Data-Driven Robust Control Design: Unfalsified Control

Abstract : Feedback control systems for aerospace applications must maintain precise control despite uncertain operating conditions and unanticipated circumstances such as battle damage. These systems must be designed to perform robustly, despite uncertain design models and difficult to analyze nonlinear effects. They must also be capable of learning and adapting when accumulating data indicates that previous models must be abandoned and that existing control strategies must be changed. We present recent developments that address the need for data-driven design methods well suited to situations in which available mathematical models are poor or unreliable. These innovative data-driven design methods, collectively known as unfalsified control theory, facilitate the creation of robust control systems that learn, discover and evolve in real time in order to rapidly and reliably compensate for the effects of battle damage, equipment failures and other changing circumstances. Potential applications include aircraft stability augmentation systems, highly maneuverable aircraft design, missile guidance systems, and precision pointing and tracking systems.

[1]  Pramod P. Khargonekar,et al.  Sufficient conditions for robust performance of adaptive controllers with general uncertainty structure , 1992, Autom..

[2]  P. M. Makila.  On autoregressive models, the parsimony principle, and their use in control-oriented system identification , 1997 .

[3]  A. Paul,et al.  Model reference adaptive control using multiple controllers and switching , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[4]  Pertti M. Mäkilä.  Robust Control-Oriented Identification , 1997 .

[5]  Michael G. Safonov,et al.  Robust switching missile autopilot , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[6]  R. Kosut.  Adaptive control via parameter set estimation , 1988 .

[7]  Robert L. Kosut.  Uncertainty model unfalsification: a system identification paradigm compatible with robust control design , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[8]  Emmanuel G. Collins,et al.  Automated PI tuning for a weigh belt feeder via unfalsified control , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[9]  Laura Giarré,et al.  Model quality evaluation in set membership identification , 1997, Autom..

[10]  Laura Giarré,et al.  Identification of approximated hammerstein models in a worst-case setting , 2002, IEEE Trans. Autom. Control..

[11]  G. Papavassilopoulos,et al.  Bilinearity and complementarity in robust control , 1999 .

[12]  Maciejowsk.  Multivariable Feedback Design , 1989 .

[13]  Mario Milanese,et al.  H∞ identification and model quality evaluation , 1997, IEEE Trans. Autom. Control..

[14]  A. Morse.  Supervisory control of families of linear set-point controllers , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

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

[16]  Bengt Mårtensson,et al.  The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization , 1985 .

[17]  Roy S. Smith,et al.  An informal review of model validation , 1994 .

[18]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[19]  R. Wang.  Unfalsified Direct Adaptive Control Using Multiple Controllers , 2004 .

[20]  Jan Willem Polderman.  Sequential continuous time adaptive control: a behavioral approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[21]  Michael G. Safonov,et al.  Fitting controllers to data , 2001, Syst. Control. Lett..

[22]  M.G. Safonov,et al.  Unfalsified direct adaptive control of a two-link robot arm , 1999, Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328).

[23]  Michael G. Safonov,et al.  The unfalsified control concept and learning , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[24]  R. Kosut,et al.  Direct unfalsified controller design-solution via convex optimization , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[25]  Richard Y. Chiang,et al.  Robust control toolbox , 1996 .

[26]  B. Barmish,et al.  Adaptive stabilization of linear systems via switching control , 1986, 1986 25th IEEE Conference on Decision and Control.

[27]  Robert Kosut.  Adaptive calibration: An approach to uncertainty modeling and on-line robust control design , 1986, 1986 25th IEEE Conference on Decision and Control.

[28]  Pramod Khargonekar,et al.  A Time-Domain Approach to Model Validation , 1992, 1992 American Control Conference.

[29]  Michael G. Safonov,et al.  Recent advances in robust control, feedback and learning , 2001 .

[30]  S. Bhattacharyya,et al.  Robust control , 1987, IEEE Control Systems Magazine.

[31]  G. Dullerud,et al.  A Course in Robust Control Theory: A Convex Approach , 2005 .

[32]  Edoardo Mosca,et al.  Lyapunov-based switching supervisory control of nonlinear uncertain systems , 2002, IEEE Trans. Autom. Control..

[33]  Multivariable Deterministic Identification: A Control Perspective , 1996 .

[34]  M.G. Safonov,et al.  Stability and convergence in adaptive systems , 2004, Proceedings of the 2004 American Control Conference.

[35]  M. Dahleh,et al.  On learning the input-output behaviour of nonlinear fading memory systems from finite data , 2000 .

