The problem of optimal attitude tracking control for a rigid spacecraft is addressed by means of synergetic control technique. As a stepping-stone, we first design an invariant manifold and construct a variable structure control (VSC) scheme. Based on the invariant manifold, the synergetic optimal control (SOC) scheme is then proposed. The Modified Rodrigues Parameter (MRP) is adopted as attitude variable due mainly to its global nonsingular description when combined with its shadow sets. Some salient features of the SOC controller are: it is shown to have optimality property with respect to a meaningful cost functional; it is robust to external disturbances; and most important, compared with standard VSC scheme, the SOC signal designed is smooth and thus free from chattering. Simulation results demonstrate the efficiency of the proposed synergetic optimal control strategy in achieving attitude tracking.
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