A neuro-optimal approach
for thrust-insensitive trajectory planning
S.H. Pourtakdoust and F. Pazooki
Science and Research Branch, Islamic Azad University, Tehran, Islamic Republic of Iran, and
M. Fakhri Noushabadi
Aerospace Department, Sharif University of Technology, Tehran, Islamic Republic of Iran
Abstract
Purpose – The purpose of this paper is to devise a new approach to synthesize closed-loop feedback guidance law for online thrust-insensitive optimal
trajectory generation utilizing neural networks.
Design/methodology/approach – The proposed methodology utilizes an open-loop variational formulation that initially determines optimal launch/
ascent trajectories for various scenarios of known uncertainties in the thrust profile of typical solid propellant engines. These open-loop optimized
trajectories will then provide the knowledge base needed for the subsequent training of a neural network. The trained network could eventually
produce thrust-insensitive closed-loop optimal guidance laws and trajectories in flight.
Findings – The proposed neuro-optimal guidance scheme is effective for online closed-loop optimal path planning through some measurable and
computable engine and flight parameters.
Originality/value – Determination of closed-loop optimal guidance law for non-linear dynamic systems with uncertainties in system and environment has
been a challenge for researchers and engineers for many years. The problem of steering a solid propellant driven vehicle is one of these challenges. Even
though a few researchers have worked in the area of non-linear optimal control and thrust-insensitive guidance, this paper proposes a new strategy forthe
determination of closed-loop online thrust insensitive guidance laws leading to optimal flight trajectories for solid propellant launch and ascent vehicles.
Keywords Trajectories, Neural nets, Control technology, Aerospace engineering
Paper type Research paper
Nomenclature
T ¼ thrust
m ¼ mass
q ¼ pitch rate
g ¼ gravitational acceleration
v
e
¼ earth rotation angular velocity
C
D
0
¼ zero angle of attack drag coefficient
C
D
a
¼ drag coefficient derivative
C
L
a
¼ lift coefficient derivative
C
N
a
¼ normal force coefficient derivative
r
¼ atmospheric density
S ¼ reference area
r ¼ vehicle distance to earth center
m
¼ earth gravity parameter
X ¼ state vector
P ¼ co-state vector
n ¼ number of layers in the network
S
0
¼ network inputs number
S
t
¼ number of neurons in each layer
1. Introduction
One of the most important desirable characteristics of guidance
and control systems of aerospace vehicles is their ability to
overcome system and environmental uncertainties in flight.
A field of research in this area is devoted to finding closed-loop
optimal control laws. Optimal control theory, although very
powerful for the design of optimal policies, is by itself unable to
generate closed-loop solution for many non-linear dynamic
systems (Kirk, 1970; Bryson and Ho, 1975) such as space-
borne vehicles, launchers and missiles. Researchers have
utilized a multitude of schemes in an attempt to solve this
problem. Rahbar and Bahrami (2000) have used neural
networks in developing a closed-loop optimal control for
pursuit guidance. Kunisch et al. (2003) have proposed a non-
linear feedback law for optimal control of evolution problem by
a combination of model reduction techniques and numerical
solution of Hamiltonian-Jaccobi-Bellman (HJB) equation.
Naidu (2002) has presented closed-loop optimal control
utilizing singular perturbation theory. Lewis and Abu-Khalaf
(2004) have proposed nearly optimal state feedback control for
constrained non-linear systems through HJB equation using
neural networks. Lee and Symth (1993) and Goh et al. (1996)
have also used neural networks in the solution of minimum time
optimal control problem. Pourtakdoust et al. (2005a) have
developed a time optimal closed-loop control for non-linear
lunar-lander problem using fuzzy networks.
Development of optimal guidance law for solid propellant
propulsion systems without cut-off mechanism is a
challenging problem due to unpredictable nature of engine
thrust profiles rising from internal ballistics and batch grain
forming. Some research in this field has focused on energy
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1748-8842.htm
Aircraft Engineering and Aerospace Technology: An International Journal
81/3 (2009) 212– 220
q Emerald Group Publishing Limited [ISSN 1748-8842]
[DOI 10.1108/00022660910954718]
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