1. Effects of System Uncertainty on Adaptive-Critic Flight Control Silvia Ferrari Advisor: Prof. Robert F. Stengel Princeton University FAA/NASA Joint University Program on Air Transportation, Ohio University, Athens, OH June 13-14, 2002

2. Introduction Stringent operational requirements introduce Complexity Nonlinearity Uncertainty Classical/neural synthesis of control systems A-priori knowledge Adaptive neural networks Action network takes immediate control action Critic network estimates projected cost Dual heuristic programming adaptive critic architecture:

3. Motivation Full envelope control Multiphase learning Initialization: match linear controllers exactly off-line On-line learning: full-scale simulations, testing, or operation On-line learning improves performance w.r.t. linear controllers: Differences between actual and assumed models Nonlinear effects not captured in linearizations Potential applications: Incorporate pilot's knowledge into controller a priori Uninhabited air vehicles control Aerobatic flight control

4. Table of Contents Adaptive-critic design approach Initialization phase On-line learning phase Adaptive controller final results Large-angle maneuvers Parameter variations Control failures Summary and conclusions

5. Full Envelope Control! Modeling On-line Training Design Approach Initialization Linear Control Linearizations

6. Linear Control Design Linearizations: Altitude (m) Velocity (m/s) Linear control design: Longitudinal Lateral-directional Flight envelope and design points: (  =  =  = 0) k  ( )

7. Proportional-Integral Linear Controller yc(t)yc(t) x(t)x(t) ys(t)ys(t) CICI CFCF CBCB HuHu HxHx + + + + - - - u(t)u(t) LINEARIZED AIRCRAFT (t)(t) Closed-loop stability:

8. CBCB P CICI C F, f[] = 0 : Algebraic Initialization, Proportional-Integral Neural Network Controller yc(t)yc(t) x(t)x(t) + + + + - u(t)u(t) uc(t)uc(t) + - uB(t)uB(t) uI(t)uI(t) xc(t)xc(t) ys(t)ys(t) e(t)e(t) a(t)a(t) NN F SVG CSG (t)(t) : On-line Training. NN I NN C NN B

9. Aircraft Response Comparison During a Large-Bank Turn Velocity (m/s) Climb Angle (deg) Roll Angle (deg) Sideslip Angle (deg) Time (sec) Aircraft Response, (H 0, V 0 ) = (7 Km, 160 m/s) Adaptive Critic Neural Control: Command Input: Initialized Neural Control:

10. Control History and Aircraft Trajectory Comparison During a Large-Bank Turn Adaptive Critic Neural Control Initialized Neural Control Time (sec)  T (%) Control History, (H 0, V 0 ) = (7 Km, 160 m/s)  S (deg)  A (deg)  R (deg) Trajectory Altitude (m) North (m) East (m)

11. Effect of Parameter Variations on Initialized Neural Control, at a Design Point Velocity (m/s) Clim b Angle (deg) Roll Angle (deg) Sideslip Angle (deg) Time (sec) Aircraft Response, (H 0, V 0 ) = (11 Km, 200 m/s) Perfect Aircraft Modeling: Parameter Variations: Command Input: Parameter Variations: C m q, C m r : 50%  C m  : 20%  C n  : 30% 

12. Velocity (m/s) Climb Angle (deg) Roll Angle (deg) Sideslip Angle (deg) Time (sec) Aircraft Response, (H 0, V 0 ) = (11 Km, 200 m/s) Aircraft Response Comparison in the Presence of Parameter Variations Initialized Control with Parameter ariations: Command Input: Initialized Control with Perfect Modeling: Adaptive Critic Neural Control (2 nd adaptation):

13. Adaptive Critic and Initialized Neural Control History Comparison in the Presence of Parameter Variations Time (sec) Velocity (m/s) Climb Angle (deg) Roll Angle (deg) Sideslip Angle (deg) Initialized Neural Control: Adaptive Critic Neural Control (2 nd adaptation): Control History, (H 0, V 0 ) = (11 Km, 95 m/s)

14. Initialized Neural Controller Performance in the Presence of Control Failures Time (sec) Aircraft Response, (H 0, V 0 ) = (3 Km, 100 m/s) Initialized Neural Control Command Input Control History Time (sec)  T (%)  S (deg)  A (deg)  R (deg) Control Failures:  T = 0, 0  t  15 sec  S = 0, 5  t  10 sec  R = 0, 5  t  10 sec  R = –34 o, t  5 or t  10 sec V (m/s)  (deg)  (deg)  (deg)  (deg)

15. Aircraft Response Comparison in the Presence of Control Failures Velocity (m/s) Climb Angle (deg) Roll Angle (deg) Sideslip Angle (deg) Time (sec) Aircraft Response after t = 10 sec, (H 0, V 0 ) = (3 Km, 100 m/s) Adaptive Critic Neural Control: Command Input: Initialized Neural Control: Yaw Angle (deg)

16. Adaptive Critic Neural Control During a Previously-Encountered Maneuver Velocity (m/s) Climb Angle (deg) Roll Angle (deg) Sideslip Angle (deg) Time (sec) Aircraft Response, (H 0, V 0 ) = (3 Km, 100 m/s) Adaptive Critic Neural Control (2 nd adaptation): Command Input: Adaptive Critic Neural Control (1 st adaptation):

17. Summary and Conclusions Learning control system:  Improves global performance  Preserves prior knowledge  Suspends and resumes adaptation, as appropriate Achievements:  Systematic approach for designing adaptive control systems  Framework for investigating neural approximation properties  Innovative (off-line and on-line) training techniques Other Potential Applications for Adaptive Neural Control: Air-traffic management, reconfiguring hardware (raw chips), process control, criminal profiling, image processing,...

18. THANK YOU! JUP