When multiplicative noise stymies control

When multiplicative noise stymies control

We consider the stabilization of an unstable discrete-time linear system that is observed over a channel corrupted by continuous multiplicative noise. Our main result shows that if the system growth is large enough, then the system cannot be stabilized in a secondmoment sense. This is done by showing that the probability that the state magnitude remains bounded must go to zero with time. Our pr...

DDT stalemate stymies malaria control initiative.

Containing Colored Multiplicative Noise

Necessary and sufficient conditiom are derived nnder which agiven set of hear hcb'onalsassume unique values over the solution sedof a hear equation; the latter property is referred to as partial uniqueness.The wefnlness of the conditions obtained for partial uniqueness is dem-onstrated by applying them to various problems of observab~tyand inputidentirLsbilit...

Phase transitions in distributed control systems with multiplicative noise

We study a simple model pertinent to distributed algorithms and control, that has been well studied in the prior literature in the presence of additive noise. The model in question belongs to the class of so-called network consensus (or gossip) algorithms, which provide a local algorithms for computing global means of values distributed over the nodes of a network. We show that this simple mode...

Exact Analytic Solutions for Optimal Control Problems Under Multiplicative Noise

Control-dependent (multiplicative) noise makes it difficult to achieve optimal control because large control signals amplify noise. This paper considers a minimal (one-dimensional) system that includes multiplicative noise and solves the optimal control problem for arbitrary cost functions. In a limit when the control-cost approaches zero, this formulation becomes analytically solvable. The ana...