2 research outputs found
Accelerating MPC by online detection of state space sets with common optimal feedback laws
Model predictive control (MPC) samples a generally unknown and complicated
feedback law point by point. The solution for the current state contains,
however, more information than only the optimal signal for this particular
state. In fact, it provides an optimal affine feedback law
on a polytope , i.e., on a full-dimensional state
space set. It is an obvious idea to reuse this affine feedback law as long as
possible. Reusing it on its polytope is too conservative, however,
because any is a state space set with a common affine law for the
entire horizon . We show a simple criterion exists for identifying the
polytopes that have a common , but may differ with respect
to . Because this criterion is too computationally
expensive for an online use, we introduce a simple heuristics for the fast
construction of a subset of the polytopes of interest. Computational examples
show (i) a considerable fraction of QPs can be avoided (10% to 40%) and (ii)
the heuristics results in a reduction very close to the maximum one that could
be achieved if the explicit solution was available. We stress the proposed
approach is intended for use in online MPC and it does not require the explicit
solution.Comment: 14 pages, 2 figure
Polygonic Representation of Explicit Model Predictive Control
The paper proposes to reduce complexity of explicit MPC feedback laws by representing regions over which the law is defined as (possibly non-convex) polygons. Each polygon is then represented only by its boundaries, which reduces the memory footprint of the feedback law. Even though significant amount of memory can be saved this way, the price to be paid is increased computational load associated by performing point location tasks in non-convex objects. Therefore we propose to devise inner and outer convex approximations of non-convex polygons to reduce the computational requirements. Such approximations allow to perform point location more effectively, leading to a reduction of the required on-line computational effort. Several ways to design suitable approximations are presented and efficacy of the proposed procedure is evaluated