Sub-optimal distributed control law with H2 performance for identical dynamically coupled linear systems

Distributed LQR Methods for Networks of Non-Identical Plants

“…Thus, distributed cooperative controllers are to be designed to solve the network stability problem. Two complementary distributed LQR methods are proposed in [8] and [9]. In the first (top-down) approach [8], the centralized optimal LQR controller is approximated by a distributed control scheme whose stability is guaranteed by the stability margins of LQR control.…”

“…In the first (top-down) approach [8], the centralized optimal LQR controller is approximated by a distributed control scheme whose stability is guaranteed by the stability margins of LQR control. The second [9] consists of a bottom-up approach in which optimal interactions between self-stabilizing agents are defined so as to minimize an upper bound of the global LQR criterion. A limitation of both methods is the assumption that networks are formed by identical plants, a fact which is often unrealistic in real applications.…”

“…A limitation of both methods is the assumption that networks are formed by identical plants, a fact which is often unrealistic in real applications. The approach proposed in this work relaxes this assumption and therefore generalizes the approaches in [8] and [9] with only minor modifications. Rather than assuming identical models for all agents, we consider a general class of possible models which share the same structure in terms of input and state dimensions and other structural properties (e.g.…”

“…In this paper, static state-feedback controllers are proposed to solve model-matching type problems with the aim at relaxing the assumption of the repetitive pattern of the network considered in [8] and [9] in terms of the plants' model. In this respect, the systems constituting the network are assumed to be linear and non-identical with their state vector being accessible for measurement.…”

“…A Linear Matrix Inequality approach is also proposed to solve the model-matching type problem for a certain family of systems. Next, the statefeedback distributed control scheme presented in [8] and [9] are modified and then the stability problem for a network of non-identical plants that are all mapped locally to the same target system is solved. The effectiveness of the method is finally illustrated via a simple example.…”