181,130 research outputs found
Sample Approximation-Based Deflation Approaches for Chance SINR Constrained Joint Power and Admission Control
Consider the joint power and admission control (JPAC) problem for a
multi-user single-input single-output (SISO) interference channel. Most
existing works on JPAC assume the perfect instantaneous channel state
information (CSI). In this paper, we consider the JPAC problem with the
imperfect CSI, that is, we assume that only the channel distribution
information (CDI) is available. We formulate the JPAC problem into a chance
(probabilistic) constrained program, where each link's SINR outage probability
is enforced to be less than or equal to a specified tolerance. To circumvent
the computational difficulty of the chance SINR constraints, we propose to use
the sample (scenario) approximation scheme to convert them into finitely many
simple linear constraints. Furthermore, we reformulate the sample approximation
of the chance SINR constrained JPAC problem as a composite group sparse
minimization problem and then approximate it by a second-order cone program
(SOCP). The solution of the SOCP approximation can be used to check the
simultaneous supportability of all links in the network and to guide an
iterative link removal procedure (the deflation approach). We exploit the
special structure of the SOCP approximation and custom-design an efficient
algorithm for solving it. Finally, we illustrate the effectiveness and
efficiency of the proposed sample approximation-based deflation approaches by
simulations.Comment: The paper has been accepted for publication in IEEE Transactions on
Wireless Communication
Uncertainty Analysis for Data-Driven Chance-Constrained Optimization
In this contribution our developed framework for data-driven chance-constrained optimization is extended with an uncertainty analysis module. The module quantifies uncertainty in output variables of rigorous simulations. It chooses the most accurate parametric continuous probability distribution model, minimizing deviation between model and data. A constraint is added to favour less complex models with a minimal required quality regarding the fit. The bases of the module are over 100 probability distribution models provided in the Scipy package in Python, a rigorous case-study is conducted selecting the four most relevant models for the application at hand. The applicability and precision of the uncertainty analyser module is investigated for an impact factor calculation in life cycle impact assessment to quantify the uncertainty in the results. Furthermore, the extended framework is verified with data from a first principle process model of a chloralkali plant, demonstrating the increased precision of the uncertainty description of the output variables, resulting in 25% increase in accuracy in the chance-constraint calculation.BMWi, 0350013A, ChemEFlex - Umsetzbarkeitsanalyse zur Lastflexibilisierung elektrochemischer Verfahren in der Industrie; Teilvorhaben: Modellierung der Chlor-Alkali-Elektrolyse sowie anderer Prozesse und deren Bewertung hinsichtlich Wirtschaftlichkeit und möglicher HemmnisseDFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli
An Improved Constraint-Tightening Approach for Stochastic MPC
The problem of achieving a good trade-off in Stochastic Model Predictive
Control between the competing goals of improving the average performance and
reducing conservativeness, while still guaranteeing recursive feasibility and
low computational complexity, is addressed. We propose a novel, less
restrictive scheme which is based on considering stability and recursive
feasibility separately. Through an explicit first step constraint we guarantee
recursive feasibility. In particular we guarantee the existence of a feasible
input trajectory at each time instant, but we only require that the input
sequence computed at time remains feasible at time for most
disturbances but not necessarily for all, which suffices for stability. To
overcome the computational complexity of probabilistic constraints, we propose
an offline constraint-tightening procedure, which can be efficiently solved via
a sampling approach to the desired accuracy. The online computational
complexity of the resulting Model Predictive Control (MPC) algorithm is similar
to that of a nominal MPC with terminal region. A numerical example, which
provides a comparison with classical, recursively feasible Stochastic MPC and
Robust MPC, shows the efficacy of the proposed approach.Comment: Paper has been submitted to ACC 201
Convex Chance Constrained Model Predictive Control
We consider the Chance Constrained Model Predictive Control problem for
polynomial systems subject to disturbances. In this problem, we aim at finding
optimal control input for given disturbed dynamical system to minimize a given
cost function subject to probabilistic constraints, over a finite horizon. The
control laws provided have a predefined (low) risk of not reaching the desired
target set. Building on the theory of measures and moments, a sequence of
finite semidefinite programmings are provided, whose solution is shown to
converge to the optimal solution of the original problem. Numerical examples
are presented to illustrate the computational performance of the proposed
approach.Comment: This work has been submitted to the 55th IEEE Conference on Decision
and Contro
On the Sample Size of Random Convex Programs with Structured Dependence on the Uncertainty (Extended Version)
The "scenario approach" provides an intuitive method to address chance
constrained problems arising in control design for uncertain systems. It
addresses these problems by replacing the chance constraint with a finite
number of sampled constraints (scenarios). The sample size critically depends
on Helly's dimension, a quantity always upper bounded by the number of decision
variables. However, this standard bound can lead to computationally expensive
programs whose solutions are conservative in terms of cost and violation
probability. We derive improved bounds of Helly's dimension for problems where
the chance constraint has certain structural properties. The improved bounds
lower the number of scenarios required for these problems, leading both to
improved objective value and reduced computational complexity. Our results are
generally applicable to Randomized Model Predictive Control of chance
constrained linear systems with additive uncertainty and affine disturbance
feedback. The efficacy of the proposed bound is demonstrated on an inventory
management example.Comment: Accepted for publication at Automatic
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