An update-and-design scheme for scenario-based LQR synthesis

This paper deals with a finite-horizon Linear Quadratic Regulator (LQR) design for unknown linear time-invariant plants. The objective is to provide a flexible approach which gives robustness guarantees on the closed-loop cost, while avoiding an overly conservative design. The proposed method consists of computing the posterior distribution of the system’s matrices, and using samples from the desired credible region to solve a convex scenario-based program; the result is an open-loop solution of the robust LQR that is then expressed as state-feedback and is used to obtain a new system trajectory. By updating the system estimates as more data are gathered, the algorithm ensures controllers the same robustness guarantees while having to cope with less dispersion in the samples.