Distributed LQR Methods for Networks of Non-Identical Plants

Two well-established complementary distributed linear quadratic regulator (LQR) methods applied to networks of identical agents are extended to the non-identical dynamics case. The first uses a top-down approach where 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 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. In this paper, local state-feedback controllers are designed by solving model-matching type problems and mapping all the agents in the network to a target system specified a priori. Existence conditions for such schemes are established for various families of systems. The single-input and then the multi-input case relying on the controllability indices of the plants are first considered followed by an LMI approach combined with LMI regions for pole clustering. Then, the two original top-down and bottom-up methods are adapted to our framework and the stability problem for networks of non-identical dynamical agents is solved. The applicability of our approach for distributed network control is illustrated via a simple example.

I. Introduction

Networks of dynamical systems, often referred to as multiagent systems have attracted a lot of attention of the control community in recent years. In such schemes, each agent has the ability to communicate with certain of its counterparts within the network. The interactions established among the agents determine the network topology and define a communication and control pattern, often modelled as a graph, the nodes of which represent agents exchanging information through links (edges) of the graph. The need for forming networks of systems in many cases arises from the fact that some problems might not be resolved by individual systems. Military applications, transport networks and supply chains are such paradigms which indicate that difficult tasks may be accomplished cooperatively [1]–[3]. In other cases, the topology of the network may be imposed by physical links such as in power systems where the agents take the role of power generators and the interconnections are represented by power transmission lines [4], [5].