Experimental Validation of L 1 Adaptive Control: Rohrs’ Counterexample in Flight

The paper presents new results on the verification and in–flight validation of an L1 adaptive flight control system, and proposes a general methodology for verification and validation of adaptive flight control algorithms. The proposed framework is based on Rohrs’ counterexample, a benchmark problem presented in the early 80s to show the limitations of adaptive controllers developed at that time. In this paper, the framework is used to evaluate the performance and robustness characteristics of an L1 adaptive control augmentation loop implemented onboard a small unmanned aerial vehicle. Hardware–in–the–loop simulations and flight test results confirm the ability of the L1 adaptive controller to maintain stability and predictable performance of the closed loop adaptive system in the presence of general (artificially injected) unmodeled dynamics. The results demonstrate the advantages of L1 adaptive control as a verifiable robust adaptive control architecture with the potential of reducing flight control design costs and facilitating the transition of adaptive control into advanced flight control systems.

[1]  Alexis Aloneftis.  Stochastic Adaptive Control Results and Simulations , 1987 .

[2]  K. Narendra,et al.  Stable model reference adaptive control in the presence of bounded disturbances , 1982 .

[3]  Romeo Ortega,et al.  Robustness of adaptive controllers - A survey , 1989, Autom..

[4]  Iven M. Y. Mareels,et al.  Non-linear dynamics in adaptive control: Chaotic and periodic stabilization , 1986, Autom..

[5]  R. Cleary.  Mathematical Models , 2009 .

[6]  K. Narendra,et al.  A New Adaptive Law for Robust Adaptation without Persistent Excitation , 1986, 1986 American Control Conference.

[7]  L. Praly,et al.  Adaptive nonlinear regulation: estimation from the Lyapunov equation , 1992 .

[8]  K. Astrom.  Interactions between excitation and unmodeled dynamics in adaptive control , 1984, The 23rd IEEE Conference on Decision and Control.

[9]  Stephen A. Jacklin,et al.  Closing the Certification Gaps in Adaptive Flight Control Software , 2008 .

[10]  Robert R. Bitmead,et al.  Transient bounds for adaptive control systems , 1994, IEEE Trans. Autom. Control..

[11]  Naira Hovakimyan,et al.  Are phase and time-delay margins always adversely affected by high-gain? , 2006 .

[12]  L. Valavani,et al.  Robustness of adaptive control algorithms in the presence of unmodeled dynamics , 1982, 1982 21st IEEE Conference on Decision and Control.

[13]  Michael Athans,et al.  Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics , 1985 .

[14]  Brian D. O. Anderson,et al.  Failures of adaptive control theory and their resolution , 2005, Commun. Inf. Syst..

[15]  Petros A. Ioannou,et al.  Robust redesign of adaptive control , 1984 .

[16]  Irene M. Gregory,et al.  Flight Validation of Metrics Driven L1 Adaptive Control , 2008 .

[17]  Brian D. O. Anderson,et al.  Adaptive systems, lack of persistency of excitation and bursting phenomena , 1985, Autom..

[18]  Petros A. Ioannou,et al.  Robust Adaptive Control , 2012 .

[19]  Naira Hovakimyan,et al.  L1 Adaptive Output Feedback Controller to Systems of Unknown Dimension , 2007, ACC.

[20]  Naira Hovakimyan,et al.  L1 Adaptive Output-Feedback Controller for Non-Strictly-Positive-Real Reference Systems: Missile Longitudinal Autopilot Design , 2009 .

[21]  Oleg A. Yakimenko,et al.  New Generation of Rapid Flight Test Prototyping System for small Unmanned Air Vehicles , 2007 .

[22]  K. Narendra,et al.  Bounded error adaptive control , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[23]  T. Georgiou,et al.  Robustness analysis of nonlinear feedback systems: an input-output approach , 1997, IEEE Trans. Autom. Control..

[24]  Bo Egardt.  Stability of Model Reference Adaptive and Self-Tuning Regulators , 1978 .

[25]  Chengyu Cao,et al.  Stability Margins of ${\cal L}_{1}$ Adaptive Control Architecture , 2010, IEEE Transactions on Automatic Control.

[26]  Petros A. Ioannou,et al.  An asymptotic error analysis of identifiers and adaptive observers in the presence of parasitics , 1982 .

[27]  Johann Schumann,et al.  Verification, Validation, and Certification Challenges for Adaptive Flight-Critical Control System Software , 2004 .