Satellite Attitude Control Using Analytical Solutions to Approximations of the Hamilton-Jacobi Equation

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Satellite Attitude Control Using Analytical Solutions to Approximations of the Hamilton-Jacobi Equation

LeBel, Stefan / Damaren, Christopher J. / Desbiens, A. / Meola, C. / Simani, S.

The solution to the Hamilton-Jacobi equation associated with the nonlinear H_∞ control problem is approximated using a Taylor series expansion. A recently developed analytical solution method is used for the second-, third-, and fourth-order terms. The proposed controller synthesis method is applied to the problem of satellite attitude control with attitude parameterization accomplished using the modified Rodrigues parameters and their associated shadow set. This leads to kinematical relations that are polynomial in the modified Rodrigues parameters and the angular velocity components. The proposed control method is compared with existing methods from the literature through numerical simulations. Disturbance rejection properties are compared by including the gravity-gradient and geomagnetic disturbance torques. Controller robustness is also compared by including unmodeled first- and second-order actuator dynamics, as well as actuation time delays in the simulation model. Moreover, the gap metric distance induced by the unmodeled actuator dynamics is calculated for the linearized system. The results indicated that a linear controller performs almost as well as those obtained using higher-order solutions for the Hamilton-Jacobi equation and the controller dynamics.