Abstract: The time-driven paradigm for modeling, sampling, estimation, control, and optimization is based on centuries of theoretical underpinnings and was further promoted by the digital technological advances of the 1970s. In a world increasingly networked, wireless, and consisting of large-scale distributed systems, the universal value of this paradigm has understandably come to question. For example, time-driven sampling and communication with energy-constrained wireless devices can be inefficient, unnecessary, and sometimes infeasible. The event-driven paradigm offers an alternative complementary look at control and optimization. The key idea is that a “clock” should not be dictating actions simply because a time step is taken; rather, an action should be triggered by an “event” which may be a well-defined condition on the system state (including a simple time step) or a random state transition.
We will discuss two areas where event-driven control and optimization have been well-developed and justify the research activity recently seen in the systems and control community in this direction. First, in distributed systems, we will show how event-driven, rather than synchronous, communication can guarantee convergence in cooperative distributed optimization while provably maintaining optimality. Second, when modeling stochastic systems with complex dynamics, systematic abstraction methods can generate hybrid models where well-defined events decompose system operation into discrete states. This facilitates the use of analytical tools which are robust with respect to modeling details which can, therefore, be safely omitted. A case in point is the use of gradient estimation techniques which boil down to a set of Infinitesimal Perturbation Analysis equations (an “IPA calculus”). We will illustrate how this IPA calculus is used to solve a large class of stochastic optimization problems.