The role and use of the stochastic linear-quadratic-Gaussian problem in control system design

TLDR

Linear‑quadratic stochastic control is a foundational approach for engineering design, especially for controlling nonlinear uncertain plants, and the design is typically performed offline. The paper aims to outline the design philosophy, modeling considerations, and problem formulation of linear‑quadratic stochastic control, presenting results for illustration without detailed proofs. The methodology integrates deterministic perturbation control, stochastic state estimation, and linearized stochastic control to construct the closed‑loop system. The study demonstrates that combining these three elements yields a complete closed‑loop control system.

Abstract

The role of the linear-quadratic stochastic control problem in engineering design is reviewed in tutorial fashion. The design approach is motivated by considering the control of a non-linear uncertain plant about a desired input-output response. It is demonstrated how a design philosophy based on 1) deterministic perturbation control, 2) stochastic state estimation, and 3) linearized stochastic control leads to an overall closed-loop control system. The emphasis of the paper is on the philosophy of the design process, the modeling issue, and the formulation of the problem; the results are given for the sake of completeness, but no proofs are included. The systematic off-line nature of the design process is stressed throughout.