This study introduces a new robust nonlinear control scheme based on the theory of nonsingular terminal sliding mode control (NTSMC). Since conventional NTSMC utilizes a discontinuous switching function, a significant flaw called chattering can occur. The main purpose of this study is to design a new switching function based upon Lyapunov stability in order to alleviate this drawback over time. There are many approaches to mitigate the chattering drawback in SMC such as utilizing a smooth approximation of the switching element, or employing higher order sliding mode control (HOSMC) strategy. However, the use of a continuous approximation affects the system's performance and a finite reaching time to the sliding manifold, and in HOSMC the estimation of high‐order derivatives of states is usually difficult and it still exhibits chattering in the presence of parasitic dynamics. In this study by employing a new sliding manifold including a time function, the chattering is attenuated as well as keeping the robustness. Finally, a second‐order nonlinear dynamical system subject to disturbance is simulated to highlight the validity and applicability of the proposed method.

This paper proposes a new approach of using differentials in aerodynamic drag in combination with thrusters to control satellite formation flying in low Earth orbits. Parameterized output regulation theory for formation flying missions with combined control action is developed based on the Schweighart-Sedwick relative dynamics equations. The theory is implemented to precisely track the different trajectories of reference relative motion and eliminates the effects of the J 2 perturbations. The parametric Lyapunov algebraic equation is proposed to ensure the stability of the linear relative model subject to saturated inputs. The main goal of this study is to approve the viability of using the differentials in aerodynamic drag to precisely control different formation flying missions. Numerical simulations using a high fidelity relative dynamics model and a high-precision orbit propagator are implemented to validate and analyze the performance of the proposed control algorithm in comparison with the linear quadratic regulator algorithm based on actual satellite models.

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Underactuated control offers fault-tolerance for satellite systems, which not only enables the position and attitude control of a satellite with fewer thrusters, but also can reduce the number of thrusters equipped on the satellite even when considering the need for backups. Due to having fewer thrusters, the coupling effect between the translational motion and rotational motion of the satellite cannot be avoided, and the coupled motion must be considered in control procedures. This paper presents a global trajectory design procedure required for the position and attitude control of an underactuated satellite. The satellite has four thrusters with constant thrust magnitudes on one plane of the satellite body. Then, an analytical solution for coupled motion between the rotation and translation of the satellite is obtained using three-step maneuvers of attitude control. The trajectory design based on the analytical solution is shown for the control of translational and rotational motion in three dimensions. Finally, a numerical simulation is performed to verify the effectiveness of the proposed design procedure.

This paper presents a new method of optimal trajectory design for formation flying. Under linearized assumptions and a quadratic performance index, we introduce an attractive set of optimal control based on the linear quadratic regulator theory. The attractive set is defined as a set of all initial states to reach a desired state for a given cost. In particular, we consider attractive sets for two problems: a fixed final-state, fixed final-time problem and an infinite-time problem, and the optimal initial state is found based on the geometry of the attractive set. The optimal trajectories for two problems are evaluated in terms of L 1-norm of control input and termination time.