Control Seminar

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

Chris Damaren

University of Toronto,Institute of Aerospace Studies
Friday, February 21, 2014
3:30pm - 4:30pm
1500 EECS

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About the Event

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.

Additional Information

Contact: Ann Pace

Phone: 763-5022


Sponsor(s): Bosch, Eaton, Ford, MathWorks, Toyota, and Whirlpool

Open to: Public