Optimal Control of Formation Flight Based on MLD Systems

In this paper, formation flight is modeled as a mixed logical dynamical (MLD) system, which is described by linear equations subject to linear inequalities involving real and integer variables. This model is built by discretizing the continuous-time nonlinear kinematical equations of formation flight system through the Euler method, quantizing its physical input variables, and integrating operating constraints. The control objective is to maintain the relative positions and orientations between aircraft close to their desired values to keep a formation geometry without potential collisions despite the maneuvering of the leader. The resulting MLD system of formation flight can be governed by the mixed integer predictive control (MIPC) law, and the optimal predictive control input can be obtained by solving an equivalent mixed integer linear programming (MILP) problem. This MLD model essentially considers the three dimensional motion of aircraft. The effectiveness of this method is demonstrated by simulation results.