Home > Seminars > The Conic Sector Theorem: Plant Characterization and Controller Synthesis

The Conic Sector Theorem: Plant Characterization and Controller Synthesis


4/10/2015 at 11:00AM


4/10/2015 at 12:00PM


258 Fitzpatrick Hall


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Vijay Gupta

Vijay Gupta

VIEW FULL PROFILE Email: vgupta2@nd.edu
Phone: 574-631-2294
Website: http://ee.nd.edu/faculty/vgupta/
Office: 275C Fitzpatrick Hall


Department of Electrical Engineering Professor and Associate Chair of Graduate Studies
Research Interests: Dr. Gupta's current research interests are in the analysis and design of cyberphysical systems. Such systems are the next generation of engineering systems and involve tightly coupled control, communication, and processing algorithms. Applications include structural health ...
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The passivity theorem states that a passive system connected in a negative feedback loop with a very strictly passive system is input-output stable. Unfortunately, sensor and actuator dynamics can violate the passive input-output map of a theoretically passive system rendering the passivity theorem inapplicable and, possibly, resulting in closed-loop instability. The small gain theorem states that the negative feedback interconnection of two finite gain systems is input-output stable if the product of the gains is strictly less than one. Imposing requirements of the small gain theorem on a controller can lead to poor closed-loop performance. Interestingly, the passivity and small gain theorems are both special cases of a more general input-output stability result, the conic sector theorem. In this talk, modern applications and extensions of the conic sector theorem will be discussed. First, the conic sector theorem will be used to guarantee input-output stability of robotic system that has had its natural passivity violated by sensor and actuator dynamics. Conic bounds will be characterized by solving a convex optimization problem subject to linear matrix inequality (LMI) constraints. Next, the synthesis of H2 optimal controllers subject to conic constraints using convex optimization and LMIs will be considered. Last, LMI conditions implying conic bounds are developed for stable linear time-invariant systems with unknown input and output delay. Combined with the conic sector theorem, this enables the design of controllers ensuring closed-loop input-output stability that is robust to input and output delay uncertainty.

Seminar Speaker:

James Forbes

James Forbes

University of Michigan

James Richard Forbes grew up in Southern Ontario, Canada. James received his B.A.Sc. in Mechanical Engineering (Honours, Co-op) from the University of Waterloo in 2006. While attending the University of Waterloo, James participated in the co-op program; James had the opportunity to work in the manufacturing, automotive, rail, and industrial automation (robotics) industries. James was awarded his M.A.Sc. and Ph.D. degrees in Aerospace Science and Engineering from the University of Toronto Institute for Aerospace Studies (UTIAS) in 2008 and 2011, respectively. He was awarded the G. N. Patterson Award for the most outstanding Ph.D. thesis in 2011. With Anton de Ruiter and Christopher Damaren, James coauthored the text “Spacecraft Dynamics and Control — An Introduction” published by Wiley in 2013 (ISBN-13: 978-1118342367). From May 2011 to August 2013 James was an Assistant Professor of Mechanical Engineering at McGill University located in Montreal, Quebec, Canada. While at McGill University he was also an associate member of the Centre for Intelligent Machines. James is currently an Assistant Professor of Aerospace Engineering at the University of Michigan. This past year James was nominated for the University of Michigan's Golden Apple award, a university wide award given to instructors who  ``not only disseminate knowledge but inspire and engage students in its pursuit". The focus of James' research is fundamental developments in nonlinear control and estimation as applied to robotic and aerospace systems.