Fixed-time adaptive general type-2 fuzzy logic control for air-breathing hypersonic vehicle

Abstract

This paper proposes a novel fixed-time adaptive general type-2 fuzzy logical control (FAGT2FLC) scheme for an air-breathing hypersonic vehicle (AHV) with uncertainties. Firstly, the AHV dynamic model is transformed into a strict feedback form. Then, the FAGT2FLC is designed based on the transformed model to improve robustness and guarantee fixed-time convergence of the closed-loop system. The general type-2 fuzzy logic system (GT2FLS) is utilized to approximate the model uncertainties; for the purpose of designing adaptive laws, the [Formula: see text]-plane method is employed to represent the GT2FLS. A parameter projection operator is used to solve the possible singularity problem of parameter adaption. Besides, a fixed-time differentiator is used to deal with the “explosion of terms” inherent in backstepping method. Theoretical analysis based on relevant lemmas shows that the closed-loop system will converge into a small error band in fixed time. Lastly, detailed simulations are carried out to demonstrate the effectiveness and superiority of the proposed control scheme.

A composite controller design using an adaptive internal type-2 fuzzy logic system and the fixed-time disturbance observer for an air-breathing hypersonic vehicle with a variable geometry inlet

“…Remark 3. For the derivative term of velocity command in (24) and altitude command in (29), _ V d and _ γ d can be directly obtained by the differentiator. For the virtual control signal α d and Q d , it is necessary to calculate the derivative of the virtual control continuously until the rudder deflection deduced in the backstepping recursion, which is easy to cause the "differential explosion" problem.…”

“…Using interval type-2 FLS to approximate nonlinear function on line can increase the accuracy of modeling. 23,24 Zadeh proposed the type-2 fuzzy system on the basis of the type-1 fuzzy system. 25 It is more capable of uncertainty expression.…”

Disturbance observer–based fixed-time robust control for constrained air-breathing hypersonic vehicle

“…Lemma 2. For all x, y ð Þ 2 R 2 , the following inequality holds 24 xy ł e p p x j j p + 1 qe q y j j q ð6Þ…”

“…The fixed-time control has been researched for AHV in recent years. [22][23][24][25][26][27][28][29] Guo et al 22 proposed an SMC approach to achieve the fixed-time convergence of tracking errors and satisfactory robustness against mismatched uncertainties. Ding et al 23 composed a fast fixed-time integral sliding surface and a continuous fixed-time super-twisting-like reaching law to enable the system to converge in fixed time.…”

“…Ding et al 23 composed a fast fixed-time integral sliding surface and a continuous fixed-time super-twisting-like reaching law to enable the system to converge in fixed time. More recently, Yu et al 24 employed a fixed-time adaptive general type-2 fuzzy logical control (FAGT2FLC) scheme, which guarantees fixed-time convergence of the closed-loop uncertain system. Disturbance observer-based control strategy is a practical approach for dealing with system uncertainties.…”