Linear Quadratic Optimal Control

Author: Tianjiang Shuo Website: https://cislunarspace.cn

Definition

For linear systems, a control design that minimizes a weighted quadratic cost of state deviation and control input. The optimal state-feedback gain is obtained by solving the Riccati equation; the weight matrices trade off tracking accuracy against control effort. In cislunar station-keeping, where nondimensional position and velocity errors are of similar magnitude, typical weights Q=10I and R=I yield favorable tracking performance.

Application Value

This control method can be applied to spacecraft attitude stabilization, orbit keeping, and maneuver trajectory optimization in cislunar space missions, improving mission execution flexibility and reliability.

References

• Zhang and Wang 2022 Continuous-thrust station-keeping of cis-lunar orbits using optimal sliding mode control with practical constraints