8,285 research outputs found
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
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
Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making
We demonstrate applications of algebraic techniques that optimize and certify
polynomial inequalities to problems of interest in the operations research and
transportation engineering communities. Three problems are considered: (i)
wireless coverage of targeted geographical regions with guaranteed signal
quality and minimum transmission power, (ii) computing real-time certificates
of collision avoidance for a simple model of an unmanned vehicle (UV)
navigating through a cluttered environment, and (iii) designing a nonlinear
hovering controller for a quadrotor UV, which has recently been used for load
transportation. On our smaller-scale applications, we apply the sum of squares
(SOS) relaxation and solve the underlying problems with semidefinite
programming. On the larger-scale or real-time applications, we use our recently
introduced "SDSOS Optimization" techniques which result in second order cone
programs. To the best of our knowledge, this is the first study of real-time
applications of sum of squares techniques in optimization and control. No
knowledge in dynamics and control is assumed from the reader
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