Monday, November 5, 2007 - 12:30 PM
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A New Approach For Adaptive Control And Identification Using Selective Memory Supervision

Eduardo J. Dozal-Mejorada and B. Erik Ydstie. Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

It is well known that adaptive controllers can modify their behavior to respond to changes in their operating environments [1]. Behavioral adjustment is typically achieved by adjusting feedback and/or feed forward control parameters using linear parameter identification techniques such as recursive least squares, finite window estimation based on SQP and interior point methods. It is worth noting that because of the parameter updating mechanism these controllers are nonlinear by nature possessing very special structure.

In spite of the underlying decomposable structure, adaptive control technologies have not yet been broadly applied in industry. One important reason is that stability and robustness were not properly addressed in the original adaptive theory [2]. Many approaches were suggested to make the controllers more stable. References [3-8] present some of the suggested techniques such as the deadzone approach, parameter leakage, persistent excitation and projection. However, most of these approaches require significant a priori information of either the process or the algorithm parameters. Adaptive control therefore has seen its greatest success in specialized applications where such specific information is readily available.

The main objective of the current paper is to introduce a new approach for adaptive control which solves the robustness problem by carefully selecting the data used for identification. The method is loosely based on Bayesian identification theory, where prior and posterior models are used to generate the prediction errors. The full description of the approach is given in reference [9]. The algorithm is implemented using a dual-model supervision strategy. One model is actually used to design the control law, whereas the other model acts as a supervisor who decides whether to adapt the controller or not. This setup effectively allows the controller parameters to be updated only when the incoming data are sufficiently excited so that an improvement in the prediction error is achieved.

In the current paper we present stability and robustness results for the supervised (selective memory) adaptive control algorithm. Two classes of results are presented. One class of results is based on the idea of moving window (horizon) estimation (MHE). These results extend the stability results presented in [10,11]. The second class of results is based on incrementing the estimation window so that the estimated parameters eventually converge. The latter result extends the celebrated 1993 stability result for the self tuning regulator by Chen and Guo to robustness [12]. Moreover, we show that the parameter estimates converge. Here the main focus is placed on robust performance. We show that the adaptive controller converges to optimal mean-square performance. Monte Carlo computational studies are presented to illustrate the supervision concept and the main theoretical results. Finally, experiments on a pilot-plant scale shell-and-tube heat exchanger are shown to highlight the capabilities of the adaptive control algorithm.

REFERENCES:

[1] Astrom, K.J. and B. Wittenmark (1995). Adaptive control. Addison-Wesley Publishing Company, Inc. Reading, M.

[2] Rohrs, C.E., L. Valavani, M. Athans and G. Stein (1985). Robustness of continuous-time adaptive control algorithm in the presence of un-modeled dynamics. IEEE Transactions on Automatic Control 30(9), 881-889.

[3] Egardt, B. (1979). Stability of adaptive controllers. Springer-Verlag. New York, NY.

[4] Peterson, B.B. and K.S. Narendra (1982). Bounded error adaptive control. IEEE Transactions on Automatic Control 27(6), 1161-1168.

[5] Middleton, R.H., G.C. Goodwin, D.J. Hill and D.Q. Mayne (1988). Design issues in adaptive control. IEEE Transactions on Automatic Control 33(1), 50-58.

[6] Ioannou, P.A. and P.V. Kokotovic (1983). Adaptive systems with reduced models. Springer. Berlin, Germany.

[7] Mareels, I. and J.W. Polderman (1996). Adaptive systems, an introduction. Birkhauser. Boston, MA.

[8] Hill, J.H. and B.E. Ydstie (2004). Adaptive control with selective memorey. Int. J. Adapt. Control Signal Process. 18, 571-587.

[9] Dozal-Mejorada, E.J. and B.E. Ydstie (2007) Stability and robustness of supervised adaptive control. Proceedings of the 8th International Symposium on Dynamics and Control of Process Systems.

[10] Dozal-Mejorada, E.J., P. Thakker and B.E. Ydstie (2007) Supervised adaptive predictive control using dual models. Proceedings of the 8th International Symposium on Dynamics and Control of Process Systems.

[11] Dozal-Mejorada, E.J. and B.E. Ydstie, Stability of supervised adaptive control. Submitted to CDC 2007.

[12] Guo, L. and H. Chen, The Astrom-Wittenmark self-tuning regulator revisited and ELS-based adaptive trackers. IEEE Transactions on Automatic Control 36(7), 802-812.