non-linear closed-loop guidance law. The main advantages of this method include characteristics such as improvement of asymptotic tracking, guaranteed time-delay margin, and smooth control input. The accuracy of the two methods is compared by introducing a high-frequency sinusoidal noise. The simulation results indicate that the L1 adaptive strategy has a better performance than the NOC method to track the nominal trajectory when the noise amplitude is increased. On the other hand, the main advantage of the NOC method is its ability to solve a non-linear, two-point, boundary-value problem in the minimum time.

A modified model reference adaptive control with application to MEMS gyroscope

“…Instead of conventional control input for MRAC, a low-pass filtered adaptive version of the control algorithm is proposed for Eq. (15) as: (22) where ( ( ) LP F s is a low-pass filter with low-pass gain 1. The design procedure for the low-pass filter has been addressed in Refs.…”

“…Cao and Hovakimian [10,19,20] developed a novel adaptive control architecture that ensures that the input and output of an uncertain linear system track the input and output of a desired linear system during the transient phase, in addition to asymptotic tracking. Zareh et al [21,22] utilized this modified MRAC for some special flight control systems. Some control algorithms had been proposed to control the MEMS gyroscope.…”

An ℒ1 fuzzy adaptive controller for a class of SISO nonaffine nonlinear systems: application to the control of an electropneumatic actuator

“…Malinga and Buckner studied real-time implementation of the L 1 adaptive control scheme to regulate the bending angle of a flexible beam, actuated by a single shape memory alloy tendon. 16 The L 1 adaptive control method has also been used in other systems: for example, spacecraft 17 and underwater vehicles, 18,19 to name a couple.…”

Non-linear solution to the maximum height orbit transfer guidance problem

“…A novel approach to synthesize the optimal feedback law for the satellite injection problem is introduced using fuzzy systems by Pourtakdoust et al [9] In this work, an attempt was made to develop the closed-loop fuzzy guidance law in the presence of environment noises and system uncertainties. Afshari et al [1,[10][11][12] and Roshanian et al [13] have tried to design optimal guidance solutions for different space missions by employing mathematical theories, such as perturbation theorem, backward sweep method, and calculus of variations in exact forms. Considering novel approaches of control theories such as fuzzy guidance law (FGL) and L 1 adaptive method has caused new guidance solutions to be achieved.…”