Multi-agent systems

From local decisions to global behaviour

More often than not, modern engineering systems cannot be treated as single machines. They are networks of interacting components. 

A power grid consists of generators, loads and power converters. A transportation network contains thousands of interacting vehicles. Large industrial plants contain many processes exchanging material, energy and information.

In principle, one could collect all available information in one place and design a single enormous controller. In practice, this quickly becomes undesirable or even impossible, for either computational or privacy limitations.

Instead, we would like each component to make decisions using local information, while still ensuring that the complete network behaves as desired. This leads to one of the recurring themes of my research: How can local control provide global guarantees?

Energy-based view

One particularly meaningful way of thinking about this problem is through energy. Suppose each subsystem i stores some abstract quantity Vᵢ — which could represent physical energy, but does not have to. Its evolution can be described through an inequality of the form

Vᵢ(xᵢ⁺) − Vᵢ(xᵢ) ≤ sᵢ,

meaning that the subsystem cannot create arbitrary amounts of energy by itself.

At the heart of dissipativity theory lies its compositional nature: if we understand the energy behaviour of the individual components and understand how they exchange energy among each other, we can draw conclusions about the entire network without constructing one gigantic model.

Dissipativity for discrete-time systems

Passivity is a powerful tool for continuous-time systems, but discrete-time systems

𝑥+ = 𝑓(𝑥, 𝑢) ,   𝑦 = ℎ(𝑥),

cannot even be passive! To cope with this issue, classical solutions include the use of virtual outputs [1], or relying on continuous-time passivity and then apply passivity-preserving discretization techniques.

We argue that quadratic supply rates incorporate and extend the effect of virtual outputs, allowing one to naturally use dissipativity directly in discrete time. For the first time, we derive decentralized (Q,S,R)-dissipativity conditions [2] for a set of nonlinear systems interconnected with arbitrary topology, so that the overall network is guaranteed to be stable. For linear systems, we develop practical dissipative control conditions that are linear in the supply rate matrices.

Dissipativity from data

What if the models of the individual subsystems are themselves unknown? By combining experimental data with dissipativity, we develop a data-driven decentralized control [3] procedure in which local controllers and global stability conditions can be obtained directly from data.

Distributed optimization

Many real-world problems involve a group of agents that need to cooperate to find a common optimal solution, relying only on local computations and communication with their neighbours.

Inspired by the recent systems theory of algorithms, we model the distributed optimization problem as a set of interconnected dynamical systems. This allows us to apply tools from dissipativity and contraction theory to systematically analyze their convergence [4], illustrating how concepts from control theory can also be used to understand and design distributed algorithms.

Plug-and-play MPC

Another challenge appears when the network itself changes over time. A generator may connect to a smart grid, a machine may be added to a production line, or an agent may leave a network. Ideally, the entire controller should not have to be redesigned every time this happens. We develop plug-and-play distributed model predictive controllers [5] that allow subsystems to join or leave a network while preserving stability and feasibility.

Disturbance propagation

A different part of my work looks at disturbances in networks. Instead of allowing a local disturbance to propagate through an entire network, we introduced the idea of identifying a cluster of nodes with enough degrees of freedom to absorb it locally. This provides a control-oriented notion of clustering: nodes are grouped not simply because they are strongly connected, but because together they have enough control authority to contain a disturbance.