Robust distributed framework of interpolation-based control for polytopic uncertain systems

Distributed control is an important framework to handle large-scale systems, however, robust distributed control for polytopic uncertain systems still being a challenge. In this work, we propose a robust distributed framework for interpolation-based control of polytopic uncertain systems. The algorithms proposed consist of both off-line and online computations. The entire system is decomposed into a number of subsystems with smaller number of control inputs. A sequence of nested invariant sets for the entire system, and sequences of state feedback gains corresponding to each subsystem are constructed off-line by minimizing the upper bound of worst-case performance cost in a centralized scheme. The invariant sets constructed are polyhedral sets. At each control iteration, when the state measured lies between any two adjacent invariant sets constructed, a state feedback gain for each subsystem is determined by an interpolation of associated state feedback gains pre-computed. The interpolation problems are based on minimization of a distant from the current state to the adjacent smaller invariant set, solved in a centralized fashion or iteratively solved in a cooperative scheme. Simulation example of quadruple tank system is used to illustrate the algorithms proposed. The cooperative algorithm is capable of inheriting the properties of centralized control scheme but requires lower computational burdens.