Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, Cleveland, OH, 44106, USA.
Department of Mathematics, Applied Mathematics, and Statistics, Department of Biology, Department of Electrical, Control and Systems Engineering, Case Western Reserve University, Cleveland, OH, 44106, USA.
Biol Cybern. 2024 Dec;118(5-6):277-309. doi: 10.1007/s00422-024-00996-x. Epub 2024 Sep 9.
Although the raison d'etre of the brain is the survival of the body, there are relatively few theoretical studies of closed-loop rhythmic motor control systems. In this paper we provide a unified framework, based on variational analysis, for investigating the dual goals of performance and robustness in powerstroke-recovery systems. To demonstrate our variational method, we augment two previously published closed-loop motor control models by equipping each model with a performance measure based on the rate of progress of the system relative to a spatially extended external substrate-such as a long strip of seaweed for a feeding task, or progress relative to the ground for a locomotor task. The sensitivity measure quantifies the ability of the system to maintain performance in response to external perturbations, such as an applied load. Motivated by a search for optimal design principles for feedback control achieving the complementary requirements of efficiency and robustness, we discuss the performance-sensitivity patterns of the systems featuring different sensory feedback architectures. In a paradigmatic half-center oscillator-motor system, we observe that the excitation-inhibition property of feedback mechanisms determines the sensitivity pattern while the activation-inactivation property determines the performance pattern. Moreover, we show that the nonlinearity of the sigmoid activation of feedback signals allows the existence of optimal combinations of performance and sensitivity. In a detailed hindlimb locomotor system, we find that a force-dependent feedback can simultaneously optimize both performance and robustness, while length-dependent feedback variations result in significant performance-versus-sensitivity tradeoffs. Thus, this work provides an analytical framework for studying feedback control of oscillations in nonlinear dynamical systems, leading to several insights that have the potential to inform the design of control or rehabilitation systems.
虽然大脑的存在理由是身体的生存，但很少有关于闭环节奏运动控制系统的理论研究。在本文中，我们基于变分分析，提供了一个统一的框架，用于研究动力冲程恢复系统中性能和鲁棒性的双重目标。为了演示我们的变分方法，我们通过为每个模型配备基于系统相对于空间扩展外部基质（例如用于进食任务的长海藻条或相对于地面的运动任务）的进展速度的性能度量来扩展两个先前发表的闭环电机控制模型。灵敏度度量量化了系统在响应外部干扰（例如施加的负载）时保持性能的能力。受寻找实现效率和鲁棒性互补要求的反馈控制最佳设计原则的启发，我们讨论了具有不同感觉反馈结构的系统的性能-灵敏度模式。在典范的半中心振荡器-电机系统中，我们观察到反馈机制的兴奋-抑制特性决定了灵敏度模式，而激活-失活特性决定了性能模式。此外，我们表明，反馈信号的 sigmoid 激活的非线性允许存在性能和灵敏度的最佳组合。在详细的后肢运动系统中，我们发现力依赖性反馈可以同时优化性能和鲁棒性，而长度依赖性反馈变化会导致性能与灵敏度之间的重大权衡。因此，这项工作为研究非线性动力系统中的反馈控制提供了一个分析框架，得出了一些有潜力为控制或康复系统设计提供信息的见解。
