Spiking Control Systems: an algorithmic theory for control design of physical event-based systems

Machines compute with bits and clocks, animals compute with spikes and rhythms. The promise of neuromorphic engineering is that we could transform digital technology by imitating the spiking nature of animal computation, combining analog adaptation and digital reliability. Thirty years after Carver Mead’s initial proposal, event cameras have become a technology and neuromorphic computing has become an intense focus both in academia and in industry. Yet, we still lack a proper theory of event-based computation and event-based design. And the very nature of computing with rhythms instead of clocks is still poorly understood.We propose that the spike is a consequence of analog computing with mixed (that is, positive and negative) feedback. We will develop a control theory of spiking systems by leveraging the control theory of negative feedback systems to a theory of mixed-feedback systems. The mathematical concept of monotonicity provides a modern and unifying foundation for control theory, convex optimisation, and circuit design. Our spiking control theory is grounded in mixed-monotonicity. It is algorithmic because it leverages the methodology of convex optimisation, and it is physical because it leverages the methodology of circuit theory. A central objective of the proposed research is a novel event-based internal model principle of significance both for control theory and neuroscience. We will investigate the unique features of event-based online adaptation, and suggest the complementary roles of inhibition and excitation in novel spiking control architectures whose learning and adaptation capabilities can be dynamically modulated.Ultimately, this proposal aims at novel design principles for physical devices that could surpass the learning and adaptation capabilities of current digital machines, advancing the promise of neuromorphic engineering.