Riccati Equation

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The matrix differential/algebraic equation used in linear quadratic optimal control (LQR) to solve for the optimal state-feedback gain, in the form A^T P + PA - PBR⁻¹B^T P + Q = 0. The symmetric positive (semi-)definite solution matrix P yields the optimal gain via K = -R⁻¹B^T P. The properties of the Riccati equation (existence, uniqueness, and convergence of the solution) guarantee the optimality and closed-loop stability of the LQR controller.

Application Value

The matrix differential/algebraic equation used in linear quadratic optimal control (LQR) to solve for the optimal state-feedback gain, in the form A^T P + PA - PBR⁻¹B^T P + Q = 0. The symmetric positive (semi-)definite solution matrix P yields the optimal gain via K = -R⁻¹B^T P. The properties of the Riccati equation (existence, uniqueness, and convergence of the solution) guarantee the optimality and closed-loop stability of the LQR controller.

Related Concepts

• Bivariate Gaussian Distribution
• Midcourse Impulse
• Zero-Thrust Reference Trajectory
• Co-state Variables

References

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