Distributed Dissipative Control

Varied autonomous areal and underwater vehicles with communication links illustrated as dashed lines between them, including clocks to represent communication delays.

This work aims to develop novel control schemes that will allow large groups of heterogeneous, autonomous agents to collaborate. This exploits on a shift in perspective on robust control from traditional ℋ∞ analysis, which lumps diverse sources of uncertainty and requires closed-loop analysis, to using Networked Dissipativity Theorems that use open-loop analysis to assess closed-loop stability. This perspective shift naturally facilitates designs with heterogenous agents that scale well as networks grow. This inherently breaks up the large-scale stability analysis problem into smaller, more tractable subproblems. Moreover, it means each subsystem can be analyzed individually, so you can tailor your modelling, data-collection, and objectives to each one individually. Key contributions have developed synthesis and analysis methods that assure stability of networks of interconnected heterogeneous systems.

Hinf vs VNDT
Dashed lines enclose systems whose IO properties are analysed to establish stability. In ℋ∞ control (left), all uncertainty is grouped into a 'delta' block and the plant-controller interconnection's closed-loop gain is minimized to compensate for it. Networked dissipativity (right) provides compatibility conditions between interconnected subsystems to ensure network-side stability. By grouping uncertainty with subsystems, only open-loop properties of the subsystems and controller must be considered, simplifying analysis and reducing conservatism.
Constraints for multiobjective control of networks. The figures in the top block represent the objectives of each subsystem, the next two blocks represent the dissipativity of each plant and controller, and the final block represents Vidyasagar’s Network Dissipativity Theorem.
Each block represents a component of the network dissipativity-based multi-objective controller synthesis problem. The top block corresponds to the performance objectives of each subsystem. The second and third blocks represent the dissipativity properties of each subsystem and its controller, respectively. Finally, the bottom block denotes the VNDT framework.

Distributed control of swarm drones.