344 research outputs found
How scaling of the disturbance set affects robust positively invariant sets for linear systems
This paper presents new results on robust positively invariant (RPI) sets for
linear discrete-time systems with additive disturbances. In particular, we
study how RPI sets change with scaling of the disturbance set. More precisely,
we show that many properties of RPI sets crucially depend on a unique scaling
factor which determines the transition from nonempty to empty RPI sets. We
characterize this critical scaling factor, present an efficient algorithm for
its computation, and analyze it for a number of examples from the literature
Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction
Considering the competitive and strongly regulated pharmaceutical industry, mathematical
modeling and process systems engineering might be useful tools for implementing quality by
design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However,
a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification
of model candidates from a set of various model hypotheses. To identify the best experimental
design suitable for a reliable model selection and system identification is challenging for nonlinear
(bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness
for model selection problems under uncertainty, and thus translates the model selection problem
to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal
controls for improved model selection trajectories are expressed analytically with low computational
costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based
method and provide an effective robustification strategy with the point estimate method for
uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating
the carboligation of aldehydes, where we successfully derive optimal controls for improved model
selection trajectories under uncertainty
Implicit predictors in regularized data-driven predictive control
We introduce the notion of implicit predictors, which characterize the
input-(state)-output prediction behavior underlying a predictive control
scheme, even if it is not explicitly enforced as an equality constraint (as in
traditional model or subspace predictive control). To demonstrate this concept,
we derive and analyze implicit predictors for some basic data-driven predictive
control (DPC) schemes, which offers a new perspective on this popular approach
that may form the basis for modified DPC schemes and further theoretical
insights.Comment: This paper is a reprint of a contribution to the IEEE Control Systems
Letters. 6 pages, 2 figure
Tailored neural networks for learning optimal value functions in MPC
Learning-based predictive control is a promising alternative to
optimization-based MPC. However, efficiently learning the optimal control
policy, the optimal value function, or the Q-function requires suitable
function approximators. Often, artificial neural networks (ANN) are considered
but choosing a suitable topology is also non-trivial. Against this background,
it has recently been shown that tailored ANN allow, in principle, to exactly
describe the optimal control policy in linear MPC by exploiting its piecewise
affine structure. In this paper, we provide a similar result for representing
the optimal value function and the Q-function that are both known to be
piecewise quadratic for linear MPC.Comment: 7 pages, 2 figures, 1 tabl
Error bounds for maxout neural network approximations of model predictive control
Neural network (NN) approximations of model predictive control (MPC) are a
versatile approach if the online solution of the underlying optimal control
problem (OCP) is too demanding and if an exact computation of the explicit MPC
law is intractable. The drawback of such approximations is that they typically
do not preserve stability and performance guarantees of the original MPC.
However, such guarantees can be recovered if the maximum error with respect to
the optimal control law and the Lipschitz constant of that error are known. We
show in this work how to compute both values exactly when the control law is
approximated by a maxout NN. We build upon related results for ReLU NN
approximations and derive mixed-integer (MI) linear constraints that allow a
computation of the output and the local gain of a maxout NN by solving an MI
feasibility problem. Furthermore, we show theoretically and experimentally that
maxout NN exist for which the maximum error is zero.Comment: 8 pages, 2 tables, to be published in the proceedings of the 22nd
World Congress of the International Federation of Automatic Control (2023
Cryptanalysis of Random Affine Transformations for Encrypted Control
Cloud-based and distributed computations are of growing interest in modern
control systems. However, these technologies require performing computations on
not necessarily trustworthy platforms and, thus, put the confidentiality of
sensitive control-related data at risk. Encrypted control has dealt with this
issue by utilizing modern cryptosystems with homomorphic properties, which
allow a secure evaluation at the cost of an increased computation or
communication effort (among others). Recently, a cipher based on a random
affine transformation gained attention in the encrypted control community. Its
appeal stems from the possibility to construct security providing homomorphisms
that do not suffer from the restrictions of ``conventional'' approaches.
This paper provides a cryptanalysis of random affine transformations in the
context of encrypted control. To this end, a deterministic and probabilistic
variant of the cipher over real numbers are analyzed in a generalized setup,
where we use cryptographic definitions for security and attacker models. It is
shown that the deterministic cipher breaks under a known-plaintext attack, and
unavoidably leaks information of the closed-loop, which opens another angle of
attack. For the probabilistic variant, statistical indistinguishability of
ciphertexts can be achieved, which makes successful attacks unlikely. We
complete our analysis by investigating a floating point realization of the
probabilistic random affine transformation cipher, which unfortunately suggests
the impracticality of the scheme if a security guarantee is needed.Comment: 8 pages, 2 figures, to be published in the proceedings of the 22nd
World Congress of the International Federation of Automatic Control (2023
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