Localization of Control Synthesis Problem for Large-Scale Interconnected System Using IQC and Dissipativity Theories
For control engineers working on large-scale systems, this offers a method to decompose global control synthesis into local problems, but the results are theoretical without concrete numerical validation.
This paper addresses the control synthesis problem for large-scale interconnected systems by using IQC and dissipativity theories to localize global performance objectives into local synthesis problems for subsystems. The approach provides a unified framework for decentralized control and performance specification.
The synthesis problem for the compositional performance certification of interconnected systems is considered. A fairly unified description of control synthesis problem is given using integral quadratic constraints (IQC) and dissipativity. Starting with a given large-scale interconnected system and a global performance objective, an optimization problem is formulated to search for admissible dissipativity properties of each subsystems. Local control laws are then synthesized to certify the relevant dissipativity properties. Moreover, the term localization is introduced to describe a finite collection of syntheses problems, for the local subsystems, which are a feasibility certificate for the global synthesis problem. Consequently, the problem of localizing the global problem to a smaller collection of disjointed sets of subsystems, called groups, is considered. This works looks promising as another way of looking at decentralized control and also as a way of doing performance specifications for components in a large-scale system.