Robust Distributed Control Beyond Quadratic Invariance
For control engineers designing large-scale systems like power grids or transportation networks, this work offers a more general and tractable approach to distributed control with non-classical information structures.
The paper addresses robust distributed control under arbitrary information constraints, proposing a tractable decomposition method that yields globally optimal controllers when Quadratic Invariance holds and provides provable upper bounds otherwise. Applied to autonomous vehicle platooning, it shows improved performance guarantees over prior methods.
The problem of robust distributed control arises in several large-scale systems, such as transportation networks and power grid systems. In many practical scenarios controllers might not have enough information to make globally optimal decisions in a tractable way. We propose a novel class of tractable optimization problems whose solution is a controller complying with any specified information structure. The approach we suggest is based on decomposing intractable information constraints into two subspace constraints in the disturbance feedback domain. We discuss how to perform the decomposition in an optimized way. The resulting control policy is globally optimal when a condition known as Quadratic Invariance (QI) holds, whereas it is feasible and it provides a provable upper bound on the minimum cost when QI does not hold. Finally, we show that our method can lead to improved performance guarantees with respect to previous approaches, by applying the developed techniques to the platooning of autonomous vehicles.