NONLINEAR TRACKING CONTROL OF MANEUVERING RIGID SPACECRAFT
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Nonlinear optimal control formulations have been considered where the state equation consists of the nonlinear state variables. These approaches seek to drive the terminal state values to zero, but require an n-th order polynomial expansion in all of the state variables, leading to tensor-based math models. As with any tensor-based models one is not assured that the control solution converges after retaining a finite number of terms. This problem is overcome by reformulating the control problem in terms of an error state relative to a reference trajectory; thereby yielding a more rapidly converging tensor series approximation for the control. The full nonlinear error dynamics for kinematics and the equation of motion is retained, yielding a tensor-based series solution for the Co-State as a function of error dynamics. A generalized Riccati matrix and disturbance rejection control formulation is presented that accounts for the state nonlinearity through second order. Modified Rodrigues Parameters (MRPs) are used for describing the tracking orientation error dynamics. Computational differentiation is used to define an array-of-arrays data structure for computing 1st, 2nd and 3rd order tensor models for the error dynamics. Spacecraft tracking control applications are presented. The proposed nonlinearly coupled Riccati disturbance rejection gain modeling approach is expected to be broadly useful for applications science and engineering.