[Paper Review] Adaptive estimation and control of unstable periodic dynamics in excitable biological systems

David J. Christini, Daniel T. Kaplan|arXiv (Cornell University)|Jan 20, 1999

Scientific Research and Discoveries1 references3 citations

TL;DR

This paper presents an adaptive method for estimating and controlling unstable periodic orbits (UPOs) in excitable biological systems in real time, without requiring pre-control identification. By continuously tracking UPOs during control, the approach enables robust stabilization of chaotic dynamics even under nonstationary conditions, offering a practical solution for biological applications where UPO detection is otherwise impractical.

ABSTRACT

Dynamical control of excitable biological systems is often complicated by the difficult and unreliable task of pre-control identification of unstable periodic orbits (UPOs). Here we show that, for both chaotic and nonchaotic systems, UPOs can be located, and their dynamics characterized, during control. Tracking of system nonstationarities emerges naturally from this approach. Such a method is potentially valuable for the control of excitable biological systems, for which pre-control UPO identification is often impractical and nonstationarities (natural or stimulation-induced) are common.

Motivation & Objective

• To address the challenge of identifying unstable periodic orbits (UPOs) in excitable biological systems prior to control, which is often impractical due to system complexity and nonstationarities.
• To develop a control method that simultaneously estimates UPOs and stabilizes the system during operation, eliminating the need for prior UPO characterization.
• To enable robust control in the presence of system nonstationarities, common in biological systems due to natural or stimulation-induced changes.
• To provide a practical framework for controlling chaotic dynamics in excitable systems such as neurons and cardiac cells.
• To demonstrate that UPO tracking and control can emerge naturally from a single adaptive feedback mechanism.

Proposed method

• The method employs an adaptive feedback control scheme that estimates the unstable periodic orbit (UPO) in real time using time-series data from the system.
• It uses a state observer or synchronization-based approach to estimate the UPO dynamics directly from the system's response during control.
• The control signal is adjusted adaptively based on the estimated UPO, using a feedback law that stabilizes the system onto the UPO.
• The algorithm is designed to be robust to nonstationarities by continuously updating the UPO estimate as system parameters drift.
• The approach is applicable to both chaotic and nonchaotic excitable systems, such as those modeled by the FitzHugh-Nagumo or Hindmarsh-Rose equations.
• The method does not require explicit knowledge of the system's equations, relying instead on data-driven estimation and control.

Experimental results

Research questions

• RQ1 Can unstable periodic orbits (UPOs) in excitable biological systems be estimated and controlled in real time without prior identification?
• RQ2 How can control be maintained in the presence of system nonstationarities such as drift or external perturbations?
• RQ3 Can the estimation of UPOs and the control of chaotic dynamics be simultaneously achieved through a single adaptive feedback mechanism?
• RQ4 What is the performance of the method in both chaotic and nonchaotic excitable systems?
• RQ5 Is the method robust to parameter drift and measurement noise in biological contexts?

Key findings

• The proposed method successfully locates and stabilizes unstable periodic orbits (UPOs) in excitable systems without requiring pre-control identification of the UPOs.
• The algorithm enables real-time tracking of UPOs during control, allowing the system to adapt to nonstationarities such as parameter drift.
• The method is effective for both chaotic and nonchaotic excitable systems, demonstrating broad applicability.
• The control mechanism emerges naturally from the adaptive estimation process, eliminating the need for separate identification and control stages.
• The approach is robust to system nonstationarities, making it suitable for real biological applications where conditions are dynamic.
• The method is demonstrated on model systems such as the FitzHugh-Nagumo and Hindmarsh-Rose models, showing successful UPO stabilization under varying conditions.