Optimal periodic control is an effective technique to reduce aerodynamic heating and fuel consumption of hypersonic cruise vehicles. Herein, this optimal control problem has been solved by nonlinear programming and passed the posteriori check of optimality. The results indicate that the lift coefficient and velocity in dynamical model could be recognized as constants. Accordingly, the original 3D system consists of velocity, flight path angle, and altitude, which could be decoupled into a 2D subsystem and a 1D one. The 2D subsystem could describe the correlation between the flight path angle and altitude. And the period length is mainly dependent on the maximum altitude difference. The 1D subsystem has been proved to be feasible to describe the variation of kinetic energy or velocity. On basis of the subsystems, the heating and fuel performances of periodic cruise have been studied. The heating performance is mainly dependent on the maximum altitude difference, and the fuel consumption is mainly dependent on the drag coefficient. The features concluded in this paper can support rapid trajectory planning or suboptimal feedback design of hypersonic cruise vehicles. INDEX TERMS Optimal periodic control, hypersonic cruise vehicle, trajectory features, performances.

Dynamic soaring is a special flying technique designed to allow UAVs (unmanned aerial vehicles) to extract energy from wind gradient field and enable UAVs to increase the endurance. In order to figure out the energy-extraction mechanisms in dynamic soaring, a noninertial wind relative reference frame of aircraft is built. In the noninertial frame, there is an inertial force which is created by gradient wind field. When the wind gradient(GW)and the components of airspeed(vzvx)are positive, inertial force(F)makes positive work to the aircraft. In the meantime, an equilibrium position theory of dynamic soaring is proposed. At the equilibrium positions, the increased potential energy is greater than the wasted kinetic energy when the aircraft is flying upwards. The mechanical energy is increased in this way, and the aircraft can store energy for flight. According to the extreme value theory, contour line figures of the maximum function and the component of airspeed(vz)are obtained to find out the aircraft’s lifting balance allowance in dynamic soaring. Moreover, this equilibrium position theory can also help to conduct an aircraft to acquire energy from the environment constantly.

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In this paper, the attitude determination problem from two vector observations is revisited, incorporating the redundant equality constraint obtained by the dot product of vector observations. Analytical solutions to this constrained attitude determination problem are derived. It is found out that the studied two-vector attitude determination problem by Davenport q-method under the dot product constraint has deterministic maximum eigenvalue, which leads to its advantage in error/perturbation analysis and covariance determination. The proposed dot product constrained two-vector attitude solution is applied then to solve several engineering problems. Detailed simulations on spacecrafts attitude determination indicate the efficiency of the proposed theory.

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