Phase-Selective Oscillator Entrainment Without State Feedback
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Solution Overview
Problem
Controlling and manipulating the phase patterns of heterogeneous nonlinear oscillator ensembles without state feedback information is challenging, especially in biological systems where precise control of neural or electrochemical processes is needed, due to uncertainties in model parameters and initial conditions.
Innovation Solution
A method using 2π-periodic control signals to detune natural frequencies and shift phases of oscillators, employing an interaction function and phase response curve to achieve specific phase patterns in oscillator ensembles, allowing for robust entrainment without requiring feedback or precise initial condition knowledge.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If feedback control techniques are used to control oscillator ensembles, then control precision can be improved, but system complexity and requirement for state information increase
Solution Approach 1:
The patent extracts and removes the feedback control component from the system, transitioning from closed-loop to open-loop control. By eliminating the need for state feedback information and complex control algorithms, the system achieves simpler implementation while maintaining effective phase pattern control through carefully designed periodic forcing signals.
Solution Approach 2:
The oscillator ensemble inherently responds to periodic forcing signals through its natural dynamics and phase response properties. The system exploits the intrinsic characteristics of the oscillators, including their phase response curves and natural frequencies, to achieve self-organization into desired phase patterns without requiring external feedback or complex control mechanisms.
2Measurement precision
If state feedback information is required for control, then control accuracy improves, but practical implementation becomes difficult in biological systems
Solution Approach 1:
The patent removes the requirement for state feedback information from the control system. By designing open-loop periodic forcing signals based on predetermined phase response curves and natural frequencies, the system achieves effective control without needing to measure or access the real-time state of individual oscillators, making it practically implementable in biological systems where such information is unavailable.
Solution Approach 2:
The control strategy relies on pre-characterizing the phase response curves and natural frequencies of the oscillators before control is applied. By preparing the periodic forcing signals in advance based on these predetermined properties, the system achieves accurate phase pattern control without requiring real-time state information or feedback during operation.
3Ease of operation
If homogeneous activation of oscillators is applied, then control simplicity is maintained, but fine manipulation of individual subsystems is lost
Solution Approach 1:
The patent applies different phase offsets to different groups or subsets of oscillators within the ensemble through the design of periodic forcing signals. By modulating the amplitude and phase of the forcing signal at different times, the system can selectively entrain specific subsets of oscillators to different phase patterns, achieving fine-grained control over individual subsystems while maintaining overall system simplicity.
4Measurement precision
If precise model specification and initial conditions are required, then control precision improves, but robustness to parameter uncertainty decreases
Solution Approach 1:
The patent designs periodic forcing signals that are robust to variations in oscillator parameters by exploiting the inherent properties of phase response curves and natural frequencies. The control approach uses frequency detuning and phase offset adjustments that maintain effectiveness across a range of parameter values, achieving both precision and robustness without requiring exact model specification or precise initial conditions.
Data Source
AI summary
A system for entraining an oscillator ensemble is disclosed that includes a plurality of oscillators in an entrained phase pattern. The system includes an entrainment device operatively coupled to each non-linear oscillator of the oscillator ensemble, and the entrainment control device is configured to deliver a 2π-periodic control signal v(θ) to all oscillators of the plurality of oscillators to induce the entrained phase pattern.