Fault-tolerant control of flexible air-breathing hypersonic vehicles in linear ODE-beam systems

ABSTRACT

This paper addresses the fault-tolerant control issue for a class of flexible air-breathing hypersonic vehicles. Firstly, a longitudinal dynamic model with process faults is established, which contains an ordinary differential equation (ODE) for rigid body, an Euler–Bernoulli beam equation for flexible modes, and a new boundary connection between them; Secondly, a novel fault-tolerant control scheme is proposed to accommodate process faults and suppress vibrations, which relies on the direct Lyapunov method and the bilinear matrix inequalities (BMIs) technique; Thirdly, in order to compute the gain matrices of the fault-tolerant control law, a two-step algorithm is provided to solve the BMI feasibility problem in terms of linear matrix inequality optimisation technique. Finally, the simulation results are provided to illustrate the effectiveness of the theoretical results.

KEYWORDS:

• Flexible air-breathing hypersonic vehicle
• ODE-beam
• process fault
• fault-tolerant control

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

1 Let X and W be Banach spaces. A linear operator from X to W is a pair $\left(\mathcal{D}\right(\mathcal{A}),\mathcal{A})$ consisting of a subspace $\mathcal{D}\left(\mathcal{A}\right)\subset X$ (called the domain of the operator) and a linear transformation $\mathcal{A}:\mathcal{D}\left(\mathcal{A}\right)\to W$.

2 Let $X_c$ be a Banach space. A family $\left\{T\right(t\left)\right\},t\ge 0$, of bounded linear operators in $X_c$ is called a strongly continuous semigroup or ${\mathcal{C}}_0$-semigroup, if it satisfies the following properties:

• $T(t+s)=T\left(t\right)T\left(s\right),t,s\ge 0$,

• $T\left(0\right)=I$,

• $[0,\mathrm{\infty })\ni t\mapsto T\left(t\right)x_c\in X_c$ is continuous for every $x_c\in X_c$.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [61533009, 61473143, 61622304], Natural Science Foundation of Jiangsu Province [BK20160035], Fundamental Research Funds for the Central Universities [NE2014202, NE2015002], and the Funding of Jiangsu Innovation Program for Graduate Education [grant number KYCX17_0271].