141 research outputs found
Compositional Set Invariance in Network Systems with Assume-Guarantee Contracts
This paper presents an assume-guarantee reasoning approach to the computation
of robust invariant sets for network systems. Parameterized signal temporal
logic (pSTL) is used to formally describe the behaviors of the subsystems,
which we use as the template for the contract. We show that set invariance can
be proved with a valid assume-guarantee contract by reasoning about individual
subsystems. If a valid assume-guarantee contract with monotonic pSTL template
is known, it can be further refined by value iteration. When such a contract is
not known, an epigraph method is proposed to solve for a contract that is
valid, ---an approach that has linear complexity for a sparse network. A
microgrid example is used to demonstrate the proposed method. The simulation
result shows that together with control barrier functions, the states of all
the subsystems can be bounded inside the individual robust invariant sets.Comment: Submitted to 2019 American Control Conferenc
Computing an Inner and an Outer Approximation of the Viability Kernel
International audienceThe viability kernel corresponds to the set of all state vectors of a controlled dynamic system that are viable, i.e., such that there exists an input such that the system will not enter inside a forbidden zone. In this paper, we propose a method which computes an inner and an outer approximation of the viability kernel in a guaranteed way. Our method is based on interval analysis and uses the notions of V-viability and capture basin. We illustrate our approach on the car on the hill problem. A software package has been developed to solve any 2D-problem
Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction
We show that, for any spatially discretized system of reaction-diffusion, the
approximate solution given by the explicit Euler time-discretization scheme
converges to the exact time-continuous solution, provided that diffusion
coefficient be sufficiently large. By "sufficiently large", we mean that the
diffusion coefficient value makes the one-sided Lipschitz constant of the
reaction-diffusion system negative. We apply this result to solve a finite
horizon control problem for a 1D reaction-diffusion example. We also explain
how to perform model reduction in order to improve the efficiency of the
method
Lagrangian Reachtubes: The Next Generation
We introduce LRT-NG, a set of techniques and an associated toolset that
computes a reachtube (an over-approximation of the set of reachable states over
a given time horizon) of a nonlinear dynamical system. LRT-NG significantly
advances the state-of-the-art Langrangian Reachability and its associated tool
LRT. From a theoretical perspective, LRT-NG is superior to LRT in three ways.
First, it uses for the first time an analytically computed metric for the
propagated ball which is proven to minimize the ball's volume. We emphasize
that the metric computation is the centerpiece of all bloating-based
techniques. Secondly, it computes the next reachset as the intersection of two
balls: one based on the Cartesian metric and the other on the new metric. While
the two metrics were previously considered opposing approaches, their joint use
considerably tightens the reachtubes. Thirdly, it avoids the "wrapping effect"
associated with the validated integration of the center of the reachset, by
optimally absorbing the interval approximation in the radius of the next ball.
From a tool-development perspective, LRT-NG is superior to LRT in two ways.
First, it is a standalone tool that no longer relies on CAPD. This required the
implementation of the Lohner method and a Runge-Kutta time-propagation method.
Secondly, it has an improved interface, allowing the input model and initial
conditions to be provided as external input files. Our experiments on a
comprehensive set of benchmarks, including two Neural ODEs, demonstrates
LRT-NG's superior performance compared to LRT, CAPD, and Flow*.Comment: 12 pages, 14 figure
Provable Run Time Safety Assurance for a Non-Linear System
Systems that are modeled by non-linear continuous-time differential equations with uncertain parameters have proven to be exceptionally difficult to formally verify. The past few decades have produced a number of useful verification tools which can be applied to such systems but each is applicable to only a subset of possible verification scenarios. The Level Sets Toolbox (LST) is one such tool which is directly applicable to non-linear systems, however, it is limited to systems of relatively small continuous state space dimension. Other tools such as PHAVer and the SpaceEx invariant of the Le Guernic-Girard (LGG) support function algorithm are specifically designed for hybrid systems with linear dynamics and linear constraints but can accommodate hundreds of continuous states. The application of these linear reachability tools to non-linear models has been achieved by approximating non-linear systems as linear hybrid automata (LHA). Unfortunately, the practical applicability and limitations of this approach are not yet well documented. The purpose of this thesis is to evaluate the performance and dimensionality limitations of PHAVer and the LGG support function algorithm when applied to a LHA approximation of a particular non-linear system. A collision avoidance scenario with autonomous differential drive robots is used as a case study to demonstrate that an over-approximated reachable set boundary can be generated and implemented as a run time safety assurance mechanism
Refining Obstacle Perception Safety Zones via Maneuver-Based Decomposition
A critical task for developing safe autonomous driving stacks is to determine
whether an obstacle is safety-critical, i.e., poses an imminent threat to the
autonomous vehicle. Our previous work showed that Hamilton Jacobi reachability
theory can be applied to compute interaction-dynamics-aware perception safety
zones that better inform an ego vehicle's perception module which obstacles are
considered safety-critical. For completeness, these zones are typically larger
than absolutely necessary, forcing the perception module to pay attention to a
larger collection of objects for the sake of conservatism. As an improvement,
we propose a maneuver-based decomposition of our safety zones that leverages
information about the ego maneuver to reduce the zone volume. In particular, we
propose a "temporal convolution" operation that produces safety zones for
specific ego maneuvers, thus limiting the ego's behavior to reduce the size of
the safety zones. We show with numerical experiments that maneuver-based zones
are significantly smaller (up to 76% size reduction) than the baseline while
maintaining completeness.Comment: * indicates equal contribution. Accepted into the IEEE Intelligent
Vehicles Symposium 202
- …