H-infinity Inverse Optimal Attitude-Tracking Control of Rigid Spacecraft

Abstract

The attitude trajectory tracking control problem for a rigid spacecraft with external disturbances is addressed using the robust inverse optimal-control method. The proposed feedback-control law is optimal with respect to a meaningful cost functional involving tracking errors, control efforts, and extended disturbances, and the associated Lyapunov function satisfies a Hamilton‐Jacobi‐Isaacs partial differential equation. The controller is H∞ optimal with respect to extended disturbances. The performance limitation of the inverse optimal feedback controller is analyzed and guidelines for the selection of the controller gains are established. Numerical simulations are performed to demonstrate the effectiveness of the proposed control algorithm and the tuning guidelines. Nomenclature � A� = induced 2-norm of the matrix A ∈ R n × n , � A �= √ [λmax(A T A)] A T = transpose of A |a| = Euclidean norm of the vectora ∈ R n , |a |= √ (a T a) d, ˆ d =e xternal disturbance and extended disturbance, respectively J = inertia matrix of the spacecraft, J = J T > 0 L f V = Lie derivative of the Lyapunov function V (x) with respect to f (x), L f V = ∂ V (x) ∂ x f (x)