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

Project Information

SpikyControl

Grant agreement ID: 101054323

DOI

10.3030/101054323

EC signature date 20 October 2022

Start date 1 January 2023

End date 31 December 2027

Funded under

• European Research Council (ERC)

Total cost

€ 2 498 741,00

EU contribution

€ 2 498 741,00

Coordinated by

KATHOLIEKE UNIVERSITEIT LEUVEN
Belgium

Periodic Reporting for period 1 - SpikyControl (Spiking Control Systems: an algorithmic theory for control design of physical event-based systems)

Reporting period: 2023-01-01 to 2025-06-30

Summary of the context and overall objectives of the project

SpikyControl aims at developing a control theory of neuromorphic machines. Neuromorphic machines take inspiration from the regulation mechanisms of neural circuits. Most importantly, they use “spikes” rather than “bits” as units of information, resulting in an event-based interaction between the machine and its physical environment. Event-based sensing and event-based actuation opens a new era for control theory. The question becomes how to close the loop between event trajectories instead of closing the loop between continuous or discrete trajectories.

The angle of attack of the proposed novel control theory is to leverage the existing theory by moving from continuous trajectories to events. Starting from the classical paradigm of the feedback amplifier, regulation theory is regarded as a theory of negative feedback, automation theory is regarded as a theory of positive feedback, and neuromorphic theory is regarded as a theory of mixed feedback. Mixing positive feedback and negative feedback results in excitability, regarded as "transient" decision making: the decision corresponds to the event, but the event nature of the decision makes it transient, enabling the return to equilibrium.

The methodology of SpikyControl is to generalize the convex optimization framework associated to negative feedback of monotone operators to a "convex-concave" optimization framework associated to mixed feedback of monotone operators. The circuit representation of biophysical neural networks is exploited to split a complex neuromorphic system into a circuit of elementary monotone operators corresponding to the memristive elements of the circuit, that is, the machine analog of ion channels and synapses in biophysical circuits. The physical model of the memristive elements is constrained to make the overal theory scalable, with the objective of designing complex machines mimicking the organization of neural circuits to solve novel engineering tasks.

A key illustration of SpikyControl is to develop novel active sensing filters for neuromorphic sensors such as event cameras, mimicking the exquisite detection and selection capabilities of animal vision.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The action is organised in three Work Packages. We report progress for each of them.

WP1: From monotone to mixed-monotone feedback systems

The first objective of the proposal is to demonstrate that the concept of mixed-monotonicity is a fruitful foundation for a control theory of spiking.
The research has made considerable progress in that direction over the past two years. Building upon the classical methodology of splitting algorithms for zero finding of monotone operators, this work demonstrates how any neuromorphic system can be represented as an interconnection of positively and negatively monotone blocks, leading to a solution of the circuit with the splitting methods of large-scale optimization of monone networks.

WP2: An internal model principle for event-based control

The second objective of this proposal is to develop an internal model principle for event-based systems. The main achievement has been to reformulate the classical control paradigm of output regulation as the task of synchronizing the trajectories of the "plant" and the trajectories of the "controller". The internal model principle of control theory states that the control system can regulate the plant output to an external reference and reject an external disturbance only if the controller includes an exact generator of those external signals. The key idea of event regulation is to relax the regulation objective from continuous trajectories to sequences of events. We have shown that event regulation can be made reliable, that is, robust to uncertainty in the description of the external signals, in contrast to trajectory regulation. In addition, we have shown the value of synchronizing the controller and the plant via synaptic rather than diffusive coupling. Synaptic coupling concentrates the feedback regulation around the events, whereas diffusive coupling requires high-gain feedback to compensate for uncertainty in the external signals.

WP3: Robust event-based control

The third objective of this proposal is to demonstrate and quantify the unique robustness properties of spiking control systems.
Theoretical main achievements include the formulation of stability margins for spiking control systems, that is, a concept of distance to bifurcation to a qualitatively different behavior. Practical main achievements include investigating event-based control in neurophysiological experiments of neuromodulation, as well as the development of neuromorphic control architectures for pneumatic actuators in sot robotics.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Neuromorphic Control.

The concept of Neuromorphic control has so far received limited attention in the control community.
The publications [1] and [2] demonstrate the value of neuromorphic control on the paradigmatic example of a mechanical pendulum.
The classical way of controlling a pendulum is to "close the loop" by designing a continuous (or discretized) mapping from the angular position sensor to the applied mechanical motor torque .
In neuromorphic control, the position sensor is replaced by an event detector (e.g. a photodetector that detects when the pendulum crosses a particular angular position)
and the motor torque is a sequence of pulsatile events. The event-based control can be thought to mimick how a child pushes a swing. Neuromorphic control of a pendulum
is shown to offer new possibilites in terms of performance (energy efficiency), robustness to uncertainty, and adaptation capabilities.

Relaxation systems

Exploiting the relaxation property of circuit theory in memristive modelling seems the most important achievement of the project so far. It acknowledges a fundamental
physical property of neuromorphic circuits, namely that they only include one type of storage elements: capacitors, but no inductors. Acknowledging the same
relaxation property in the modelling of memristive elements has unlocked the bottleneck of scaling up neuromorphic control systems from single neurons
to large-scale populations.

[1] Neuromorphic Control of a Pendulum. IEEE Control Systems Letters, 2023.
[2] Regulation without calibration, IEEE Control Systems Magazine, in press, 2025.