Signal design using nonlinear oscillators and evolutionary algorithms: application to phase-locked loop disruption.

Area of Science:

• Control Systems Engineering
• Signal Processing
• Computational Intelligence

Background:

• Designing effective input signals for dynamical systems is crucial for controlling their behavior.
• Traditional methods often struggle to analytically derive optimal inputs, especially for complex systems like phase-locked loops (PLLs).
• Evolutionary algorithms offer a powerful approach for exploring complex design spaces.

Purpose of the Study:

• To develop an efficient method for designing input signals to shape the response of fixed dynamical systems.
• To investigate the capability of waveforms generated by nonlinear ordinary differential equations (ODEs) in disrupting a phase-locked loop (PLL).
• To explore the implications of different ODE-generated input models for system control.

Main Methods:

• Utilizing an evolutionary algorithm to search for optimal input waveforms.
• Generating candidate waveforms from a space defined by nonlinear ordinary differential equations (ODEs).
• Evaluating input signal efficiency based on desired system response and constraints like signal power.
• Testing disruption capabilities against a model phase-locked loop (PLL).

Main Results:

• Identified specific nonlinear ODEs that generate input signals with varying degrees of effectiveness in disrupting a PLL.
• Demonstrated that evolutionary search can yield efficient input signals that meet specific response criteria.
• Quantified the differences in disruption capabilities among the investigated ODE sets.

Conclusions:

• The proposed approach using evolutionary algorithms and ODE-generated waveforms is effective for designing control inputs.
• Different nonlinear ODEs provide distinct advantages for generating disruptive signals for systems like PLLs.
• This methodology has broad applicability beyond PLLs to any input/output system where analytical input design is challenging.