Using Radial Basis Functions to Approximate the LQG-Optimal Event-Based Sampling Policy

摘要

A numerical method using radial basis functions (RBF) has been developed to find the optimal event-based sampling policy in an LQG problem setting. The optimal sampling problem can be posed as a stationary partial differential equation with a free boundary, which is solved by reformulating the optimal RBF approximation as a linear complementarity problem (LCP). The LCP can be efficiently solved using any quadratic program solver, and we give guarantees of existence and uniqueness of the solution. The RBF method is validated numerically, and we showcase what the different types of optimal policies look like for 2D systems.