Development of Analysis Tools for Certification of Flight Control Laws UC Berkeley, Andrew Packard, Honeywell, Pete Seiler, U Minnesota, Gary Balas. Region-of-attraction Disturbance-to-error gain Verify set containments in state-space with SOS proof certificates. Long-Term PAYOFF
Flight Control Laws
UC Berkeley, Andrew Packard,
Honeywell, Pete Seiler, U Minnesota, Gary Balas
Verify set containments in state-space with SOS proof certificates.
Convex outer bound
Aid nonconvex proof search (Lyapunov fcn coeffs) with constraints from simulation
“Stability region analysis using simulations and SOS programming,” 2007 ACC
“Stability region analysis via composite Lyap. functions & SOS programming,” IEEE TAC, 10/07.
“Local stability analysis using simulations & SOS programming,” sub. Automatica (12/06, 4/07)
“Stability region analysis for uncertain nonlinear systems,” to appear 2007 CDC
“Local stability analysis for uncertain nonlinear systems,” submitted IEEE TAC (6/07)
Ufuk Topcu, Tim Wheeler, Weehong Tan
LABORATORY POINT OF CONTACT
Dr. Siva Banda, Dr. David Doman
ROA for Uncertain Systems
A feasible path towards attacking problems with, eg., 10 states, 5 uncertainties, and cubic (in state) vector fields
Dynamics have strong dependence on δ
35 partitions of [0 1], quadratic and quartic V, quadratic and quartic SOS multipliers for each partition, <5 minutes on 8-machine PC cluster.
Analysis gives binary tree that partitions parameter-space, with certificates at each subdomain
Best literature estimate from Chesi, et.,al.
Application to flight control, with gain and time delay (Pade) variations
A. Packard/ UC Berkeley, P. Seiler/Honeywell, G. Balas / University of Minnesota