A passage to complex systems

Abstract

Complex systems are the new scientific frontier which was emerging in the past decades with advance of modern technology and the study of new parametric domains in natural systems. An important challenge is, contrary to classical systems studied so far, the great difficulty in predicting their future behaviour from an initial instant as by their very structure the interactions strength between system components is shielding completely their specific individual features. So these systems are a counterexample to reductionism so strongly influential in Science with Cartesian method only valid for complicated systems. Whether complex systems are obeying strict laws like classical systems is still unclear, but it is however possible today to develop methods which allow to handle some dynamical properties of such system. They should comply with representing system self organization when passing from complicated to complex, which rests upon the new paradigm of passing from classical trajectory space to more abstract trajectory manifolds associated to natural system invariants characterizing complex system dynamics. So they are basically of qualitative nature, independent of system state space dimension and, because of generic impreciseness, privileging robustness to compensate for not well known system parameter and functional variations. This points toward the importance of control approach for a complex system, the more as for industrial applications there is now evidence that transforming a complicated man made system into a complex one is extremely beneficial for overall performance improvement. But this requires larger intelligence delegation to the system, and a well defined control law should be set so that a complex system described in very general terms can behave in a prescribed way. The method is to use the notion of equivalence class within which the system is forced to stay by action of the control law constructed in explicit terms from mathematical (and even approximate) representation of system dynamics. © 2009 Springer-Verlag Berlin Heidelberg.