33,865 research outputs found
Data-driven computation of invariant sets of discrete time-invariant black-box systems
We consider the problem of computing the maximal invariant set of
discrete-time black-box nonlinear systems without analytic dynamical models.
Under the assumption that the system is asymptotically stable, the maximal
invariant set coincides with the domain of attraction. A data-driven framework
relying on the observation of trajectories is proposed to compute
almost-invariant sets, which are invariant almost everywhere except a small
subset. Based on these observations, scenario optimization problems are
formulated and solved. We show that probabilistic invariance guarantees on the
almost-invariant sets can be established. To get explicit expressions of such
sets, a set identification procedure is designed with a verification step that
provides inner and outer approximations in a probabilistic sense. The proposed
data-driven framework is illustrated by several numerical examples.Comment: A shorter version with the title "Scenario-based set invariance
verification for black-box nonlinear systems" is published in the IEEE
Control Systems Letters (L-CSS
Probabilistic Guarantees for Nonlinear Safety-Critical Optimal Control
Leveraging recent developments in black-box risk-aware verification, we
provide three algorithms that generate probabilistic guarantees on (1)
optimality of solutions, (2) recursive feasibility, and (3) maximum controller
runtimes for general nonlinear safety-critical finite-time optimal controllers.
These methods forego the usual (perhaps) restrictive assumptions required for
typical theoretical guarantees, e.g. terminal set calculation for recursive
feasibility in Nonlinear Model Predictive Control, or convexification of
optimal controllers to ensure optimality. Furthermore, we show that these
methods can directly be applied to hardware systems to generate controller
guarantees on their respective systems
A data-driven method for computing polyhedral invariant sets of black-box switched linear systems
In this paper, we consider the problem of invariant set computation for
black-box switched linear systems using merely a finite set of observations of
system trajectories. In particular, this paper focuses on polyhedral invariant
sets. We propose a data-driven method based on the one step forward reachable
set. For formal verification of the proposed method, we introduce the concepts
of -contractive sets and almost-invariant sets for switched linear
systems. The convexity-preserving property of switched linear systems allows us
to conduct contraction analysis on the computed set and derive a probabilistic
contraction property. In the spirit of non-convex scenario optimization, we
also establish a chance-constrained guarantee on set invariance. The
performance of our method is then illustrated by numerical examples.Comment: To appear in IEEE Control Systems Letter
Statistical Model Checking : An Overview
Quantitative properties of stochastic systems are usually specified in logics
that allow one to compare the measure of executions satisfying certain temporal
properties with thresholds. The model checking problem for stochastic systems
with respect to such logics is typically solved by a numerical approach that
iteratively computes (or approximates) the exact measure of paths satisfying
relevant subformulas; the algorithms themselves depend on the class of systems
being analyzed as well as the logic used for specifying the properties. Another
approach to solve the model checking problem is to \emph{simulate} the system
for finitely many runs, and use \emph{hypothesis testing} to infer whether the
samples provide a \emph{statistical} evidence for the satisfaction or violation
of the specification. In this short paper, we survey the statistical approach,
and outline its main advantages in terms of efficiency, uniformity, and
simplicity.Comment: non
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