106 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
Learning the cost-to-go for mixed-integer nonlinear model predictive control
Application of nonlinear model predictive control (NMPC) to problems with
hybrid dynamical systems, disjoint constraints, or discrete controls often
results in mixed-integer formulations with both continuous and discrete
decision variables. However, solving mixed-integer nonlinear programming
problems (MINLP) in real-time is challenging, which can be a limiting factor in
many applications. To address the computational complexity of solving mixed
integer nonlinear model predictive control problem in real-time, this paper
proposes an approximate mixed integer NMPC formulation based on value function
approximation. Leveraging Bellman's principle of optimality, the key idea here
is to divide the prediction horizon into two parts, where the optimal value
function of the latter part of the prediction horizon is approximated offline
using expert demonstrations. Doing so allows us to solve the MINMPC problem
with a considerably shorter prediction horizon online, thereby reducing the
online computation cost. The paper uses an inverted pendulum example with
discrete controls to illustrate this approach
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