1. L. Moreau and E.D. Sontag. Balancing at the border of instability. Phys. Rev. E (3), 68(2):020901, 4, 2003. [PDF] Keyword(s): bifurcations, adaptive control. Abstract:

   Some biological systems operate at the critical point between stability and instability and this requires a fine-tuning of parameters. We bring together two examples from the literature that illustrate this: neural integration in the nervous system and hair cell oscillations in the auditory system. In both examples the question arises as to how the required fine-tuning may be achieved and maintained in a robust and reliable way. We study this question using tools from nonlinear and adaptive control theory. We illustrate our approach on a simple model which captures some of the essential features of neural integration. As a result, we propose a large class of feedback adaptation rules that may be responsible for the experimentally observed robustness of neural integration. We mention extensions of our approach to the case of hair cell oscillations in the ear.




2. L. Moreau, E.D. Sontag, and M. Arcak. Feedback tuning of bifurcations. Systems Control Lett., 50(3):229-239, 2003. [PDF] Keyword(s): bifurcations, adaptive control. Abstract:

   This paper studies a feedback regulation problem that arises in at least two different biological applications. The feedback regulation problem under consideration may be interpreted as an adaptive control problem for tuning bifurcation parameters, and it has not been studied in the control literature. The goal of the paper is to formulate this problem and to present some preliminary results.

1. L. Moreau, E.D. Sontag, and M. Arcak. How feedback can tune a bifurcation parameter towards its unknown critical bifurcation value. In Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003, pages 2401-2406, 2003.

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