1 Gary J. Balas Aerospace Engineering and Mechanics University of Minnesota Minneapolis, MN Systems Research in the Aerospace Engineering and Mechanics at the University of Minnesota SAE Aerospace Controls and Guidance Meeting 19 October 2005

2 University of Minnesota Aerospace 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

3 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, June 2006, Minneapolis, MN

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

5 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

6 Quantitative Nonlinear Analysis Initial focus –Region of attraction estimation – 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

7 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