Abstract: To satisfy the stringent accuracy requirement of maintenance for repeat ground-track (RGT) orbits, a differential algebra-based semi-analytical method is proposed for the orbit design and control while considering high-fidelity geopotential dynamics with the effects of realistic perturbations, including drag, solar radiation pressure, and third body. The method is based on the high-order expansion availability of Poincaré mapping expressed by polynomials with different orders for the forward propagation of a point on an equatorial plane for one or more repeat cycles by the repetitive evaluation of Taylor polynomials. Consequently, the mapping can approximate the conventional numerical orbit propagation, thus yielding the final orbit states at the end of the repeat cycles via the analytical evaluation of polynomials. The numerical results show that the approximation accuracy is ensured, provided that the initial conditions remain close to the reference values under an appropriate range. This approach allows one to efficiently investigate the effect of velocity increment applied at the Poincaré section crossing on the repeat pattern, thus providing a foundation for accurate RGT orbit design and control strategy. By formulating the optimization problem with multiple objective functions for RGT orbits, the proposed method allows one to compute the initial conditions, thus guaranteeing the repetition of ground tracks with high accuracy and low time consumption via nonlinear optimization techniques. Subsequently, based on second-order cone programming (SOCP), a multi-impulsive control strategy is developed to target the initial conditions at the beginning of each repeat cycle. Specifically, the orbit before the targeted Poincaré section crossing is discretized, and a set of linear maps is computed to propagate forward the effect of velocity discontinuities. These maps are constructed with differential algebra integrations of the dynamical model using the uncontrolled trajectory as the reference, which delivers the deviation sequence of position and velocity states relative to the reference trajectory via a series of orbit maneuvers. The trajectory derived based on the maneuver sequence is targeted to the final state and subsequently begins the new repeat conditions. The multi-impulsive RGT control is formalized as the nonlinear programming problem with a set of maneuver velocity increments to be minimized and nonlinear constraints to be enforced. These maneuvers are minimized by formulating a SOCP problem via a lossless convexification with the introduction of slack variables (i.e., impulse magnitude) while enforcing position and velocity state constraints at the Poincaré crossings. As each single velocity impulse can be constrained in magnitude and the time discretization can be extremely fine, both impulsive and continuous maneuvers can be addressed. Owing to the proven existence and uniqueness of the solution, as well as the computational advantages ensured by polynomial complexity, the proposed control approach is particularly suitable for autonomous onboard utilization. The proposed technique is applied to the TerraSAR-X mission repeat pattern with repeat-cycle durations and orbits of up to 11 days and 167 revolutions, respectively. The results show that the design approach enables the realization of high-precision RGT orbit designs and that the orbit control strategy is efficient.