Discrete lossless convexification for pointing constraints

TL;DR

This paper extends Discrete Lossless Convexification (DLCvx) to handle pointing constraints in discrete-time optimal control, providing a convex relaxation with guarantees and broadening applicability to mixed-integer problems.

Contribution

It introduces a new DLCvx formulation for control pointing constraints and mixed-integer problems, expanding the method's scope and providing theoretical guarantees.

Findings

The extended DLCvx guarantees solution feasibility at most grid points.

A new convex relaxation for control pointing constraints is proposed.

Numerical example demonstrates the method's effectiveness.

Abstract

Discrete Lossless Convexification (DLCvx) formulates a convex relaxation for a specific class of discrete-time non-convex optimal control problems. It establishes sufficient conditions under which the solution of the relaxed problem satisfies 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 DLCvx to problems with control pointing constraints. Additionally, it introduces a novel DLCvx formulation for mixed-integer optimal control problems in which the control is either inactive or constrained within an annular sector. This formulation broadens the feasible space for problems with pointing constraints. A numerical example is provided to illustrate its application.