Piecewise-affine controller synthesis for a model of 2D orbital path following

This paper investigates the feasibility of a new controller synthesis methodology for spacecraft orbital path following based on a piecewise-affine (PWA) control law. More specifically, the paper presents a technique to synthesize PWA controllers to solve the orbital path following problem by extending previous research on land vehicles. The desired orbital path parameterization avoids singularities because it does not compute the point in the trajectory closest to the spacecraft, which might not be well defined for certain configurations. The PWA controller synthesis problem is cast as an optimization problem subject to bilinear matrix inequalities (BMIs) and solved locally using available software packages. Although the proposed method is applied to a numerical example on circular orbital path following, the method is general and can be used for any parameterized trajectory