Polynomial approximation of optimal event triggers for state estimation problems using SOSTOOLS

This paper uses polynomials to approximate the optimal event triggers in state estimation problems, and efficiently computes the polynomial approximation with SOSTOOLS. From the examples under study, the polynomial approximation provides a tight lower bound on the optimal cost, and a tight upper bound on the suboptimal cost. The cost generated by the polynomial suboptimal event trigger is very close to the lower bound on the optimal cost. We also apply this polynomial suboptimal event trigger to an 8 dimensional 3DOF helicopter to demonstrate that one can efficiently compute the polynomial suboptimal event triggers for highly nonlinear high dimensional systems. To our best knowledge, this is the first time the suboptimal trigger has been applied to a system whose dimension is greater than 2.