A DMPC-based three-dimensional cooperative guidance scheme with impact time and impact angle constraints

In this paper, a distributed model predictive control (DMPC)-based three-dimensional (3D) cooperative guidance scheme is proposed for multiple interceptors with controllable thrust and constrained acceleration, to simultaneously attack a maneuvering target at desired terminal angles. The cooperative guidance scheme consists of a fractional power function-based extended state observer (FPESO) for disturbance estimation, and a DMPC controller to generate the control actions. By introducing the assumed state trajectory, the DMPC controller (of each interceptor) can simultaneously employ the zebra optimization algorithm (ZOA) to solve the constrained optimization problem, and generate the real-time guidance commands with no need of any global information. For restricting the uncertain deviation between the assumed state trajectory and the actual one, a compatibility constraint is designed, and the terminal ingredients are developed for coupling and decoupling stage costs, respectively. By applying the above designed constraints and the terminal ingredients, the recursive feasibility of the resulting optimization problem and the closed-loop stability of multi-interceptor system are both ensured. Through numerical simulations, it is verified that the proposed cooperative guidance scheme can achieve cooperative interception with impact time and angle constraints in various scenarios, and has advantageous performance.