Distributed control design for a class of compartmental systems and application to eulerian models of air traffic flows

Decentralized H∞ control for air traffic flow networks modeled by a class of compartmental systems

“…D Remark 1: From (11) in Lemma 1, one can see that the controller gain matrix K is coupled with the Lyapunov matrix P, and thus additional constraints on P may be induced when K is parametrized, which will inevitably make the corresponding result conservative [4]. The advantage of condition (12) is twofold: First, we separate P from K, which can be further parametrized by any X > 0; Second, the existence of X is naturally satisfied, and it can be designated to be with any structure, which will greatly facilitate the design of K subsequently.…”

“…Since the traffic flow management problem is more concerned with the aggregating properties of groups of aircraft rather than the dynamic behavior of individual aircraft, the Eulerian approach may be more efficient in real applications. In addition, the computational complexity for Eulerian approach depends on the spatial division of the air traffic environment, not the number of aircraft in it, and thus Eulerian models have become increasingly popular in the control-oriented modeling of ATF networks [1] [3] [4] [5] [6].…”

“…In this sense, the Eulerian approach for ATF networks can be exactly char acterized in the framework of compartmental networks [3] [4]. In addition to the conservation property, a key physical characterization of such systems is that the transfers between compartments are intrinsically positive.…”

“…Thus, the management policy to be designed should only rely on local information, which can be characterized as a decentralized control problem in AFT networks [4] [5] [11]. In fact, with the advent of complex systems, decentralized control has become increasingly important in real applications, and it has been well known that the decentralized constraint added to the controller generally renders the control design prob lem to be non-convex, or even intractable [12].…”

Modeling Inter-Sector Air Traffic Flow and Sector Demand Prediction

“…The cell transmission model is a typical Eulerian model for land road traffic [8], [9]. This modeling approach is extended and applied to air traffic flow [10]- [13]. One of the authors proposed an extended version of cell transmission model that reflects topology of the airspace [14].…”