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**Control Lyapunov function optimal sliding mode controllers for attitude tracking of spacecraft.**
*(English)*
Zbl 1254.93055

Summary: The attitude tracking control problem for a rigid spacecraft using two optimal sliding mode control laws is addressed. Integral Sliding Mode (ISM) control is applied to combine the first-order sliding mode with optimal control and is applied to quaternion-based spacecraft attitude tracking maneuvers with external disturbances and an uncertainty inertia matrix. For the optimal control part, the Control Lyapunov Function (CLF) approach is used to solve the infinite-time nonlinear optimal control problem, whereas the Lyapunov Optimizing Control (LOC) method is applied to solve the finite-time nonlinear optimal control problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking maneuvers is presented and simulation results are included to demonstrate and verify the usefulness of the proposed controllers.

### MSC:

93B12 | Variable structure systems |

93D30 | Lyapunov and storage functions |

70P05 | Variable mass, rockets |

### Keywords:

Lyapunov function optimal sliding mode controller; integral sliding mode (ISM) control; external disturbances; uncertainty inertia matrix; Lyapunov optimizing control (LOC); finite-time nonlinear optimal control problem
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\textit{C. Pukdeboon} and \textit{A. S. I. Zinober}, J. Franklin Inst. 349, No. 2, 456--475 (2012; Zbl 1254.93055)

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