187 research outputs found
Maximum Likelihood Methods for Inverse Learning of Optimal Controllers
This paper presents a framework for inverse learning of objective functions
for constrained optimal control problems, which is based on the
Karush-Kuhn-Tucker (KKT) conditions. We discuss three variants corresponding to
different model assumptions and computational complexities. The first method
uses a convex relaxation of the KKT conditions and serves as the benchmark. The
main contribution of this paper is the proposition of two learning methods that
combine the KKT conditions with maximum likelihood estimation. The key benefit
of this combination is the systematic treatment of constraints for learning
from noisy data with a branch-and-bound algorithm using likelihood arguments.
This paper discusses theoretic properties of the learning methods and presents
simulation results that highlight the advantages of using the maximum
likelihood formulation for learning objective functions.Comment: 21st IFAC World Congres
Bayesian model predictive control: Efficient model exploration and regret bounds using posterior sampling
Tight performance specifications in combination with operational constraints
make model predictive control (MPC) the method of choice in various industries.
As the performance of an MPC controller depends on a sufficiently accurate
objective and prediction model of the process, a significant effort in the MPC
design procedure is dedicated to modeling and identification. Driven by the
increasing amount of available system data and advances in the field of machine
learning, data-driven MPC techniques have been developed to facilitate the MPC
controller design. While these methods are able to leverage available data,
they typically do not provide principled mechanisms to automatically trade off
exploitation of available data and exploration to improve and update the
objective and prediction model. To this end, we present a learning-based MPC
formulation using posterior sampling techniques, which provides finite-time
regret bounds on the learning performance while being simple to implement using
off-the-shelf MPC software and algorithms. The performance analysis of the
method is based on posterior sampling theory and its practical efficiency is
illustrated using a numerical example of a highly nonlinear dynamical
car-trailer system
Quantization Design for Distributed Optimization
We consider the problem of solving a distributed optimization problem using a
distributed computing platform, where the communication in the network is
limited: each node can only communicate with its neighbours and the channel has
a limited data-rate. A common technique to address the latter limitation is to
apply quantization to the exchanged information. We propose two distributed
optimization algorithms with an iteratively refining quantization design based
on the inexact proximal gradient method and its accelerated variant. We show
that if the parameters of the quantizers, i.e. the number of bits and the
initial quantization intervals, satisfy certain conditions, then the
quantization error is bounded by a linearly decreasing function and the
convergence of the distributed algorithms is guaranteed. Furthermore, we prove
that after imposing the quantization scheme, the distributed algorithms still
exhibit a linear convergence rate, and show complexity upper-bounds on the
number of iterations to achieve a given accuracy. Finally, we demonstrate the
performance of the proposed algorithms and the theoretical findings for solving
a distributed optimal control problem
Stochastic Model Predictive Control for Linear Systems using Probabilistic Reachable Sets
In this paper we propose a stochastic model predictive control (MPC)
algorithm for linear discrete-time systems affected by possibly unbounded
additive disturbances and subject to probabilistic constraints. Constraints are
treated in analogy to robust MPC using a constraint tightening based on the
concept of probabilistic reachable sets, which is shown to provide closed-loop
fulfillment of chance constraints under a unimodality assumption on the
disturbance distribution. A control scheme reverting to a backup solution from
a previous time step in case of infeasibility is proposed, for which an
asymptotic average performance bound is derived. Two examples illustrate the
approach, highlighting closed-loop chance constraint satisfaction and the
benefits of the proposed controller in the presence of unmodeled disturbances.Comment: 57th IEEE Conference on Decision and Control, 201
Generalised Regret Optimal Controller Synthesis for Constrained Systems
This paper presents a synthesis method for the generalised dynamic regret
problem, comparing the performance of a strictly causal controller to the
optimal non-causal controller under a weighted disturbance. This framework
encompasses both the dynamic regret problem, considering the difference of the
incurred costs, as well as the competitive ratio, which considers their ratio,
and which have both been proposed as inherently adaptive alternatives to
classical control methods. Furthermore, we extend the synthesis to the case of
pointwise-in-time bounds on the disturbance and show that the optimal solution
is no worse than the bounded energy optimal solution and is lower bounded by a
constant factor, which is only dependent on the disturbance weight. The
proposed optimisation-based synthesis allows considering systems subject to
state and input constraints. Finally, we provide a numerical example which
compares the synthesised controller performance to - and
-controllers.Comment: Accepted at IFAC WC 202
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