2,607 research outputs found
Safety Control Synthesis with Input Limits: a Hybrid Approach
We introduce a hybrid (discrete--continuous) safety controller which enforces
strict state and input constraints on a system---but only acts when necessary,
preserving transparent operation of the original system within some safe region
of the state space. We define this space using a Min-Quadratic Barrier
function, which we construct along the equilibrium manifold using the Lyapunov
functions which result from linear matrix inequality controller synthesis for
locally valid uncertain linearizations. We also introduce the concept of a
barrier pair, which makes it easy to extend the approach to include
trajectory-based augmentations to the safe region, in the style of LQR-Trees.
We demonstrate our controller and barrier pair synthesis method in
simulation-based examples.Comment: 6 pages, 7 figures. Accepted for publication at the 2018 American
Controls Conference. Copyright IEEE 201
Control Barrier Function Based Quadratic Programs for Safety Critical Systems
Safety critical systems involve the tight coupling between potentially
conflicting control objectives and safety constraints. As a means of creating a
formal framework for controlling systems of this form, and with a view toward
automotive applications, this paper develops a methodology that allows safety
conditions -- expressed as control barrier functions -- to be unified with
performance objectives -- expressed as control Lyapunov functions -- in the
context of real-time optimization-based controllers. Safety conditions are
specified in terms of forward invariance of a set, and are verified via two
novel generalizations of barrier functions; in each case, the existence of a
barrier function satisfying Lyapunov-like conditions implies forward invariance
of the set, and the relationship between these two classes of barrier functions
is characterized. In addition, each of these formulations yields a notion of
control barrier function (CBF), providing inequality constraints in the control
input that, when satisfied, again imply forward invariance of the set. Through
these constructions, CBFs can naturally be unified with control Lyapunov
functions (CLFs) in the context of a quadratic program (QP); this allows for
the achievement of control objectives (represented by CLFs) subject to
conditions on the admissible states of the system (represented by CBFs). The
mediation of safety and performance through a QP is demonstrated on adaptive
cruise control and lane keeping, two automotive control problems that present
both safety and performance considerations coupled with actuator bounds
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
Kuhn-Tucker-based stability conditions for systems with saturation
This paper presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented can be extended to handle a dead-zone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn-Tucker) conditions for optimality are used to derive linear and quadratic constraints which characterize the saturation. After selecting a candidate Lyapunov function, we pose the question of whether the Lyapunov function is decreasing along trajectories of the system as an implication between the necessary conditions derived from the saturation optimization, and the time derivative of the Lyapunov function. This leads to stability conditions in terms of linear matrix inequalities, which are obtained by an application of the S-procedure to the implication. An example is provided where the proposed technique is compared and contrasted with previous analysis methods
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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