Gary J. Balas

1
Systems Research in theAerospace Engineering and
Mechanicsat the University of Minnesota

• Gary J. Balas
• Aerospace Engineering and Mechanics
• University of Minnesota
• Minneapolis, MN
• balas_at_aem.umn.edu

SAE Aerospace Controls and Guidance Meeting 19
October 2005
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University of MinnesotaAerospace Engineering and
Mechanics Systems Faculty

• William Garrard, Department Head
• Modeling, flight control, parachutes
• Yiyuan Zhao
• Optimization, air traffic control, rotorcraft
• Demoz Gebre-Egziabher
• Navigation, GPS, sensor fusion
• Gary Balas
• Robust control, real-time embedded systems,
  flight control
• Bernard Mettler (starts Jan 2006)
• Real-time control, planning, rc helicopters and
  planes

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Current Research

• Control Reconfiguration and Fault Detection and
  Isolation Using Linear, Parameter Varying
  Techniques, NASA Langley Research Center, NASA
  Aviation Safety Program, Dr. Christine Belcastro
  Technical Monitor
• Stability and Control of Supercavitating
  Vehicles, ONR, Dr. Kam Ng Program Manager
• Special Session planned for the 2006 American
  Control Conference entitled Modeling and Control
  of High-Speed Underwater Vehicles
• Local Arrangements Chair, 2006 American Control
  Conference, 14-16 June 2006, Minneapolis, MN

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Control of Projectiles
Using control thruster firings, the projectile
maneuvers to the optimum angle of attack

• Tradeoff between many small maneuvers and wider
  spaced, large maneuvers
• Controllability of projectile given a finite
  number of impulses
• Optimal control of a number of thrusters.
• Effect of
• Burn time
• Impulse size and number
• Achievable performance

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Development of Analysis Tools for Certification
of Flight Control Laws - AFOSR

• Andy Packard (UC Berkeley), Pete Seiler
  (Honeywell)
• Initial focus is on nonlinear robustness analysis
• Region-of-attraction
• Disturbance-to-error gains
• Inner and Outer Bounds
• Connection to MilSpecs

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Quantitative Nonlinear Analysis

• Initial focus
• Region of attraction estimation
• induced norms
• induced norms
• for
• finite-dimensional nonlinear systems, with
• polynomial vector fields
• parameter uncertainty (also polynomial)
• Main Tools
• Lyapunov/HJI formulation
• Sum-of-squares proofs to ensure nonnegativity
• Semidefinite programming (SDP), Bilinear Matrix
  Inequalities
• Optimization interface YALMIP and SOSTOOLS
• SDP solvers Sedumi
• BMIs using PENBMI (academic license from
  www.penopt.com)

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Estimating Region of Attraction

• Dynamics, equilibrium point
• User-defined function whose sub-level sets are to
  be in region-of-attraction
• By choice of positive-definite V, maximize ? so
  that