FUNDING ($K) TRANSITIONS “Stability region analysis using sum-of-squares programming,”
2
FUNDING ($K) TRANSITIONS “Stability region analysis using sum-of-squares programming,” 2006 American Control Conference, pp. 2297- 2302. “Local gain analysis of nonlinear systems,” 2006 American Control Conference, pp. 92-96 STUDENTS, POST-DOCS Ufuk Topcu, Tim Wheeler, Weehong Tan LABORATORY POINT OF CONTACT Development of Analysis Tools for Certification of Flight Control Laws UC Berkeley, Andrew Packard, Honeywell, Pete Seiler, U Minnesota, Gary Balas APPROACH/TECHNICAL CHALLENGES •Analysis based on Lyapunov/storage fcn method •Non-convex sum-of-squares (SOS) optimization •Merge info from conventional simulation-based assessment methods to aid in the nonconvex opt •Unfavorable growth in computation: state order, vector field degree and # of uncertainties. •Reliance on SDP and BMI solvers, which remain under development, unstable and unreliable Long-Term PAYOFF Direct model-based analysis of nonlinear systems OBJECTIVES •Develop robustness analysis tools applicable to certification of flight control laws: quantitative analysis of locally stable, uncertain systems •Complement simulation with Lyapunov- based proof techniques, actively using simulation •Connect Lyapunov-type questions to MilSpec-type measures of robustness and performance Region-of-attraction Disturbance-to-error gain Verify set containments in state-space with SOS proof certificates. V 1 p 2 p 3 p x 0 f dx dV 1 V x . FY04 FY05 FY06 FY07 FY08 AFOSR Funds 97 141 Other 0 0 Aid nonconvex proof search (Lyapunov fcn coeffs) with constraints from simulation Convex outer bound
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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 - PowerPoint PPT Presentation
Transcript of FUNDING ($K) TRANSITIONS “Stability region analysis using sum-of-squares programming,”
FUNDING ($K)
TRANSITIONS“Stability region analysis using sum-of-squares programming,”2006 American Control Conference, pp. 2297-2302.“Local gain analysis of nonlinear systems,” 2006 American Control Conference, pp. 92-96STUDENTS, POST-DOCSUfuk Topcu, Tim Wheeler, Weehong Tan
LABORATORY POINT OF CONTACT Dr. Siva Banda, Dr. David Doman
Development of Analysis Tools for Certification of Flight Control Laws
UC Berkeley, Andrew Packard, Honeywell, Pete Seiler, U Minnesota, Gary Balas
APPROACH/TECHNICAL CHALLENGES• Analysis based on Lyapunov/storage fcn method• Non-convex sum-of-squares (SOS) optimization• Merge info from conventional simulation-based
assessment methods to aid in the nonconvex opt• Unfavorable growth in computation: state order,
vector field degree and # of uncertainties.• Reliance on SDP and BMI solvers, which remain
under development, unstable and unreliable
ACCOMPLISHMENTS/RESULTS Pointwise-max storage functions Parameter-dependent storage functions Benefits of employing simulations
Long-Term PAYOFFDirect model-based analysis of nonlinear systemsOBJECTIVES• Develop robustness analysis tools applicable to
certification of flight control laws: quantitative analysis of locally stable, uncertain systems
• Complement simulation with Lyapunov-based proof techniques, actively using simulation
• Connect Lyapunov-type questions to MilSpec-type measures of robustness and performance
Region-of-attractionDisturbance-to-error gainVerify set containments in state-space with SOS proof certificates.
1V
1p
2p
3p
x
0fdx
dV
1V
x .
FY04 FY05 FY06 FY07 FY08
AFOSR Funds 97 141
Other 0 0
Aid nonconvex proof search (Lyapunov fcn coeffs) with constraints from simulation
Convex outer bound
•Unseeded PENBMI solutions (red)•500 simulations•50 samples of Lyapunov outer bound set
•PENBMI solutions seeded with samples. Improved estimate, consistent and reliable execution
Region of attraction estimate for 2211221 1, xxxxxx
Constraints from simulation effectively aid nonconvex search for Lyapunov function proving
region-of-attraction “radius”
A. Packard/ UC Berkeley, P. Seiler/Honeywell, G. Balas / University of Minnesota
Convex outer bound
Convex Constraints on Lyapunov coefficients, obtained from simulation. Initialize nonconvex
search within this set
0 0.2 0.4 0.6 0.8 10
2
4
6
8
4th order V, LP
0 0.2 0.4 0.6 0.8 10
10
20
30
40
4th order V, BMI
0 0.2 0.4 0.6 0.8 10
5
10
6th order V, LP
0 0.2 0.4 0.6 0.8 10
10
20
30
40
50
6th order V, BMI
samples
PENBMI results, seeded with samples
