Hybrid Linear Quadratic Optimal Control for Aerospace Systems with Continuous and Impulsive Inputs

We consider linear systems described by hybrid dynamics; that
is systems described by linear (potentially time-varying) models
with continuous control inputs and "jump dynamics" at discrete
time instants where impulsive control inputs are applied. A
quadratic performance index is formulated and the necessary conditions
for optimality are determined. The solution to the control problem
is obtained using two types of Riccati equations: the usual continuous-time
Riccati differential equation and a discrete Riccati equation which
yields discontinuous jumps in the continuous-time solution. Necessary
conditions for optimal timing of the impulsive inputs are also presented.
The hybrid LQR solution is applied to the problem of spacecraft formation
flying in low Earth orbit where the deputy spacecraft mitigates the
effects of the J2 perturbation using a combination of the
geomagnetic Lorentz force and impulsive thrusting for actuation.
It is shown that the required amount of thruster actuation for
formation keeping can be significantly reduced when used in concert
with Lorentz force actuation.

Chris Damaren received the BASc, MASc, and PhD
degrees in aerospace engineering from the University of
Toronto in 1985, 1987, and 1990 respectively. His
graduate research was in the area of dynamics and
control of flexible spacecraft. From 1990 to 1995 he
as an Assistant Professor in the Department of Engineering
at Royal Roads Military College in Victoria, BC, Canada.
From 1995 to 1999 he was a Senior Lecturer in the Department
of Mechanical Engineering at the University of Canterbury in
Christchurch, New Zealand. From 1999-2010, he held the
position of Associate Professor at the University of Toronto
Institute for Aerospace Studies and was promoted to the rank of
Professor in 2011. From 2008 to 2013, he was the Vice-Dean
Graduate Studies for the Faculty of Applied Science and Engineering
at the University of Toronto. His research interests are mainly
in the areas of spacecraft dynamics and control.
He has also published several articles
on the dynamics and control of structurally
flexible robotic manipulators and the transient hydrodynamics of
floating structures.