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A multi-resolution theory for systems and control across scales

Periodic Reporting for period 4 - switchlet (A multi-resolution theory for systems and control across scales)

Reporting period: 2020-04-01 to 2021-09-30

The central question underlying this project is how control and robustness can coexist and be effective across a range of temporal and spatial scales.
Should the tiny be regarded as noise when it ultimately shapes and modulates the large ? Control across scales is a key challenge to address in an increasingly
interconnected world where engineered systems span a range of temporal and spatial scales to transport information, goods, and energy.

Our proposal is that the organisation of neural circuits in the animal world teaches us novel control principles across scales, that are currently not part of control theory.
In particular, our objective is to demonstrate the key importance of neuronal excitability and neuromodulation in animal circuits. We wish to leverage
such organisation principles in the design of novel artificial devices.

This objective requires novel analysis and design tools. The Switchlet project addresses through the concept of mixed feedback.
While control theory is fundamentally a theory of regulation, centered on the concept of negative feedback, the project aims at developing a theory of feedback systems that balance positive and negative feedback at different scales. This is thought to be the core mechanism of robust selective amplification. The project aims at understanding the prevalence of this mechanism in natural systems, in particular neural circuits, with the goal of inspiring novel developments in artificial systems with multiscale sensing and actuating capabilities.
A key effort of the project has been to bridge the separate worlds of neurophysiology and control theory through the common modelling language of circuit theory.

Mixed feedback has been the central concept of the project: multi-resolution systems that can dynamically and robustly signal across scales are modelled as interconnections of simple mixed-feedback motifs. Each mixed-feedback motif controls one threshold localised in amplitude and in time by the balance between a fast/local positive feedback loop and a slow/global negative feedback loop. Such systems are realised as nonlinear circuits that interconnect positive and negative conductance elements with specific amplitude and temporal activation ranges. Interconnections of such motifs and modulation of the thresholds via the modulation of maximal is the central control principle studied to signal across scales.

Four key results can be singled out at the end of the switchlet project:

1. The project has identified a novel role of cellular bursting in the organisation of neural circuits. By modeling cellular bursting as a motif with two distinct thresholds, we demonstrated that the modulation of the slow threshold is an ubiquitous control mechanism to shape the functional topology of large networks. This mechanism was shown to be robust to uncertainty and far more efficient than the classical view that topology is controlled by synaptic interactions. This result, published in [Drion et al,, Plos Computational Biology, 2018], establishes for the first time the significance of a classical cellular phenomenon for circuit organisation. By highlighting the distinct roles of a fast and a slow negative conductances, our theory also challenges established views in neurodynamics that bursting only requires a fast negative conductance.

2. Dissipativity theory is the state-of-the art methodology to analyse nonlinear feedback systems. A key limitation of that theory is that it is only concerned with dynamical systems that converge to equilibrium when disconnected from their environment. A key outcome of the switchlet project is the novel dominance theory, that leverages the existing theory of dissipativity to analyse feedback systems that switch and oscillate. This new result, published in [Forni and Sepulchre, IEEE Transactions on Automatic Control, 2019], was awarded the Axelby best paper award 2021. It opens the way to analyze novel types of nonlinear feedback systems, that include the mixed feedback circuits of neuroscience.
3. A third major outcome of the action is a novel adaptive online estimator for the maximal conductances of an arbitrary neural circuit model. This result provides a novel bridge between neurophysiology and the classical theory of adaptive control. While adaptive control has been traditionally driven by and applied to robotics and the control of electro-mechanical systems, its application to neuronal circuits is novel and significant. It opens novel estimation algorithms of relevance for experimental neurophysiology. More fundamentally, it suggests that the neuromodulatory principles of neuroscience closely resemble conventional adaptation schemes of control engineering.

4. A fourth major outcome of the action is the first application of neuromodulation principles in a neuromorphic circuit. While previous neuromorphic circuits have successfully replicated specific behaviors observed in neural circuits, the article [Ribar and Sepulchre, IEEE Transactions on Circuits and Systems, 2019] is the first experimental demonstration of a neuromorphic circuit that replicates the robust neuromodulation of a single cell between spiking and bursting.
The switchlet project is the first attempt to bridge cellular neurophysiology and control theory with the aim of inspiring novel neuromorphic control principles in the design of artificial control systems.
A major outcome of the project is to unfold the role of positive feedback (in the language of control theory), or negative conductances (in the language of circuit theory), as a mechanism of
key importance to signal across scales. While the emphasis of classical control theory is on negative feedback, as a fundamental mechanism to reduce sensitivity, the emphasis
of the switchlet project is on balancing positive and negative feedback at distinct temporal and spatial scales. Each balance creates a threshold, and thresholds allow to signal across
distinct scales. A key illustration has been to show that 'slow' thresholds at the cellular scale can shape robustly and dynamically the spatio-temporal field of an entire neuronal population.
This mechanism unfolds a distinct role of cellular bursting in shaping the sensitivity of a (possibly large) neural network.

The principle that the topology of a network can be dynamically modulated via nodal (or intrinsic) rather than edge (or extrinsic) conductances is novel in control theory and a conceptual
breakthrough in the control of networks. Because this mechanism necessitates excitable nodes, it suggests a fundamental advantage of spiking (or event-based) communication rather
than conventional digital or analog architectures. This is of particular interest at a time of accelerated developments in event-based technology such as event-based cameras.

The principle that neuromodulation in biological circuits could closely ressemble the conventional architecture of adaptive control and adaptive internal models is another major outcome
of the action. It paves the way to leverage a pillar of control theory from its classical application to robotics and electro-mechanical systems to the neural circuits of neurophysiology, opening
entirely novel possibilities in the design of neuromorphic circuits and brain-machine interfaces.
The mixed-feedback motif is the core motif of switchlets