Abstract—In this study, the H-infinity tracking control
problem of a linearized hypersonic vehicle model with the
bounded external disturbance is investigated. Firstly, the
nonlinear longitudinal dynamics of hypersonic vehicle is
linearized as a linear time-invariant system with the bounded
external disturbance, a reference model is introduced for the
aim of tracking control. And then an observer-based output
feedback tracking controller design approach is proposed by
using the linear matrix inequalities (LMIs) technique. The
asymptotical stability of the closed-loop system is analyzed in
the framework of Lyapunov method. Finally, the simulation
results are given to illustrate the applicability of the developed
control approach.
I. INTRODUCTION
A hypersonic vehicle is a vehicle that travels at least 5
times faster than the speed-of-sound, or greater than Mach 5.
A hypersonic vehicle can be an airplane, missile, or
spacecraft. Some hypersonic vehicles have a special type of jet
engine called a supersonic combustion ramjet or scramjet to
fly through the atmosphere [1]. Compared with the existing
airships, space shuttles and aeroplanes, hypersonic vehicle has
many advantages in launch cost, maintainability, reusability,
flight performance and so on. Consequently, it is not
surprising that the controller design and stability analysis
problem of hypersonic vehicle have been extensively
considered by many researchers [2]. In [3], a robust output
feedback control scheme is proposed for the longitudinal
model with partial state measurements of a flexible
air-breathing hypersonic vehicle by using the combination of
the high-order sliding mode controller and observer. In [4], a
nonlinear controller is exploited and analyzed for the
nonlinear longitudinal dynamics of a generic hypersonic
vehicle by combining the nonlinear observer and
back-stepping technique. In [5], a fuzzy guaranteed cost state
feedback controller is designed for a flexible air-breathing
hypersonic vehicle to guarantee that the closed-loop system is
asymptotically stable and the proposed performance index has
an upper bound. In [6], a novel gain-scheduled switching
control approach is proposed for the longitudinal motion of a
flexible air-breathing hypersonic vehicle, the designed
gain-scheduled controller could guarantees the closed-loop
system to be asymptotically stable and satisfy a given tracking
*Resrach supported by the National Natural Science Foundation of China
(61304106), the NJUPT Research Funding (NO. NY211046), and the
Natural Science Foundation of the Jiangsu Higher Education Institutions of
China (13KJB510028).
Z. F. Gao, T. Cao and J. X. Lin are with College of Automation, Nanjing
University of Posts and Telecommunications, Nanjing 210046, China
(gaozhifeng80@126.com).
M. S. Qian is with Research Institute of UAV, Nanjing University of
Aeronautics and Astronautics, Nanjing 210016, China
(xianglin_ming@163.com).
error performance criterion. In [7], the adaptive Kriging
controller is investigated for the longitudinal dynamics of a
generic hypersonic flight vehicle. The Kriging system is used
to estimate the uncertainty, which is described as the
realisations of Gaussian random functions. In [8], a
non-fragile tracking control scheme is presented for a flexible
hypersonic air-breathing vehicles, which guarantees the
tracking error dynamics to be robustly stable. In [9], the robust
flight control problem for the longitudinal dynamics of a
generic airbreathing hypersonic vehicles under mismatched
disturbances is investigated by using the nonlinear-
disturbance-observer-based control method, the proposed
method obtains not only promising robustness and disturbance
rejection performance but also the property of nominal
performance recovery. It is noted that most of the existed
control approach described above must utilize the state
information of the flight control system, however, some state
variables of the flight control systems is not obtained in real
engineering applications. So the results described above have
some limitations in actual application. To the best of our
knowledge, the observer-based output feedback tracking
control problem for hypersonic vehicle with external
disturbance has not been fully investigated yet, which remains
challenging and motivates us to do this study.
In this paper, we design an observer-based output feedback
tracking control approach for a linearized dynamical system of
hypersonic vehicle subject to bounded external disturbance.
Firstly, the nonlinear longitudinal dynamics of an hypersonic
vehicle is introduced, which can be linearized at nominal
hypersonic cruise flight condition. By considering the external
disturbance, a linearized dynamical model of hypersonic
vehicle is given. And then, a novel observer-based tracking
control scheme is proposed for hypersonic vehicle in the
framework of Lyapunov approach. The existence conditions
for tracking controller are formulated in the form of LMIs, and
the tracking control design problem is cast into a convex
optimization problem. If the optimization problem is solvable,
a desired tracking controller can be readily constructed. The
simulation results are provided to show the effectiveness of
the proposed tracking approach.
II. P
ROBLEM STATEMENT
The nonlinear longitudinal equations of motion flying for
hypersonic vehicle at orbital altitudes must include both an
inverse-square-law gravitational model and the centripetal
acceleration for the non-rotating Earth. The state space
equations for the longitudinal dynamics are governed by the
set of differential equations for velocity
V , flight-path
angle
, altitude h , angle of attack
α
, and pitch rate q as
Observer-based H-infinity Tracking Control Design for A Linearized
Hypersonic Vehicle Model with External Disturbance*
Zhifeng Gao, Teng Cao, Jinxing Lin, and Moshu Qian
1649
Proceedings of 2014 IEEE Chinese Guidance, Navigation and Control Conference August 8-10, 2014 Yantai, China
978-1-4799-4699-0/14/
31.00©2014 IEEE