2,303 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
Reinforcement Learning Based Minimum State-flipped Control for the Reachability of Boolean Control Networks
To realize reachability as well as reduce control costs of Boolean Control
Networks (BCNs) with state-flipped control, a reinforcement learning based
method is proposed to obtain flip kernels and the optimal policy with minimal
flipping actions to realize reachability. The method proposed is model-free and
of low computational complexity. In particular, Q-learning (QL), fast QL, and
small memory QL are proposed to find flip kernels. Fast QL and small memory QL
are two novel algorithms. Specifically, fast QL, namely, QL combined with
transfer-learning and special initial states, is of higher efficiency, and
small memory QL is applicable to large-scale systems. Meanwhile, we present a
novel reward setting, under which the optimal policy with minimal flipping
actions to realize reachability is the one of the highest returns. Then, to
obtain the optimal policy, we propose QL, and fast small memory QL for
large-scale systems. Specifically, on the basis of the small memory QL
mentioned before, the fast small memory QL uses a changeable reward setting to
speed up the learning efficiency while ensuring the optimality of the policy.
For parameter settings, we give some system properties for reference. Finally,
two examples, which are a small-scale system and a large-scale one, are
considered to verify the proposed method
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