Mixed feedback systems

Event-based technology is developing at a fast pace (e.g. via neuromorphic computing and event-based cameras) but we currently lack a control theory of event-based systems. The general aim is to conceive physical machines that combine the reliability of discrete automata and the robustness and adaptation of physical control systems.

The theory of mixed feedback systems aims at leveraging the existing theory of control, optimization, and learning while acknowledging the inherent out-of-equilibrium nature of event-based machines.

The theory is grounded in the operator-theoretic framework of maximal monotonicity in Reproducing Kernel Hilbert Spaces. The course will introduce those mathematical tools at a basic level and present how they can be used to analyze and design neuromorphic event-based machines.

The course consists of six sessions over three days. Each session will cover one of the following modules

Module1: Feedback and memory (RS)

1.1. Examples of mixed feedback systems. Motivation. Current limitations of control theory, machine learning, and neuromorphic engineering.

1.2. Static mixed feedback

1.3. Dynamic mixed feedback. Questions and challenges

Module 2: Feedback system analysis (TC)

2.1. Systems as operators. Phase and Gain. Monotonicity and Lipschitz operators. The passivity and the small-gain theorems.

2.2. Graphical representations. Nyquist plots. Scaled Relative Graphs.

2.3. Mixed feedback systems. Mixed gain and mixed phase feedback systems.

Module 3: Feedback algorithms (TC)

3.1. Fixed point algorithms and zero finding algorithms.

3.2. Splitting algorithms and circuit representations

3.3. Algorithmic solutions of mixed feedback systems

Module 4: Modelling at scale (RS)

4.1. Reproducing Kernel Hilbert Spaces

4.2. Gradient systems in Reproducing Kernel Hilbert Spaces

4.3. Feedback neural networks at scale

Module 5: Tuning at scale (RS)

5.1. Recursive least square estimation

5.2. A robust internal model principle for mixed feedback systems

5.3 Adaptive control and online learning at scale

Module 6: Neuromorphic control (RS)

6.1. Physical Spiking Neural Networks

6.2. Control as neuromodulation at scale

6.3. Neuromorphic event-based machines

Course material

• Slides, exercises, and references will be available

Evaluation

• An assignment that will be released during the course

The SOCN Graduate School gathers Belgian teams (UAntwerp, UNamur, KUL, UCLouvain, UGent, ULB, ULg, UMONS, VUB) active in the area of Systems, Optimization, Control and Networks, or have strong interest in topics related to it. The main objective of the Graduate School is to provide a high quality scientific environment and a well-balanced graduate-level program for the Belgian doctoral students in Systems, Optimization, Control and Networks.

A common research theme pursued by the participating teams consists in the modelling of certain systems and phenomena with the purpose of controlling or optimizing their behavior and performance.

These models are based on dynamical systems, differential (or difference) equations and mathematical programming formulations. Research of the participating teams focusses on the identification, analysis, control and optimization of these models, including the corresponding theory, algorithmic aspects and numerical resolution techniques.

This area of growing interest finds numerous applications in various fields such as automatic control, biotechnology and biomedical engineering, mechanical and electrical engineering, production and supply chain management and planning, process engineering, robotics, routing, traffic or service networks and signal processing.