Spikes and rhythms organize control and communication in the animal world, in contrast to the bits and clocks of digital technology. As continuous-time signals that can be counted, spikes have a mixed nature. This article reviews ongoing efforts to develop a control theory of spiking systems. The central thesis is that the mixed nature of spiking results from a mixed feedback principle, and a control theory of mixed feedback can be grounded in the operator theoretic concept of maximal monotonicity. As a nonlinear generalization of passivity, maximal monotonicity acknowledges at once the physics of electrical circuits, the algorithmic tractability of convex optimization, and the feedback control theory of incremental passivity. We discuss the relevance of a theory of spiking control systems in the emerging age of event-based technology.

中文翻译：

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 尖峰控制系统


与数字技术的比特和时钟形成鲜明对比的是，动物世界中的尖峰和节奏组织着控制和交流。作为可计数的连续时间信号，尖峰具有混合性质。本文回顾了为开发尖峰系统控制理论所做的持续努力。中心论点是，尖峰的混合性质源于混合反馈原理，混合反馈的控制理论可以基于最大单调性的算子理论概念。作为无源性的非线性推广，最大单调性同时承认电路的物理特性、凸优化的算法易处理性以及增量无源性的反馈控制理论。我们讨论了尖峰控制系统理论在基于事件的技术新兴时代的相关性。