A system model is developed where the criterion to partition the world into a system and a rest is based on the functional relation between its states. This approach implies that the gestalt of systems becomes very dynamic. Especially interactions between systems may create temporary super systems "on the fly". The reference to the function notion establishes the link to computation. Based on the distinction between the intended determinism versus nondeterminism of the interaction, two classes of system interactions are distinguished: composition and cooperation. Composition means that by interaction super systems are created and the interacting systems become subsystems. Cooperation means that systems sensibly interact loosely without creating any identifiable super system function and therefore without super system creation from the perspective of the interacting systems. Cooperative system interactions are described with the help of the protocol notion based on shared states, interpreted as the stateful exchange of characters via Shannon channels between roles - the projection of systems onto the interaction channels. It is shown that roles can be internally coordinated by a set of rules, leading to a very flexible process notion which unfolds its full potential only in a new type of execution environment capable of executing spontaneous transitions. The system model has immediate implications for componentization which can be viewed as an attempt to either hide functional recursion and provide only functionality whose composition behavior is easy to understand, or to provide loosely coupled interactions via protocols. To be complete, component models should therefore at least support three general classes of components: one for loose coupling, one for hierarchical composition, and one for pipes.
In @cite_43 David Harel and Amir Pnueli distinguish between ''transformational'' and ''reactive'' systems. They define: "A transformational system accepts input, performs transformation on them and produces outputs'' - which is consistent with the definition of a system. They further define ''Reactive systems ... are repeatedly prompted by the outside world and their role is to continuously respond to external inputs ... A reactive system, in general, does not compute or perform a function, but is supposed to maintain a certain ongoing relationship, so to speak, with its environment.''
@cite_43
2130154921
We deal with nonlinear dynamical systems, consisting of a linear nominal part perturbed by model uncertainties, nonlinearities and both additive and multiplicative random noise, modeled as a Wiener process. In particular, we study the problem of finding suitable measurement feedback control laws such that the resulting closed-loop system is stable in some probabilistic sense. To this aim, we introduce a new notion of stabilization in probability, which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability. This notion requires that, given a target set, a trajectory, starting from some compact region of the state space containing the target, remains forever inside some larger compact set, eventually enters any given neighborhood of the target in finite time and remains thereinafter, all these events being guaranteed with some probability. We give a Lyapunov-based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem. Finally, we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems, which at least include feedback linearizable systems. The generality of the result is promising for applications to other classes of stochastic nonlinear systems. In the deterministic case, our results recover classical stabilization results for nonlinear systems.