4,335 research outputs found
Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference
We consider data-driven reachability analysis of discrete-time stochastic
dynamical systems using conformal inference. We assume that we are not provided
with a symbolic representation of the stochastic system, but instead have
access to a dataset of -step trajectories. The reachability problem is to
construct a probabilistic flowpipe such that the probability that a -step
trajectory can violate the bounds of the flowpipe does not exceed a
user-specified failure probability threshold. The key ideas in this paper are:
(1) to learn a surrogate predictor model from data, (2) to perform reachability
analysis using the surrogate model, and (3) to quantify the surrogate model's
incurred error using conformal inference in order to give probabilistic
reachability guarantees. We focus on learning-enabled control systems with
complex closed-loop dynamics that are difficult to model symbolically, but
where state transition pairs can be queried, e.g., using a simulator. We
demonstrate the applicability of our method on examples from the domain of
learning-enabled cyber-physical systems
Verisig: verifying safety properties of hybrid systems with neural network controllers
This paper presents Verisig, a hybrid system approach to verifying safety properties of closed-loop systems using neural networks as controllers. We focus on sigmoid-based networks and exploit the fact that the sigmoid is the solution to a quadratic differential equation, which allows us to transform the neural network into an equivalent hybrid system. By composing the network’s hybrid system with the plant’s, we transform the problem into a hybrid system verification problem which can be solved using state-of-theart reachability tools. We show that reachability is decidable for networks with one hidden layer and decidable for general networks if Schanuel’s conjecture is true. We evaluate the applicability and scalability of Verisig in two case studies, one from reinforcement learning and one in which the neural network is used to approximate a model predictive controller
Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions
Controllers for dynamical systems that operate in safety-critical settings
must account for stochastic disturbances. Such disturbances are often modeled
as process noise in a dynamical system, and common assumptions are that the
underlying distributions are known and/or Gaussian. In practice, however, these
assumptions may be unrealistic and can lead to poor approximations of the true
noise distribution. We present a novel controller synthesis method that does
not rely on any explicit representation of the noise distributions. In
particular, we address the problem of computing a controller that provides
probabilistic guarantees on safely reaching a target, while also avoiding
unsafe regions of the state space. First, we abstract the continuous control
system into a finite-state model that captures noise by probabilistic
transitions between discrete states. As a key contribution, we adapt tools from
the scenario approach to compute probably approximately correct (PAC) bounds on
these transition probabilities, based on a finite number of samples of the
noise. We capture these bounds in the transition probability intervals of a
so-called interval Markov decision process (iMDP). This iMDP is, with a
user-specified confidence probability, robust against uncertainty in the
transition probabilities, and the tightness of the probability intervals can be
controlled through the number of samples. We use state-of-the-art verification
techniques to provide guarantees on the iMDP and compute a controller for which
these guarantees carry over to the original control system. In addition, we
develop a tailored computational scheme that reduces the complexity of the
synthesis of these guarantees on the iMDP. Benchmarks on realistic control
systems show the practical applicability of our method, even when the iMDP has
hundreds of millions of transitions.Comment: To appear in the Journal of Artificial Intelligence Research (JAIR).
arXiv admin note: text overlap with arXiv:2110.1266
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