Singhal Bharat, Li Jr-Shin
Department of Electrical & Systems Engineering, Washington University in St. Louis, St. Louis, MO, 63130, USA.
Syst Control Lett. 2025 Jul;201. doi: 10.1016/j.sysconle.2025.106084. Epub 2025 Apr 8.
The effective control of synchronization patterns in an oscillator ensemble is essential for optimal functioning of natural and engineered systems, with applications across diverse domains, including power systems, robotics, and medical device development. In this work, we address the problem of designing a feedback law to establish a desired synchronization structure in a pair of oscillators with model uncertainties. These oscillators are modeled using phase models with uncertainties in their phase response curves and oscillation frequencies. Our principle idea is to design a switching input by utilizing the periodicity of system dynamics. The input parameters for this switching strategy are determined by solving a simple convex quadratic program with inequality constraints. In addition, we derive analytic expressions of feedback inputs for anti-phase and in-phase synchronization of a pair of sinusoidal and SNIPER phase oscillators. The effectiveness of the proposed approach is demonstrated on both phase models and complex biophysical models of spiking neurons.
振荡器集合中同步模式的有效控制对于自然系统和工程系统的最佳运行至关重要，其应用涵盖多个领域，包括电力系统、机器人技术和医疗设备开发。在这项工作中，我们解决了在存在模型不确定性的一对振荡器中设计反馈律以建立所需同步结构的问题。这些振荡器使用相位模型进行建模，其相位响应曲线和振荡频率存在不确定性。我们的主要思想是利用系统动力学的周期性来设计一个切换输入。这种切换策略的输入参数通过求解一个具有不等式约束的简单凸二次规划来确定。此外，我们推导了一对正弦和SNIPER相位振荡器反相和同相同步的反馈输入的解析表达式。所提出方法的有效性在尖峰神经元的相位模型和复杂生物物理模型上均得到了验证。
