Lately, the importance of understanding complex systems has received much attention [2,3]. Networks of decentralized adaptive systems are common. For example, economic systems, biological systems, chemical plants, communication networks, power and energy grids, supply chains and transportation systems are all examples of systems which can be viewed as complex adaptive systems. In these systems, most of the decision making is distributed throughout the network to low levels. However, at present, very limited theory exists which can be used to study and elucidate the behavior of these systems once complexity sets in. One of the main reasons for this lack of understanding is that complexity can be due to many factors including nonlinearity, high (infinite) dimensionality and uncertainty.
In this paper we model complex adaptive systems using network theory as introduced in . This modeling framework provides the necessary starting condition for analyzing the dynamics, distributed control, and optimization of complex process networks [4,5]. An important result found in  states that stability and optimality for the networks follow as a consequence of the network topology. We use this topological result to design the architecture of the network so that each node is equipped with an adaptive controller which interacts with the rest of the network using localized sensor-actuator pairs. The local adaptive controller has a two-fold task. First it has to be able to learn how to control the corresponding local system. Second it needs to learn how the local system is connected to other systems so that it can recognize when disturbances change and upset the local behavior.
Here we develop a novel approach for the adaptive network problem by coupling the topological results from the process networks with adaptive optimal control and identification in order to successfully meet the dual objective adaptive control problem. The method selects data so that uninformative data are excluded from the adaptive control estimation problem . This approach has been shown to yield stable and converging controls in the case of single input single output control with disturbances [7,8].
The current paper presents a general approach for decentralized adaptive control of complex networks. Here we show how a large network of the adaptive controllers can give stable and close to optimal performance. The approach we develop is an indirect version of the Q-learning approach which has found applications in chemical engineering and computer science. Here, a model of the system is first developed and then an optimal controller is designed. Computational studies of a large industrial chemical plant and a highly distributed supply chain system are presented showcasing the stabilization properties of the proposed method.
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