3 ms·
I read a paper on this—it's convex because any optimal trajectory will have the engines at full throttle whenever they're on, so they just fill up the parameter
by CarVac 8y ago
I read a paper on this—it's convex because any optimal trajectory will have the engines at full throttle whenever they're on, so they just fill up the parameter space, confident that illegal values will never be required.
- chasd00 8y agocan you link to the paper please?
- theoh 8y agoI don't know which paper they mean, but here's a relevant paragraph from one of the papers available from Blackmore's page: "In this paper, we unify the convex optimization approaches of [1], [2], [17] and extend them to handle thrust pointing constraints. While convexifying the problem with nonconvex thrust pointing constraints, we develop a geometrical insight into the problem that establishes a connection with “normal systems” [18]. A normal linear system is defined in the context of optimal control theory where the system is said to be normal with respect a set of feasible controls if it maximizes the Hamiltonian at a unique point of the set of feasible controls. In the case when the set of feasible controls is convex, a system being normal implies that the Hamiltonian is maximized at an extreme point of the set [18]. Our convexification result has a similar geometric interpretation since it establishes lossless convexification by ensuring that the Hamiltonian is maximized at the extreme points of a projection of the relaxed set of feasible controls. This set is then shown to be contained in the original nonconvex set of feasible controls, thereby estab- lishing that we can obtain optimal solutions of the original nonconvex problem via solving its convex relaxation."