4,382 research outputs found
A Statistical Learning Theory Approach for Uncertain Linear and Bilinear Matrix Inequalities
In this paper, we consider the problem of minimizing a linear functional
subject to uncertain linear and bilinear matrix inequalities, which depend in a
possibly nonlinear way on a vector of uncertain parameters. Motivated by recent
results in statistical learning theory, we show that probabilistic guaranteed
solutions can be obtained by means of randomized algorithms. In particular, we
show that the Vapnik-Chervonenkis dimension (VC-dimension) of the two problems
is finite, and we compute upper bounds on it. In turn, these bounds allow us to
derive explicitly the sample complexity of these problems. Using these bounds,
in the second part of the paper, we derive a sequential scheme, based on a
sequence of optimization and validation steps. The algorithm is on the same
lines of recent schemes proposed for similar problems, but improves both in
terms of complexity and generality. The effectiveness of this approach is shown
using a linear model of a robot manipulator subject to uncertain parameters.Comment: 19 pages, 2 figures, Accepted for Publication in Automatic
Application of Statistical Learning Control to the Design of a Fixed-Order Controller for a Flexible Beam
This paper shows how probabilistic methods and statistical learning theory can provide approximate solutions to “difficult” control problems. The paper also introduces bootstrap learning methods to drastically reduce the bound on the number of samples required to achieve a performance level. These results are then applied to obtain more efficient algorithms which probabilistically guarantee stability and robustness levels when designing controllers for uncertain systems. The paper includes examples of the applications of these methods
A Randomized approach to the H2/H? Control Problem via Q-parameterization
We show that the mixed H2/H? control problem can be efficiently solved using randomized algorithms. Q-parameterization provides a mechanism to search over all stabilizing controllers, and thus gives us the ability to search for H2 minimizing controllers, while still providing stability robustness. Finally, we are able to show that we can get results comparable to a more traditional approach such as gradient search, but in addition, we can solve more complex problems. With very little modification, we are able to deal with multiple objectives, plant uncertainty, and fixed order controllers
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
Statistical controller design for the linear benchmark problem
In this paper some fixed-order controllers are designed via statistical methods for the benchmark problem originally presented at the 1990 American Control Conference. Based on some recent results by the authors, it is shown that the statistical approach is a valid method to design robust controllers. Two different controllers are proposed and their performance are compared with controllers with the same structure, designed using different techniques
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