Comprehending Complexity: Data-Rate Constraints in Large-Scale Networks

Abstract

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Control of Two Satellites Relative Motion over the Packet Erasure Communication Channel with Limited Transmission Rate Based on Adaptive Coder

“…Extensions of this result for stabilizing nonlinear systems in the vicinity of the origin and observing nonlinear systems through finite capacity communication channels, including large networks, were obtained in the series of the subsequent papers, see [58][59][60][61][62] to mention a few.…”

Adaptive Coding in Control of Two Satellites Relative Motion Over the Packet Erasure Communication Channel

“…Extensions of this result for stabilizing nonlinear systems in the vicinity of the origin and observing nonlinear systems through finite capacity communication channels, including large networks, were obtained in the series of the subsequent papers, see [62][63][64][65][66] to mention a few.…”

On Topological Entropy of Interconnected Nonlinear Systems

“…In the next result, h(f, K) stands for the entropy of the system (14) as defined in Section II-A for the system (1) of which ( 14) is a special case. (16) with a + ii as defined in Lemma 1.…”

“…The entropy estimates that we derive involve upper bounds on the matrix measures and induced norms of the Jacobian matrices arising from the interconnection. (We note that entropy bounds of this form are very different from those obtained in [16].) For the case of a general interconnection, we establish an upper bound on the entropy that involves the largest eigenvalue of the interconnection matrix obtained from these Jacobians, multiplied by the system dimension.…”

“…Recently there has been some work on applying entropy concepts in the context of interconnected systems (in discrete time): [11] studies invariance entropy of a network of control systems and relates it to entropies of the subsystems and to associated control data rates; [22] explores invariance feedback entropy for a network of uncertain systems; [16] analyzes observability rates of a networked system and relates them to the topological entropy of the entire system and to certain auxiliary quantities (storage functions and supply rates) defined for the linearizations of the subsystems. However, much still remains to be understood about the basic question considered here, namely: given an interconnection of deterministic nonlinear systems, under what conditions can we derive an explicit bound on its topological entropy and relate it to bounds on the entropies of the subsystems?…”