Sporadic event-based control using path constraints and moments

Control is traditionally applied using periodic sensing and actuation. In some applications, it is beneficial to use instead event based control, to communicate or make a change only when necessary. There are no known general closed form solutions to such event based control problems. We consider stationary event-based control problems with mixed continuous/discrete time dynamics and stochastic disturbances. The system is modelled by a set of path constraints, which are converted into constraints on trajectories' moments up to some order N; upper and lower bounds on the control objective for any system that meets the constraints are derived using sum-of-squares techniques and convex semidefinite programming. Joint optimization of upper bound and controller parameters is non-convex in general; approaches to such controller optimization are investigated, including local optimization using bilinear matrix inequalities. Examples show that the bounds are significantly tighter than earlier results obtained using quadratic value functions.