A PDE viewpoint on basic properties of coordination algorithms with symmetries

Several recent control applications consider the coordination of subsystems through local interaction. Often the interaction has a symmetry in state space, e.g. invariance with respect to a uniform translation of all subsystem values. The present paper shows that in presence of such symmetry, fundamental properties can be highlighted by viewing the distributed system as the discrete approximation of a partial differential equation. An important fact is that the symmetry on the state space differs from the popular spatial invariance property, which is not necessary for the present results. The relevance of the viewpoint is illustrated on two examples: (i) ill-conditioning of interaction matrices in coordination/consensus problems and (ii) the string instability issue. ©2009 IEEE.

AI in the 21st century - With historical reflections

The discipline of Artificial Intelligence (AI) was born in the summer of 1956 at Dartmouth College in Hanover, New Hampshire. Half of a century has passed, and AI has turned into an important field whose influence on our daily lives can hardly be overestimated. The original view of intelligence as a computer program - a set of algorithms to process symbols - has led to many useful applications now found in internet search engines, voice recognition software, cars, home appliances, and consumer electronics, but it has not yet contributed significantly to our understanding of natural forms of intelligence. Since the 1980s, AI has expanded into a broader study of the interaction between the body, brain, and environment, and how intelligence emerges from such interaction. This advent of embodiment has provided an entirely new way of thinking that goes well beyond artificial intelligence proper, to include the study of intelligent action in agents other than organisms or robots. For example, it supplies powerful metaphors for viewing corporations, groups of agents, and networked embedded devices as intelligent and adaptive systems acting in highly uncertain and unpredictable environments. In addition to giving us a novel outlook on information technology in general, this broader view of AI also offers unexpected perspectives into how to think about ourselves and the world around us. In this chapter, we briefly review the turbulent history of AI research, point to some of its current trends, and to challenges that the AI of the 21st century will have to face. © Springer-Verlag Berlin Heidelberg 2007.