6,410 research outputs found
Computation of Parametric Barrier Functions for Dynamical Systems using Interval Analysis
International audienceThe formal verification of safety properties for hybrid systems is an important but challenging problem. Recently, barrier functions have been introduced to prove safety without requiring the computation of the reachable set of continuous or hybrid dynamical systems. This paper presents a new approach for the construction of barrier functions for safety verification of nonlinear dynamical systems. The proposed method is based on the search for the parameters of a parametric barrier function using interval analysis. This technique allows considering complex dynamics without needing any relaxation of constraints in the barrier function
Construction of parametric barrier functions for dynamical systems using interval analysis
International audienceRecently, barrier certificates have been introduced to prove the safety of continuous or hybrid dynamical systems. A barrier certificate needs to exhibit some barrier function, which partitions the state space in two subsets: the safe subset in which the state can be proved to remain and the complementary subset containing some unsafe region. This approach does not require any reachability analysis, but needs the computation of a valid barrier function, which is difficult when considering general nonlinear systems and barriers. This paper presents a new approach for the construction of barrier functions for nonlinear dynamical systems. The proposed technique searches for the parameters of a parametric barrier function using interval analysis. Complex dynamics can be considered without needing any relaxation of the constraints to be satisfied by the barrier function
Analysis of parametric biological models with non-linear dynamics
In this paper we present recent results on parametric analysis of biological
models. The underlying method is based on the algorithms for computing
trajectory sets of hybrid systems with polynomial dynamics. The method is then
applied to two case studies of biological systems: one is a cardiac cell model
for studying the conditions for cardiac abnormalities, and the second is a
model of insect nest-site choice.Comment: In Proceedings HSB 2012, arXiv:1208.315
Active Sampling-based Binary Verification of Dynamical Systems
Nonlinear, adaptive, or otherwise complex control techniques are increasingly
relied upon to ensure the safety of systems operating in uncertain
environments. However, the nonlinearity of the resulting closed-loop system
complicates verification that the system does in fact satisfy those
requirements at all possible operating conditions. While analytical proof-based
techniques and finite abstractions can be used to provably verify the
closed-loop system's response at different operating conditions, they often
produce conservative approximations due to restrictive assumptions and are
difficult to construct in many applications. In contrast, popular statistical
verification techniques relax the restrictions and instead rely upon
simulations to construct statistical or probabilistic guarantees. This work
presents a data-driven statistical verification procedure that instead
constructs statistical learning models from simulated training data to separate
the set of possible perturbations into "safe" and "unsafe" subsets. Binary
evaluations of closed-loop system requirement satisfaction at various
realizations of the uncertainties are obtained through temporal logic
robustness metrics, which are then used to construct predictive models of
requirement satisfaction over the full set of possible uncertainties. As the
accuracy of these predictive statistical models is inherently coupled to the
quality of the training data, an active learning algorithm selects additional
sample points in order to maximize the expected change in the data-driven model
and thus, indirectly, minimize the prediction error. Various case studies
demonstrate the closed-loop verification procedure and highlight improvements
in prediction error over both existing analytical and statistical verification
techniques.Comment: 23 page
Safe Learning of Quadrotor Dynamics Using Barrier Certificates
To effectively control complex dynamical systems, accurate nonlinear models
are typically needed. However, these models are not always known. In this
paper, we present a data-driven approach based on Gaussian processes that
learns models of quadrotors operating in partially unknown environments. What
makes this challenging is that if the learning process is not carefully
controlled, the system will go unstable, i.e., the quadcopter will crash. To
this end, barrier certificates are employed for safe learning. The barrier
certificates establish a non-conservative forward invariant safe region, in
which high probability safety guarantees are provided based on the statistics
of the Gaussian Process. A learning controller is designed to efficiently
explore those uncertain states and expand the barrier certified safe region
based on an adaptive sampling scheme. In addition, a recursive Gaussian Process
prediction method is developed to learn the complex quadrotor dynamics in
real-time. Simulation results are provided to demonstrate the effectiveness of
the proposed approach.Comment: Submitted to ICRA 2018, 8 page
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