[36]  G. Zames.  On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivity , 1966 .

[37]  Michael G. Safonov,et al.  Controller parameter adaptation algorithm using unfalsified control theory and gradient method , 2002 .

[38]  M.G. Safonov,et al.  Fitting controllers to data: the MIMO case , 2004, Proceedings of the 2004 American Control Conference.

[39]  Tom M. Mitchell,et al.  Version Spaces: A Candidate Elimination Approach to Rule Learning , 1977, IJCAI.

[40]  Michael G. Safonov,et al.  Automatic PID tuning: an application of unfalsified control , 1999, Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design (Cat. No.99TH8404).

[41]  Michael G. Safonov.  RECENT ADVANCES IN ROBUST CONTROL THEORY , 2003 .

[42]  Michael G. Safonov.  Unfalsified control: a behavioral approach to learning and adaptation , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[43]  Michael G. Safonov,et al.  LMI multiplierKm/μ-analysis of the Cassini spacecraft , 1998 .

[44]  Mario Milanese,et al.  Optimality, approximation, and complexity in set membership H∞ identification , 2002, IEEE Trans. Autom. Control..

[45]  M. G. Safonov,et al.  Controller identification , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[46]  Edoardo Mosca,et al.  Controller falsification based on multiple models , 2003 .

[47]  Anuradha M. Annaswamy,et al.  Stable Adaptive Systems , 1989 .

[48]  Stephan Bohacek,et al.  Stability Issues in Hop-by-Hop Rate Based Congestion Control , 1999 .

[49]  James M. Krause,et al.  Stability Margins with Real Parameter Uncertainy: Test Data Implications , 1989, 1989 American Control Conference.

[50]  Minyue Fu,et al.  Localization based switching adaptive control for time-varying discrete-time systems , 2000, IEEE Trans. Autom. Control..

[51]  Michael G. Safonov,et al.  A data driven approach to learning dynamical systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[52]  Masami Saeki.  Unfalsified control approach to parameter space design of PID controllers , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[53]  Michael G. Safonov,et al.  The unfalsified control concept: A direct path from experiment to controller , 1995 .

[54]  M. Safonov,et al.  Robustness of interconnected systems with controller saturation and bounded delays , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[55]  Michael G. Safonov,et al.  Unfalsified model reference adaptive control using the ellipsoid algorithm , 2004 .

[56]  R. L. Kosut.  Iterative unfalsified adaptive control: analysis of the disturbance-free case , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[57]  A. Morse.  Supervisory control of families of linear set-point controllers Part I. Exact matching , 1996, IEEE Trans. Autom. Control..

[58]  Edoardo Mosca,et al.  Discrete-time supervisory control of families of two-degrees-of-freedom linear set-point controllers , 1999, IEEE Trans. Autom. Control..

[59]  Laura Giarré,et al.  Identification and Model Quality Evaluation , 1997 .

[60]  A. Morse,et al.  Applications of hysteresis switching in parameter adaptive control , 1992 .

[61]  Minyue Fu,et al.  Further results on localization-based switching adaptive control , 2001, Autom..

[62]  Thomas R. Kurfess,et al.  Force control of a reciprocating surface grinder using unfalsification and learning concept , 2001 .

[63]  M. Safonov,et al.  SAFE ADAPTIVE SWITCHING THROUGH INFINITE CONTROLLER SET: STABILITY AND CONVERGENCE , 2005 .

[64]  Michael G. Safonov,et al.  Adaptive Control using Multiple Controllers & Switching , 2003 .

[65]  I. W. Sandberg,et al.  On the L 2 -boundedness of solutions of nonlinear functional equations , 1964 .

[66]  Thomas G. Dietterich.  What is machine learning? , 2020, Archives of Disease in Childhood.

[67]  Robert L. Kosut.  Adaptive Uncertainty Modeling: On-Line Robust Control Design , 1987, 1987 American Control Conference.

[68]  Mario Sznaier,et al.  Robust Systems Theory and Applications , 1998 .

[69]  Michael G. Safonov,et al.  UNFALSIFIED ADAPTIVE SPACECRAFT ATTITUDE CONTROL , 2003 .

[70]  Petros A. Ioannou,et al.  Design of strictly positive real systems using constant output feedback , 1999, IEEE Trans. Autom. Control..

[71]  Roy S. Smith,et al.  Model Invalidation: A Connection between Robust Control and Identification , 1989 .

[72]  Stephen P. Boyd,et al.  Set-membership identification of systems with parametric and nonparametric uncertainty , 1992 .