Robustness vs. Control in Distributed Systems

Understanding and controlling the behavior of dynamical distributed systems, especially biological ones, represents a challenging task. Such systems, in fact, are characterized by a complex web of interactions among their composing elements or subsystems. A typical pattern observed in these systems is the emergence of complex behaviors, in spite of the local nature of the interaction among elements in close spatial proximity. Yet, we point out that each element is a proper system, with its inputs, its outputs and its internal behavior. Moreover, such elements tend to implement feedback control or regulation strategies, where the outputs of a subsystem A are fed as inputs to another subsystem B and so on until, eventually, A itself is influenced. Such complex feedback loops are understood only by considering, at the same time, low- and high-level perspectives, i.e., by regarding such systems as a collection of systems and as a whole, emerging entity. In particular, dynamical distributed systems show nontrivial robustness properties, which are, from one side, inherent to the each subsystem and, from another, depend on the complex web of interactions. In this chapter, therefore, we aim at characterizing the robustness of dynamical distributed systems by using two coexisting levels of abstraction: first, we discuss and review the main concepts related to the robustness of systems, and the relation between robustness, model and control; then, we decline these concepts in the case of dynamical distributed systems as a whole, highlighting similarities and differences with standard systems. We conclude the chapter with a case study related to the chemotaxis of a colony of E. Coli bacteria. We point out that the very reason of existence of this chapter is to make accessible to a vast and not necessarily technical audience the main concepts related to control and robustness of dynamical systems, both traditional and distributed ones.