Optimal consensus control for multi-satellite assembly in elliptic orbit with input saturation. (July 2023) - Atallah, Mohammed; Okasha, Mohamed; Dief, Tarek N.; Jallad, Abdul-Halim
Abstract: This paper presents an optimal control design method for multi-satellite assembly in an elliptic orbit in close proximity operations considering input saturation constraints. Tschauner–Hempel (T–H) equations are utilized to model the relative motion dynamics of the satellites in the Local Vertical Local Horizontal (LVLH) frame of the target satellite, where every satellite in the assembly is modeled as a point mass. The communication topology between the satellites in the assembly is modeled using graph theory, where the graph has several nodes representing the satellites and several edges representing the data exchange direction. It is assumed that every satellite exchanges its states with a few neighbors in the team, where the neighbors of every satellite are prespecified and do not change during the mission. This graph is utilized to construct the global dynamic model of the assembly, in which every node is represented by the dynamic model of a single satellite. The local control law, which is applied to every satellite in the assembly, consists of a state feedback gain and a coupling gain. The state feedback gain is designed using the discrete-time periodic Riccati equation to guarantee the local stability of every satellite separately, while the coupling gain is selected to satisfy the Lyapunov condition to guarantee the global stability of the assembly. The invariant-set method is utilized to prove the stability of the global dynamic system that is subjected to symmetric input saturation. The precision and optimality of the proposed control law are successfully demonstrated by numerical nonlinear simulations in a MATLAB environment for a cubic formation satellite assembly. Highlights: Assembling multiple satellites into an elliptic orbit in a cubic configuration. Controlling a discrete-time periodic multi-agent system. Designing an optimal control system using the discrete-time periodic Riccati equation. Analyzing the stability of a discrete-time periodic multi-agent system under input saturation.