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This 2-hour tutorial session will be scheduled to the afternoon of Tuesday September, 12th, from 16h30-18h30,
and will be open to all registrants in CONTROLO'2006.
THE ROBUST MULTIPLE-MODEL ADAPTIVE CONTROL METHOD: A TUTORIAL
by
Michael Athans
Invited Research Professor, Instituto de Sistemas e Robotica, Instituto Superior Tecnico,
Lisbon, Portugal
and
Professor of EE&CS (emeritus), MIT, Cambridge, Mass., USA
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EXTENDED ABSTRACT
Dozens of books and hundreds of papers have been written on the topic of Adaptive Control
starting at about 1965. Often, the research on adaptive control has been akin to the
"search for the gold at the end of the rainbow". In spite of dozens of claims and
counterclaims and myriad of polite and heated discussions (by "fuzzies" and "crispies"
alike) we are a long way from having a practical engineering approach and solution
to the adaptive control problem.
In this tutorial presentation we present some very recent promising developments to the
so-called robust adaptive control problem using a novel architecture called "Robust
Multiple-Model Adaptive Control (RMMAC)", based upon Dr. Sajjad Fekri's recently
completed Ph.D. thesis. We shall discuss its key characteristics and present several
nontrivial simulations that demonstrate its superior performance. We also demonstrate
situations in which it does not work quite well; these lead to suggestions for future
research (enough for at least 20 Ph.D. theses!!!).
The general characteristics of the methodology are:
- RMMAC is a novel engineering design methodology for robust adaptive control, not a theory.
- RMMAC integrates, for the first time, results from stochastic dynamic hypothesis testing (using multiple-model adaptive estimation) and robust compensator design (using the mixed- synthesis method and associated MATLAB software).
- The RMMAC design methodology can deal with unmeasurable stochastic plant disturbances, unmeasurable measurement noise, unmodeled dynamics and one or more uncertain real parameters (constant or slowly-time varying).
- The RMMAC methodology is valid for both the single-input single-output (SISO) and the multi-input multi-output (MIMO) case.
- The complexity of the RMMAC architecture, quantified by the number of parallel models, is the explicit byproduct of designer-posed performance specifications for the adaptive system.
- The precise specification of each of the multiple models in the RMMAC architecture is the outcome of explicit performance optimization for the posed performance specifications. The potential performance of the RMMAC design can be evaluated a priori (via stability-mismatch tables, Bode sensitivity plots, RMS calculations, …) after asymptotic system identification has taken place.
- There is a clear-cut understanding of the adaptive performance improvements compared to the best nonadaptive feedback design.
- A precise methodology for designing each "local" compensator in the RMMAC architecture is presented using the mixed- design method.
- A precise methodology for designing each "local" Kalman filter is presented using the so-called Baram proximity measure (BPM). This includes "tuning" each Kalman filter using "fake white plant noise" to compensate for the unmodeled dynamics and local parameter errors.
The numerical simulations that will be presented involve:
- Studies include plants with one or two uncertain real parameters, one or two noisy measurements, one or two control variables and one or two performance outputs. Several systems have been evaluated using thousand of Monte Carlo simulations.
- We have found that the RMMAC feedback system works very well when the theoretical assumptions are not violated.
- The RMMAC feedback system works quite well when some of the theoretical assumptions are mildly violated.
- The RMMAC feedback system may perform poorly, or even become unstable, when the theoretical assumptions are severely violated. In these cases, we have isolated the reasons that cause poor performance and we suggest ways of modifying the RMMAC design to avoid such behavior, including the development of the variant RMMAC/XI architecture and of "fail-safe" mechanisms.
Since the RMMAC system is highly nonlinear, stochastic and time-varying it is impossible to provide
theoretical guarantees for global asymptotic stability, since such stability-theoretic results are
not yet available. The RMMAC concepts suggest several fruitful areas for future theoretical and
applied research
RELEVANT REFERENCES
- S. Fekriasl, Robust Adaptive MIMO Control Using Multiple-Model Hypothesis Testing and Mixed- Synthesis, Ph.D. Dissertation, Instituto Superior Tecnico, December 2005
- S. Fekri, M. Athans and A. Pascoal, "Issues, Progress and New Results in Robust Adaptive Control," Intern. Journal on Adaptive Control and Signal Processing, 2006 (in press)
- M. Athans, S. Fekri and A. Pascoal, "Issues on Robust Adaptive Feedback Control," Invited Plenary paper, Preprints 16th IFAC World Congress, pp. 9-39, July 2005
- S. Fekri, M. Athans and A. Pascoal, "A Two-Input Two-Output Robust Multiple Model Adaptive Control (RMMAC) Case Study," Proc. 2006 American Control Conference, Minneapolis, Minn., USA, June 2006
- S. Fekri, M. Athans and A. Pascoal, "RMMAC: A Novel Robust Adaptive Control Scheme - Part I: Architecture," Proc. IEEE Conf. On Decision and Control, Paradise Island, Bahamas, Dec. 2004, pp. 1134-1139
- S. Fekri, M. Athans and A. Pascoal, "RMMAC: A Novel Robust Adaptive Control Scheme - Part II: Performance Evaluation," Proc. IEEE Conf. On Decision and Control, Paradise Island, Bahamas, Dec. 2004, pp. 1140-1145
- S. Fekri, M. Athans and A. Pascoal, "A New Robust Adaptive Control Method Using Multiple-Models," Proc. 12th IEEE Mediterranean Conference on Control and Automation (MED´04), Kusadasi, Turkey, June 2004
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