90 research outputs found
An Improved Data Augmentation Scheme for Model Predictive Control Policy Approximation
This paper considers the problem of data generation for MPC policy
approximation. Learning an approximate MPC policy from expert demonstrations
requires a large data set consisting of optimal state-action pairs, sampled
across the feasible state space. Yet, the key challenge of efficiently
generating the training samples has not been studied widely. Recently, a
sensitivity-based data augmentation framework for MPC policy approximation was
proposed, where the parametric sensitivities are exploited to cheaply generate
several additional samples from a single offline MPC computation. The error due
to augmenting the training data set with inexact samples was shown to increase
with the size of the neighborhood around each sample used for data
augmentation. Building upon this work, this letter paper presents an improved
data augmentation scheme based on predictor-corrector steps that enforces a
user-defined level of accuracy, and shows that the error bound of the augmented
samples are independent of the size of the neighborhood used for data
augmentation
Characterization and Lower Bounds for Branching Program Size using Projective Dimension
We study projective dimension, a graph parameter (denoted by pd for a
graph ), introduced by (Pudl\'ak, R\"odl 1992), who showed that proving
lower bounds for pd for bipartite graphs associated with a Boolean
function imply size lower bounds for branching programs computing .
Despite several attempts (Pudl\'ak, R\"odl 1992 ; Babai, R\'{o}nyai, Ganapathy
2000), proving super-linear lower bounds for projective dimension of explicit
families of graphs has remained elusive.
We show that there exist a Boolean function (on bits) for which the
gap between the projective dimension and size of the optimal branching program
computing (denoted by bpsize), is . Motivated by the
argument in (Pudl\'ak, R\"odl 1992), we define two variants of projective
dimension - projective dimension with intersection dimension 1 (denoted by
upd) and bitwise decomposable projective dimension (denoted by
bitpdim).
As our main result, we show that there is an explicit family of graphs on vertices such that the projective dimension is , the
projective dimension with intersection dimension is and the
bitwise decomposable projective dimension is .
We also show that there exist a Boolean function (on bits) for which
the gap between upd and bpsize is . In contrast, we
also show that the bitwise decomposable projective dimension characterizes size
of the branching program up to a polynomial factor. That is, there exists a
constant and for any function , . We also study two other
variants of projective dimension and show that they are exactly equal to
well-studied graph parameters - bipartite clique cover number and bipartite
partition number respectively.Comment: 24 pages, 3 figure
Stability Properties of the Adaptive Horizon Multi-Stage MPC
This paper presents an adaptive horizon multi-stage model-predictive control
(MPC) algorithm. It establishes appropriate criteria for recursive feasibility
and robust stability using the theory of input-to-state practical stability
(ISpS). The proposed algorithm employs parametric nonlinear programming (NLP)
sensitivity and terminal ingredients to determine the minimum stabilizing
prediction horizon for all the scenarios considered in the subsequent
iterations of the multi-stage MPC. This technique notably decreases the
computational cost in nonlinear model-predictive control systems with
uncertainty, as they involve solving large and complex optimization problems.
The efficacy of the controller is illustrated using three numerical examples
that illustrate a reduction in computational delay in multi-stage MPC.Comment: Accepted for publication in Elsevier's Journal of Process Contro
Mixed-Integer MPC Strategies for Fueling and Density Control in Fusion Tokamaks
Model predictive control (MPC) is promising for fueling and core density
feedback control in nuclear fusion tokamaks, where the primary actuators,
frozen hydrogen fuel pellets fired into the plasma, are discrete. Previous
density feedback control approaches have only approximated pellet injection as
a continuous input due to the complexity that it introduces. In this letter, we
model plasma density and pellet injection as a hybrid system and propose two
MPC strategies for density control: mixed-integer (MI) MPC using a conventional
mixed-integer programming (MIP) solver and MPC utilizing our novel modification
of the penalty term homotopy (PTH) algorithm. By relaxing the integer
requirements, the PTH algorithm transforms the MIP problem into a series of
continuous optimization problems, reducing computational complexity. Our novel
modification to the PTH algorithm ensures that it can handle path constraints,
making it viable for constrained hybrid MPC in general. Both strategies perform
well with regards to reference tracking without violating path constraints and
satisfy the computation time limit for real-time control of the pellet
injection system. However, the computation time of the PTH-based MPC strategy
consistently outpaces the conventional MI-MPC strategy
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