Three ways to control dynamical systems robustly

Robustness is widely considered a desirable feature for a decision strategy, yet the concept itself is often only loosely defined.   In this talk, I review three classes of strategies for controlling dynamical systems robustly:  feedforward, feedback, and worst case.  The first class, feedforward strategies, control the dynamics knowing only the initial state of the system and thus do not require sensors.  Surprisingly, there are systematic ways to make feedforward commands more robust, combining damping and clever manipulations of control parameters.  I illustrate the basic ideas on a toy model (transport of a harmonic oscillator) that is related to the problem of designing broadband antireflection coatings in optics.  Another example is the control of the time it takes a eukaryotic cell to complete DNA replication.  The second class of strategies is to apply feedback.  Generic feedback strategies are effective for simple systems subject to small disturbances and are widely used in biological systems, for example to reduce variations in transcription levels (proportional feedback) or to give robustness against constant disturbances in chemotaxis (integral feedback).  More general feedback strategies linearize about nonlinear feedforward commands generated using optimal control and again are effective for moderate disturbances and uncertainties.   But these local feedback techniques can fail in the face of larger uncertainties, leading to a third class of “worst-case” control strategies having roots in game theory, economics and notions of risk.   The main idea is to partition events into two classes, “normal” and “disaster,”and optimize among normal events assuming that one encounters the worst case among that set.  Disasters are dealt with via contingency plans.  Too often, the partition process itself is not made explicit, and the implicit choices become apparent only when disaster strikes.  I argue for a more up-front accounting of partitioning.