Discrete-Time Lossless Convexification for Pointing Constraints

Discrete-Time Lossless Convexification (DT-LCvx) formulates a convex relaxation for a specific class of discrete-time non-convex optimal control problems. It establishes sufficient conditions under which solutions of the relaxed problem satisfy the original non-convex constraints at specified time grid points. Furthermore, it provides an upper bound on the number of time grid points where these sufficient conditions may not hold, and thus the original constraints could be violated. This paper extends DT-LCvx to problems with control pointing constraints. Additionally, it introduces a novel DT-LCvx formulation for mixed-integer optimal control problems in which the control is either inactive or constrained within an annular sector. Such formulation broadens the feasible space for problems with pointing constraints. A numerical example is provided to illustrate its application.